The Emergence of Consciousness in a Physical Universe

Consciousness appears so mysterious and hard to formulate within physical sciences because the present day scientiﬁc thinking excludes an element of reality and a general mechanics of its processing from its consideration. The primary missing element is the reality of information in the physical universe as an intrinsic causal correlate of observable physical states. Moreover, there exists a general formalism of information processing that is universally applicable to the processing resulting from each physical interaction. As shown, the formalism further enables a general mechanism to construct arbitrary structured and abstract semantics or object description in modular hierarchy as well as a powerful mechanism of population coding to represent arbitrary precision and variation in object description resolving the combinatorial problem. Here, a semantic value, or simply semantics, is equivalent ( ≡ ) to the content of information of causal correlation, and treated as a value to enable its formal processing. The primary motive here is to lay down a formal account of information (semantic) processing that leads to bridging the conceptual gap between the objectively observable elements in nature and the subjective consciousness. It is shown that the qualities we associate with consciousness are causally correlated semantics of relation that a represented agency holds with other objects within a dynamically evolving semantic structure, where the state of the population of physical systems (neurons) correlating with the structure holds causal powers to effect appropriate behavior. Since the information (semantic value) arises from natural causal dependence, the correlation based consciousness forms an undeniable reality of existence. It is derived here how a semantic value equivalent to ‘a self as an observer of objects and controller of actions’ is constructed. If the semantic components of a conscious experience, such as the self, the objects of experience, and the relation of experience attributing the self as the owner or experiencer, causally correlate with a system’s state having causal inﬂuence in action, then it sufﬁces to bridge the gap between the objective reality and the subjective consciousness. That is, the semantic value corresponding to the thoughts and senses is the reality of nature the semantics of self relates to as the owner. Moreover, the semantics of ‘self as an observer and controller of action’ is itself shown to form a part of observed objects giving rise to self awareness.


Introduction and definitions
The phenomenon of consciousness is the most apparent reality of nature to us all as humans.It must therefore be explicable and expressible in terms of the objective function in nature.No description of nature can be said to be comprehensive if it does not lead to the understanding of consciousness.Since we aim to bridge the gap between the objective function and the subjective consciousness, it is imperative that this work clearly establishes the interpreter independent reality of information, lays down the mechanics of processing that is testable on artificial devices and observable in the brain, quantifies the mechanics of integration and abstraction, derives the emergence of semantics of an agency that satisfies the criterion of, or qualifies to, being a conscious agent, resolves contentious problems in the domains of information and consciousness, and makes testable predictions.Since this work is based on the undeniable objective causal function of elements in nature, even the subjectivity is shown to have an objective basis.Causal function refers to the function of an object or a state, physical or representational, to effect a regular change within limits, in the respective domains, by which the object or the state is identifiable.Unless specified otherwise, in this work the term 'representation' exclusively refers to the causal correlation of a coherent physical state without any symbolism.
The idea and the plan: The basic idea here is that the qualities we associate with consciousness are the semantics of relation that a represented agency holds with the represented objects.Stated differently, 1 https://doi.org/10.32388/1KC9TH.3 within a structured or integrated semantics, the relation that one specific object bears with other objects, has the qualities that we have come to refer to as consciousness.The plan: 1.The reality of information is shown to arise from the regularity of causal function in nature.An information necessarily expresses or qualifies objects in terms of implicit or explicit relation.The content of information is treated as a value enabling a general formalism for its processing.2. Given the same regularity of causal function an interaction is definable as mutually inter-dependent, hence bounded, transitions in the state of physical entities (systems).This perspective allows a generic expression to be constructed to formally evaluate the causal dependence (correlate) of a resultant state of a system on precursor states of interacting systems.3.This generic expression is then shown to be potent to express all relations, including temporal and causal relations enabling such relations to be represented by a state as its correlate.4. The same generic expression also enables a mechanism of population coding that allows a relation to be represented with arbitrary variations and precision without requiring the mathematical consistency.5.The mechanism of representing arbitrary relations is then shown to capture structured and abstract semantics of complex systems and their functions.Abstraction is defined as the formation of a class from the instances and from functional relations, which serves as a semantic space.6.A simplified example of echolocation is then worked out to show how active state of an agent in a network of inter-dependence can represent the relative placement of an observing system itself with respect to other systems in the field of view, which forms a component of self.7. The ability to represent causal relations further allows a systematic integration of semantics in modular hierarchy that expresses a class of structural configurations and dynamic functions of an evolved system or organism.The referable semantics of the structured class as a unified system is then shown to possess several characteristics of self.8. Evolution based on selection creates a system with causal function towards survival.A processing system like brain may 'then evolve' to represent the dynamics and the causal function of the unified system.It is shown how the integration of the structured semantics of 'a unified system with abilities of observing, referencing, acting, and controlling the actions' takes place.It is then inferred how the semantics of the function of the unified system (self) posits it as the bearer of the properties we identify with consciousness.9.The process is then extended to include how the referential and causal relations of the represented self with the objects form a part of observable objects leading to a semantic structure of self conscious agency.10.Lastly, the conclusion section is especially devoted to discuss and present resolution to several known problems relating to consciousness.A subsection is especially included to enlist predictions that are testable via implementation on artificial devices and observable in the brain.
Our understanding of consciousness today lacks any relation it may have with the third person observable causal function in nature.Therefore, they appear as different in category or as independent elements of reality.On a subjective experiential level, consciousness forms the basis of all perceptions, senses, knowledge, memories, interpretative and modeling abilities, the rationale of decision making and action.In fact, the very perception of the undeniable reality of 'self as a conscious agency' is also based on the same consciousness as Descartes observed.Yet, inter-personal objective access to the same conscious perceptions remains impossible making an objective account difficult.
As we look around, we observe objects and their inter-relations embedded in 4.π steradian (sr) space; consider relations and processes as objects, for they are referable.We especially note that the perceived features of objects, see Fig. 1, are constructed of semantic values.For instance, semantic value associated Figure 1: The observed features of objects, such as shape, size, color, relative placement, are undeniably apparent semantics; therefore, they must be constructible and referable by natural processes.
with a book or a ball in the field of view is constructed of shape, size, polygonal surfaces, roundness, color, texture, placement relative to other objects, regular array of leaves, etc.We are concerned here with semantics, not with their conscious perception.We further notice the apparent realism of the semantics of information; it is undeniable, concrete, and non-probabilistic regardless of the external reality of the book and the ball.For instance, can we deny the knowledge of the semantics of rectangular shape of the book and roundness of the ball?Moreover, do we require any language, symbolism, or interpretation to know it?As per the norm in science, we must accept this observed reality as part of the natural universe and seek to establish its foundational basis.One may draw an immediate inference that all elements of consciousness, including the self and its relation with objects we call perception, are constructed of such semantic values, as shown here.Since information does not interact physically, yet undeniably apparent, it must have a non-falsifiable existence in reality.That is, the causal function in nature must be directly responsible for this reality.The categorically different reality of information [1,2] is not constructible from physically measurable entities in nature.Overriding different senses in which the term 'information' is used in natural sciences [3,4], here, it is used to refer to what it expresses, the semantic value content.

Grounding of information as an element of reality
In its endeavor to build a physical model of natural phenomena, humanity has ignored certain elements of natural processes that relate physically observable elements to subjective reality.Three fundamental paradigms are identified as missing in our present day model of the natural world that are critical for our understanding of the emergence of consciousness.First missing element is the basis of information in the constancy of causal function [1].The physical universe, as observed from within, undergoes change.The changes follow certain uniformity and regularity (constancy), such that an observable state, S, of a physical system, P, bears a dependence on certain other states {S x } within specific limits, where {S x } may include relative static or dynamic quantities (space, time, rates of change, etc.) in conjunction and / or disjunction.That is, if {S x } were not to form a part of contextual reality within the limits, the state S of P could not have an existential reality either.Therefore, S of P intrinsically and causally must correlate with the semantic specification of {S x }.It is noteworthy that individual elements of {S x } is not said to cause S of P, but rather S of P causally depends on specific conjunctions of elements in {S x }.This relation of the 'present to the precursor' or 'posterior to the prior', is referred to here as 'natural causal dependence'.It is referred to as 'natural' to imply the independence of this relation from any model or interpretation to mean what really exists, an ontological connotation.
For instance, 'mass state' of a physical system Q is a relatable quality, for it determines Q's causal function in an interaction and a basis of Q's relation with other objects.Hence, the information of 'mass state' of Q forms a primitive of semantic value, a meaningful object grounded in reality without a qualifying label.An interacting system P responds to the relative measure of this quality, which reflects in relative transition in P's state, such as the angle of deflection as marked by two arrows in Fig. 2. Similarly, the information of spatial placement of Q relative to P is a semantic value of consequence to P. As P undergoes a transition in its trajectory due to the causal function of mass M and relative placement R of Q, as shown in Fig. 2, the resultant state S of P must 'correlate with' (symbol ⇒) the semantic values of specification of mass and relative placement of Q, symbolically denoted as follows.
Since this correlation arises from natural causal function, it must include whatever reality, fundamental M,R Q X P S P Figure 2: In an interaction with system Q, P transitions into state S, designated as S P .S P is then said to correlate with precursor causal states of interacting systems including its own prior state X P .
or emergent, the semantics of the qualities of mass and spatial placement entail and their measures.A qualitative character can be thought of as an abstraction of a class or parametric space.The value on RHS includes positive correlation with causally permissible limits of (M,R) in reality and negative correlation with the rest of space as briefed below.Here, R denotes a composite of temporal relation of Q's placement to P. While a positive correlation indicates a possible range of values or configurations for precursor states in reality that may result in S P , a negative correlation indicates forbidden values for precursor states [1].This is how the semantic values are grounded in the causal function as covered by the laws advanced in [1] and summarized below.
On semantics: The term semantics is often associated with the study of meaning, or just the meaning; it is also used in literature in the contexts of semantic information, semantic memory, semantic knowledge, semantic processing, and semantic categories [1].In this work, it is used to designate the value or content of information that arises as a causal correlate of a physical state.It is shown here how the semantic values forming thoughts and perceptions emerge as the causal correlate of neural states.Hence the term semantic value as a reference to the content of information is rather accurate.One must ask, what is it that a physical state causally correlates with that entails quality and quantity of states and relations in nature?Yet, if a reader finds this notion of 'semantics' troublesome to reconcile, one may replace it with a new term 'semcorr' for 'Semantic Value of Correlation' (SVC) to designate the quality of the causal correlate.
S P is said to correlate with or represent the semantic value, but this representation is neither symbolic nor artificially assigned.It is a direct and intrinsic association of a state with the value not accessible to a third person observation.Although a projection of intrinsic correlation is analyzable within the limits of constraints of causal dependence and the initial conditions as is the case while analyzing the result of an experiment.The transformed state of P, S P , has a causal influence that conforms to this correlation.
Second missing element is a generic formalism [1] to express universally all relations, which also captures the causal dependence of an observable resultant state on the precursor states of interacting systems.The formalism quantifies information processing resulting from an interaction; the resultant value constitutes an intrinsic correlate of the resultant state.It is remarkable to note that the same expression also serves as a generic constructor of all semantics, structured and abstract, as shown in [1] and briefed here.Moreover, the expression also leads to the population coding system as shown below and as computationally simulated in [1].
Third missing element is a conceptual framework for the self to be a part of a structured semantics as any other objects the self is said to be conscious of.That is, it is the represented semantics of a relation that expresses the self as an observer of objects and controller of actions.Moreover, by virtue of being a causal correlate of a state, the semantic value is correlatable with the representable semantics of the consequence of the state.Therefore, the problem of constructing the description of consciousness reduces to the problem of representing the semantics of self and its relation to the objects of experience.The critical components of the semantics of self are, 'self as an embodiment of the carrying system', 'self as an observer', 'self as an actor', 'self as the owner of senses', and 'self as a controller of action / behavior'.For the purpose of constructing a causal description of consciousness, the development here is based on causal function in nature without a dependence on specific system like brain, even though the examples are picked from it.
Since we aim to construct a semantic representation of all that is referable, we need a generic term for such a reference.In this text, the term 'object' is used as a universal reference to all, including elements of physical reality, relations and expressions, temporal events and processes, discrete and analog values, symbolic references -elemental, structured, or abstract.An abstract object exclusively refers to the semantics expressed by a disjunctive relation among objects or instances that form a class.For instance, a disjunction of instances of 'right angle' is an abstract object referable as a class.In fact, referability arises for an object only when a semantic value is constructed within the domain of representation.A language also emerges from such referability (Section.8.4 of [1]).Withstanding limitations of linguistic expressions, unless a reference is created via causal correlate, no object is referable.It may be noted that with every interaction, a reference is created via causal correlate.Hence, all elements of our thoughts and experiences as well as linguistic expressions are represented objects (semantics) without exception; it is also apparent from this development.Since an object has a description as a structural relation among its components and a functional relation with other objects within a system or a frame of reference, it is always expressed only via relation among objects.Therefore, an object description or definition is equivalent to semantics of relation among objects.When referring to identity, we use the term 'object', and when referring to the quality of description, we use the term 'semantics'.

A definition of consciousness
The mystery surrounding consciousness only intensifies with time.The number of proposals to deal with it grows so rapidly that it has become difficult to summarize them within the scope and limitations of this article.An uninitiated reader may begin with [5,6,7].A reader may refer to some of the reviews of common and important variants on this topic -Butlin et.al.: Consciousness in Artificial Intelligence [8]; Sattin et.al.: Theoretical Models of Consciousness [9]; Francken et.al.:An academic survey on theoretical foundations [10]; Ned Block: Comparing the major theories [11]; Uriah Kriegel: Theories of consciousness and self-representational approaches [12,13]; Melanie Boly: Consciousness in humans and non-human animals: recent advances and future directions [14]; Sun and Franklin: Computational models of consciousness [15].
The work presented here differs from all others in a few critical ways.First, no causal or non-causal hypothesis is proposed here to connect consciousness directly to the physical world.Instead, it is shown to emerge from semantic values grounded in natural causal function; it may be referred to as Emergence of Consciousness from Causal Information (ECCI, pronounced 'ekki' as per the first syllable of the terms).Second, a formal mechanism of semantic processing is presented, which is directly applicable to neural systems and implementable on artificial devices.Third, a principle based on constancy of relations is introduced as a uniform mechanism to construct object description via structural and functional relations.Fourth, mechanism of population coding of semantic values is laid down quantitatively, which is testable on artificial devices and observable in neural systems.For a deeper comparison with a few noted models, one may refer to Supplement-1.
A functional definition of consciousness: Consciousness refers to a dynamic structured relation R that an object U holds with other objects within a causally constructed semantic structure S, where R includes a referential relation (reference) to the objects and a causal relation to effect specific change to the referent.A referential relation designates U as the bearer of the ability to refer to an object, and causal relation the ability to effect a change to an object.All of this is shown to be contained in the constructed semantic structure S. Clearly, the relation R defines the object U as the observer of objects and the agency of specific change.Here, an object is a semantic value having a temporal dimension or a dynamic character.The relation R is stated to be dynamic even if certain specifics may not change during a reference, for no static relation bears an intrinsic property to change, and for the referential and causal relations remain undefined for static contexts.A change to the referent includes both a change in the perspective of U or to the objects; in either case, the referent semantics undergoes a change.In every perception of thoughts and senses, it is the object U that relates to other objects of perception, where the thoughts and senses constitute the structured semantics S. That is, the seer, the seen, and the act of seeing, or the perceiver and the perception, are parts of uniformly constructed semantic structure with causal consequence.What is explicit in this definition is that the phenomenon of consciousness has no existence out of such semantic structures.Instantiating a causal relation (action) affects the objects represented, where the signals in physical substrate is transported to effect internal or external change, which in turn can be observed for conformance.In this work, we aim to lay down the construction of semantic structure of referential and causal relations to the referent objects.This definition is minimal, primary, or first order, which only requires a constitution of an observing self without self referentiality, relating to other objects resulting in causal control of action.A stronger or second order definition includes the relation R that the object U holds with other objects as a part of referable objects relating to a new U, U-new.This makes it possible to refer to 'an observing and controlling self, U'.The controller element is necessary from the evolutionary perspective as discussed in Section.4.4.The second order definition permits the construction and reporting of semantics like, "I am conscious of X", "I experience X", and "I effected the change X".

The mechanics of information processing
In order to construct an information based emergence of consciousness, we take the following steps.First, information is established as an interpreter independent reality from the causal function of the physical universe.Second, a general expression E is advanced to quantify the information processing at each physical interaction organizable in modular hierarchy to represent higher order structured semantics.
Third, this expression is shown to be general to express all semantics, structured and abstract.Fourth, an implementable uniform principle is formulated to construct description of all objects including relations and processes.Fifth, a population coding mechanism [16,17,18] is derived from E to express combinatorially unlimited variation in object description.These principles and formalisms are also presented in [1] from a different standpoint.For self sufficiency, the relevant points are presented below.
1.As stated above, an observable resultant state intrinsically correlates with the specification of precursor states with limits of positive and negative correlation.The following law quantifies the semantic correlation as presented first in [1] and demonstrated with a computer simulation.This is amenable to empirical verification via observation of neural function and organization.One may consider this as a hypothesis, but this is also self evident and comprehensive.
The law: Post-interaction, an observable resultant state S of a physical system P correlates with a definite semantic value C that is derived from all causally equivalent configurations of reality, specifiable in terms of values of precursor states of interacting systems, that result in the state S of P. The components of semantic value C are given by the following expressions: ( i) disjunction of conjunctions of values of respective states in each configuration; (ii) disjunction of conjunctions of semantic values of correlation, from arbitrary spaces of mutual relevance, of respective states in each configuration within the constraints of Rule.(i).
We may observe that the law depends on transition of states, for that is what is observable in a measurement, not the underlying law or the relation, which may form a part of correlation.Let A and O designate infix binary operators for conjunction and disjunction respectively, with A having a higher precedence.Since each of the operators is commutative, no specific ordering is required for their respective operands.For higher precedence of A , parentheses on RHS in Eqn.2 are redundant.
Here, LHS specifies a state S of P and RHS its causal correlation; v i j specifies j th value in conjunction of i th term in disjunction.v i j is an arbitrary semantic value specified with positive and negative limits, which could be a state value itself as per (i), or a value of its correlation as per (ii) above.This causal correlation is transparent to classical or quantum consideration (see Section 2.3 in [1]), for it depends on observable states alone.In general, LHS may have an expression like RHS, a disjunction of conjunctions of arbitrary state values, in which case, the RHS replicates the same expression but each state value substituted by its correlation, as expressed on the RHS.For instance, in the neural system, a neuron is activated by the active states of (signals from) multiple projecting neurons, each having its own correlation profile as given by RHS.Fig. 3 illustrates the mechanism of quantitative evaluation as used in a computer simulation in [1].
Rule.(ii) inductively takes care of continued causal dependence.With the limits of correlation in (i), (ii) extends the correlation to other parametric spaces of relevance under the limits of causal dependence, which includes the extended space and time to the past and the future.For instance, when a ray of light activates a neuron in the retina, the active state not only correlates with the conjunction of state of photons in the ray as per (i), but further correlates with the relevant causal context or constraints of the ray of light as per (ii), which includes positive correlation with a narrow range of angle of incidence and negative correlation with the rest of space with respect to the ocular system.Active states of neighboring neurons similarly correlate with overlapping values of angles of incidence in a neighborhood, making the space of angles mutually relevant.What is important to note here is that no component of the neural system or organization is required to encode, decode, or interpret in any way what a neural state correlates with or represents; the activation pattern of neurons in retina holds the same relation that the rays of light activating them hold, which in turn correlates with the characteristic features in the visual field.Rule.(ii) plays a critical role in constructing higher order structured and abstract semantics.Since this constitutes a paradigm shift from the present day consideration of information, a reader is advised to take a special note of its foundational basis to follow the discussion and derivation laid down here.In fact, the causal basis of information is tested every time the result of an experiment in physical sciences is interpreted with presumed laws of causal dependence.
2. In this work, conjunction and disjunction are not logical operators to accept True or False as their operands referring to arbitrary propositions.These binary operators accept three values of correla-tion, Positive (Pos), Negative (Neg), and Null (Nul) as operands that refer to positive, negative, and null correlation with limits of semantic values -relative limits of causal state description (Fig. 2) are an instance of such values.In fact, a binary representation of {Pos, Neg, Nul} as {01, 00, 11} maps conjunction and disjunction to binary operations of AND and inclusive OR respectively.The set of values {Pos, Neg, Nul} together with conjunction and disjunction operators forms a mathematical structure, a new kind of comprehensive mechanism of information processing as detailed in Section.3.1 of [1] and presented here in

Conjunction
Correlation values as operands -Positive, -Negative, -Null Visual representation of function of conjunction and disjunction and mechanism of population coding Disjunction Figure 3: A graphical illustration of methods of conjunction and disjunction, and mechanism of population coding.Each horizontal color bar under conjunction represents a correlation profile of an active agent (say a neuron) in arbitrary space of semantics as per the causal correlation (Green: Positive, Blue: Negative).For example, an active state of a neuron may correlate positively with a range of orientation of a line segment, and negatively with the rest of space.The actual data for the figure is taken from a simulation presented in Section.7 of [1] by the same author.Each bar represents the same range of space; a negative correlation is implied for the rest of space.The result of conjunction on columns of values is displayed below the black line which shows a sharp positive correlation as a result of conjunction, where the red mark on each black line shows the instance of actual orientation value presented for simulation.Therefore, when a set of these agents together activate another agent, the active state of the recipient agent represents the value below the black line.If the recipient agent can be activated by subsets of input signals, then its state correlates with the disjunction of conjunctions in specific subsets as shown on the right.The correlation profile may vary dynamically in a re-entrant system.The salient properties of population coding in representing arbitrary variations, higher precision, robustness, and in graceful degradation at the loss of individual agents are apparent and noteworthy.It is instructive to consider the color bars as representing the angle between two lines resulting in sharp angular relation as a result of conjunction among a population.The mechanism remains consistent even when each column of the width of the red mark on the color bars is taken from different semantic spaces, or when the bar represents a continuous range in a space.
A conjunction of semantic values evaluates to greater specificity with narrower positive correlation when the values overlap in an object space, or to a specific composition when the values come from non-overlapping spaces.For instance, a line segment is specifiable by a conjunction of extents of overlapping points or pixels.The resultant value functionally further correlates with specific limits of length, width, and orientation, extending the mutually relevant parametric spaces.Disjunction functions as a mechanism of generalization giving rise to abstract semantics of a class, relation, or structure [1], e.g., semantics of 'right angle' from instances of right angle as shown in Fig. 4. A class object encapsulates a relation that holds on the instances (members) of the class as presented in [1].Hence, the disjunction causes the emergence of an irreducible abstract semantics, making available a reference to a class object without referring to an instance.This abstraction arising from a limited range of observed instances cannot be a part of a consistent, formal mathematical system [1].But it can be included as a rule or an axiom and interpreted by a system with abilities to represent a class via disjunction, which may even hold for all possible instances, such as a+b=b+a for numbers.Now, since all objects and expressions are constructed of objects including inter-relations, the method of conjunction to capture a composition and the method of disjunction to represent the class of structure together form a comprehensive mechanism to construct semantics of all objects [1].The mechanism is suitable for implementation by evolving biological systems via population coding (See Fig. 3).
3. Evidently, the mechanism of information processing, as laid down above, directly corresponds to neural function and their re-entrant network in modular hierarchy.Neurons in the brain process information via a coherence building mechanism based on temporal synchronization that directly maps to the function of conjunction and disjunction.A neuron turns active when a number of synchronized (closely spaced) action potentials (APs) is received at its input ports (dendrites / soma) that cross the activation threshold, where the threshold may be reached even by subsets of input signals.Therefore, the active state of a neuron at the moment of activation qualifies to represent the semantics of a disjunction of conjunctions of semantic values resulting from each subset of APs of the presynaptic active neurons.As shown below, a disjunction of such subsets allows a system a flexibility to require sufficiency of limit of conjunction via active inhibition in a re-entrant network to select appropriate level of specificity and abstraction.The fundamental mechanism of representation and processing of semantics of information is thus established.

4.
A point to note here is that an observable state's intrinsic correlation with causal information is not equivalent to a coding via a signal structure that can be decoded by any means.The transmission of information occurs due to the causal dependence, expressible by Eqn.2.For experiments in a controlled setting, the function of constraint of interaction is known, which is used to evaluate the correlation of the resultant state.For this reason, the semantic value of correlation is considered as a product of interpretation as well as specific to the constraint taken into account.Here, disjunction of conjunctions of states encapsulates all possible specification of precursor states in reality that may cause the state S of P, hence no specific artificial interpretation is required beyond this generic expression.That is, the processing in modular hierarchy may depend on this fact alone to capture constancy of relation to build structured and abstract semantics, as shown below.For a neuron the active state is rather well defined by an Action Potential (AP) that serves as a discrete state and offers a mechanism to cohere with other neurons bearing relatable correlation.Signal structures and neuronal functions may just serve as a mechanism to build coherence and to develop connections as discussed in the text.It resolves an insurmountable problem of coding and complementary decoding via signal structuring to represent increasingly complex and abstract semantics that must respond to dynamic variations.The method of information (semantic) processing vis-a-vis computing [19], is provided by Eqn.2.
5. The physical states transform as per the causal function of the states of interacting systems, not by the information of their correlation; hence information remains intrinsic and non-measurable.Since information arises from the objective causal relation, the causal function of a state in a context creates an opportunity to associate the resultant semantics with the causal function of the semantics of correlation of precursor states (details in Section.5).Therefore, it is entirely possible for a system, processing the information of causal function of represented objects in hierarchy, to have a state that represents the semantics of 'a system in control of action appropriate for a context' towards a predetermined effect.As an addendum, it may be noted that it serves no purpose to the evolutionary processes whatsoever if the represented semantics does not 'causally relate' with objects to effect change via action.In other words, the evolution of semantics of self and its purposeful function for effective adaptation and perpetuation could not arise if it was not based on the causal function attributable to such semantics.

The basis and mechanism of object description
We begin with a question, "What may constitute a common basis to define a general object such that a uniform mechanism serves as a general constructor of its referable representation?"An object is relatable in two fundamental ways, one, bottom-up structural relations that include components and their inter-relations, and another, top-down functional relations [20] with objects in encapsulating context.A component naturally includes its own structural and functional relations.While the former is intrinsic, the latter is relative to other objects.Moreover, an object is referable or has an identity by virtue of certain constancy in structural and / or functional relations.Without such constancy in structure or function there is no definable characteristics, no objectivity, and no referability, hence no existential reality even in the domain of representation (Section.4.1 of [1]).A relation refers to the constancy that holds among objects even when the objects undergo change or transformation.In a broader sense, the 'constancy of relation' refers to the limits of variability or specification of mutual constraint among objects in relation as formally expressed below.An object, serving as a variable, may vary within certain parametric space of its description, but its identity defining structural and functional relations must stay within certain limits.The following statement abstractly quantifies the limit of constancy (or variability) of a relation among objects with discrete values.If the number of possible values (states) for an object A is N A and for B, N B , yet if the number of possible combinations is less than their Cartesian product N A × N B , then the objects are related (expression from [21]), even though for a given value of A, B can have a range of values that forms a class.This expression of relative dependence is extensible to analog variables [21] or to values with arbitrary overlapping extents that can be dealt with conjunction and disjunction as shown in Fig. 3.
The constancy forms the basis of an object's identity, be it a physical system, a state description, a relation, an expression, or a process.Specific constancy in an object's structure and function readily suggests how to construct its semantic representation in modular hierarchy.As shown in Fig. 4 and expressed in Eqn.3 (also see Section.3 of [1]), a conjunction of elemental objects, including inter-relations, describes one composition, whereas a disjunction of instances of compositions represents a structured object as an equivalence class that endows it with an identity.This method of structure formation readily suggests the mechanics of integration.As stated above, an elemental object may itself be an abstract or a structured object.For example, a paper possesses a variety of structural and functional relations that remain preserved within limits under transformations.An observable transformation is relative to an observing system, which also includes the identity operation corresponding to no relative change.Under regular transformation of a paper, such as a translation or rotation, several relative properties (elemental objects) remain preserved.The relative placement and orientation of the edges, shape, size, color, texture, reflectance of the surface as well as the measures of relative distance and orientation of the markings on the surface remain unchanged.Similarly, the continuity of the edge and the surface remains preserved.Even under irregular transformations, e.g., when the paper is folded (crumpled) randomly, or even cut randomly, the causal continuity in the temporal elemental transformations preserves the correspondence with the prior identity due to the constancy of causal relations.Moreover, the resultant state of the folded paper maintains its own constancy, such as topological continuity, thickness, color, texture, reflectance, mass, and statistical distribution of the folds under further displacements.
Similarly, for a mathematical expression object, y = sin(x), the components x, y, sin, and = form a structural relation, where x and y belong to a class, x, y ∈ R, bearing a specific relation such that for each value (state) of x the value of y is unique, and for each value of y, x belongs to a class such that x = x 0 ± 2nπ, n ∈ Z.The constancy of this relation is labeled as a sine function; = is a function object specifying assignment of the value of the structured object on the right to the elemental object on the left.Hence, the expression object is defined by the constancy of structural and functional relation among objects.Moreover, the expression object can be evaluated as a conjunction of semantics expressed by each element, where the elements x and y serve as variables (see Section 8.4 in [1]).
Similarly, 'right angle' is a class object that expresses the constancy of a relation between two lines, an instance of which is constructible with lines at arbitrary orientation, where the inter-relation holds.Within the contexts of observation and realization of instances, variation within limits may remain non differentiable or ignorable forming a referable class of equivalence.A precision independent or precision limited reference to the semantic value of 'right angle' as an object functions as a reference to an irreducible abstract discrete semantic value, for it is not equivalent to an instance of a right angle.Moreover, in conjunction with the semantics of class (space) of relative angles within limits of variation the referable semantics of 'right angle' also serves as a determinator rule when testing or constructing an instance of 'right angle'.In physical realization of a mapping system, such as a neural connectivity, the agents whose active state represents the class of 'right angle', may map to other agents at higher levels in hierarchy, where semantics of the class or relation itself is an element.Depending on the context, the terms for the relation and the class can be used interchangeably.For instance, the term 'right angle' refers to both a relation and a class object.
With this understanding, we express the abstraction of structured semantics resulting from a topdown and bottom-up mapping as follows.
p A q 1 A q 2 O p A q 3 A q 4 O p A q 5 A q 6 O ... = p A (q 1 A q 2 O q 3 A q 4 O q 5 A q 6 O ...) The equation simply exemplifies the distributive law -conjunction, A , is distributive over disjunction, O .The RHS expresses the object p without an explicit dependence on any one conjunction q i A q j .For instance, in a bottom-up mapping, each element in a pair may represent a line segment at a particular orientation independent of any other lines at any other orientation, then a conjunction of the two forms a semantics of a composite, which forms a basis of integration ( [22]) at each step in hierarchy.If each of the conjunctions q i A q j bear a common relation p, then the disjunction creates a reference to p without any dependence on or reference to a specific conjunction [1] as shown in Fig. 4. A noteworthy point is that the disjunction creates a referable object that does not necessitate a reference to an instance.But in a top-down mapping, it enhances the weight for, or coheres with, right angles over others.Therefore, disjunction becomes a source of emergence making representation independent of the values of states for the second order correlation (as per part (ii) of the law).Similarly, in a top-down mapping, a disjunction captures the generic base class object in each of the higher level contexts (objects) as expressed in Eqn.3 and as shown in Fig. 4(d).
A relation among arbitrary objects including precursors to their causal effect is expressible as a map.
Each symbol in the list {A, B, ..., X} refers to a class or parametric space.A map F defines a relation as a function, where specific conjunctions of values from {A, B, ...} map to specific values in {X}, where {X} may be a space of composites or higher resolution specifics (Fig. 3), or a space of arbitrary relation among values in {A,B,...}.In terms of sets, morphism F is a selection of a subset of A × B × ... × X.
A disjunction of such conjunctions of elements in the subset represents the function / relation F itself.Extensions to the usual interpretation of a map include non-discrete (analog) values that may overlap, spaces that are dependent to include multiple variables covering the same space, and non-exclusive, oneto-many, mapping from domain to codomain, as the function of conjunction and disjunction is independent of such requirements (Section.3.1 of [1], and Fig. 3 here).That is, the scheme transparently maps analog, discrete, structured, abstract, and symbolic values to the space of codomain.In a re-entrant system, the current value in space {X} can be looped back to form a conjunction with new values in {A, B, ...} forming a temporal or iterative process as shown in Eqn.5.This also enables a self referential mapping within limits.Eqn.4,5 present a general scheme to represent a relation computable with conjunction and disjunction and implementable via connections.A population coding method, as presented in [1] and shown here in Fig. 3, becomes a necessity to implement such a system with finite number of elements at the cost of consistency and completeness.In this work, this mapping scheme is used to designate causal, compositional, and reference relations.The first two lines in Eqn.5 symbolize a disjunctive mapping to a single valued space of function F itself as shown in Fig. 4(c), where the LHS includes all specific conjunctions as per the relation F. This amounts to enumeration of all possible conjunctions on LHS if the values are discrete and finite.For analog values with overlaps or for infinite variations, the population coding is required.This creates a reference to the relation F itself, which in turn serves as a functional object with temporal and causal significance in its further mapping.For instance, the third part of Eqn.5 includes the function F as part of LHS in the prediction of temporal evolution of values in {A, B, ...}.This mapping scheme forms a recursive constructor in hierarchy without limits.
Given the function of negative range of correlation of a state of agents in limiting the positive correlation in conjunction (Fig. 3), it is computationally efficient if the correlation profile of agents vary widely within a module to cover the semantic space yet dynamically synchronize within temporal limits via a coherence building mechanism in order to support most probable value in the context.That is, the mechanism of population coding presented here predicts diverse tuning (dissimilar initial correlation) profiles and low pairwise signal correlations among the neurons [23,24].Moreover, the variability in neural response [25] is a part of competitive coherence building [26] rather than reportable representation of object specification.The current notions of noise and noise correlation in neural activity [27,28] remain misconceived in light of the population coding presented here for building coherence.Moreover, this work challenges the general assumption that specifics of information in the neural system is coded in the spike rate or their temporal structure.
As detailed in [1] and briefed here, 'disjunction of conjunctions of semantic values' forms a universal constructor of all expressible semantics.Temporal processes merely include values or functions of relative time in the expression as shown in Eqn.10 and Fig. 6.In a bottom-up mapping to a higher level object, the disjunction of conjunctions of elemental objects expresses semantics of a structure, whereas, in a top-down reference, the abstraction of the generic structure and its functional relation form the object specification.Such a reference is clearly evidenced in our thoughts; when one refers to 'right angle' as an abstract object, one does not refer to an instance of it.In other words, in a top-down reference to the object, sufficiently specific higher level context must form to down refer to any particular instance of an object at lower level.Since this holds at each step in hierarchy, agents in higher level modules have much wider sensitivity to encompass all possible specifics representable at lower levels; in a given moment though, the bottom-up construction determines the integrated value the higher level agents represent.The graphical examples in Fig. 4 illustrate the mechanisms of conjunction and disjunction as bottom-up and top-down constructor of structured and abstract semantics.
As shown in Fig. 4(a), a conjunction of 4 line segments of specific width and length in specific relative position and orientation forms an instance of a rectangle, where any two adjacent lines form a right angle.This structured object (rectangle) may form an element of yet another object, e.g., a paper.When a rectangular piece of paper rotates about a point, or undergoes displacement, its four edges (lines) sweep through orientation space, but the relation between any two adjacent lines remain preserved (invariant) under the transformation as schematically presented in Fig. 4(c).Consider for a moment different active sub-populations of agents in module M1 representing different line segments map to another module M2.The agents in M2, receiving inputs from M1, can be dynamically constrained in a re-entrant network to build a sustainable coherence over time among a sub-population.A sustainable coherence is possible only if the population competitively represents a feature or relation that remains invariant over time, as suggested in Eqn.5 and discussed in Section.3.1 below, which is the relative angle between the lines here.The term 're-entrant network' is used to refer both to local recurrent loops within a module as well as to feedback connections from other modules.The specific case shown in Fig. 4(c) is idealized as a static map, whereas it is population coded dynamic map in a re-entrant system.
In each of the illustrations in Fig. 4, the represented objects may be limited in resolution, or may have non-discrete overlapping description.That is, ∆t in (b), and orientation of line segments in (c) may have a width of resolution to cover the temporal or orientation space with finite number of elements, but the method of population coding sharpens the specification as shown in Fig. 3.The methods apply universally to all semantics or objects as conjunction and disjunction are type or category independent operators.Moreover, a mapping system may capture an arbitrary relation -e.g., a mapping of two values from the space of numbers to the space of numbers may represent the relation of sum, difference, product, or any other if observed consistently.That is, a difference relation is achievable via mapping, not necessarily by a mechanism of differentiation.A disjunction of all such combinations that covers the orientation space gives rise to an emergent semantics of 'right angle', an abstract semantic value with no physical counterpart.The same mapping is also shown as a network of connectivity from a set of agents (such as neurons) that represent line segments at specific orientation to a higher level agent A, such that each active conjunction in the map, shown in the same color, may activate the agent A. The active state of A then represents the irreducible semantics of right angle that emerges from a bottom up mapping here.(d) A series of composite (structured) objects may share a common feature; a disjunctive relation among such objects evaluates to the common feature as a base class as expressed in Eqn.3 and 6, without any particular dependence on another feature in each conjunction.
At this point we note that the active state of an agent functions as a reference to represented semantics.The agents representing different elements of an active context turn active in close synchrony of time.As the paper incrementally transforms relative to an observing system, the constancy of various relations provides ample opportunity to self organize the activities of agents in modular hierarchy to connect the temporal sequence of activation at one level to a specific set of agents at the next level under the population coding scheme.Such activations strengthen the connectivity on the recurrence of the same relations while pruning any randomly occurring correlations based on statistical significance.In the limited domain of observation, an emerged class is not complete, yet it serves as a class descriptor in its further mapping.
An object specification may also emerge from a top-down process from objects of greater complexity, and from relations in encapsulating context.Consider a structured object S 1 describable as (p 1 A p 2 A p 3 A ...), where (p 1 , p 2 , p 3 , ...) are descriptive elements.Similarly, another object S 2 can be described as (q 1 A q 2 A q 3 A ...), where one of the components, say q 1 is equivalent to p 1 .We may replace q 1 with p 1 in the expression of S 2 to get (p 1 A q 2 A q 3 A ...).Now, the disjunction of all such structured objects S i , where p 1 is the common element, can be evaluated as per Eqn.3.
As per the evaluation method provided in Table .1,since there is no common element among the terms in disjunction within the parenthesis on the right hand side of Eqn.6, it amounts to no particular dependence on any one of the terms, a null correlation with each instance, reducing the correlation to p 1 .This is how a disjunctive relation expresses the base class element common to all terms.In fact, in extreme atomic case, the functional relations are the only way to refer to an object, as for a structureless charge, mass, or a point in the visual field.In strictly top-down references, all objects serve as atomic.The method is visually presented in Fig. 4(d).Similarly, the objects where an instance of right angle manifests are papers, tables, walls, doors, windows, trees standing vertical to the ground, etc.Each of these objects can be expressed in the form of a conjunction of specific elemental objects, where right angle is one of the common elements.If the common element is a structured class object, it may have a bottom-up reference to the object in addition to the functional relations as discussed above for the right angle class, but this is not a necessary requirement.

Representing structured relations and temporal events
As suggested above, processing is organizable in modular hierarchy, where a module is shared among, or connected to, several other modules via feed forward and feedback projections [29].A module is a densely connected recurrent localized network of elemental agents [29] to process and represent the structure present in the dynamics of objects represented by the active states of projecting agents from other modules.It is then possible to designate locally lower, higher, and equivalent level modules based on the mapping configuration such that the higher level modules represent more complex and abstract semantics.Each module serves as a structured parametric space.The neural organization of the brain is an instance of the scheme, it must have the following characteristics.Since the disjunction of conjunctions of countably finite elements forms a constructor of a singular semantic value, it requires the agents to have singular (discrete) output state to represent the expressed semantics; here, we refer to that as the active state such as an action potential of a neuron.Moreover, since output of an agent is distributed among many agents for coherence building, the information flow between two agents must only be one way to avoid direct and non-linear mutual dependence in an interaction.Similarly, since a module receives input from several modules representing elemental specifics, a context becomes specific and sparsely distributed; a tree like branched structure is rather suitable to receive inputs to map closely related elements of a context with greater probability of occurring together in close proximity on the branches for greater cohesion [30,31,22].Therefore, the observed anatomy and function of the neurons provide a strong evidence that the neurons emulate the constructor expression advanced here.
The artificially devised mechanisms of exchanging information is based on encoding information and communicating the same to other agents that must already have information that the codes correspond to [32].This is also the case with linguistic communication between two individuals.The function and organization of our brain implements a mapping that uses the terms as a reference to semantic values, where terms are communicated via graphemes and syllables.The artificial systems often re-encode the linguistic terms for communication [32] that is decoded to recover the terms, but their mapping to the semantics is left for a system like brain.Demanding a similar coding system from neural function in terms of signal structure misses the point that the codes must be mapped to the semantics.Such a demand misdirects a scientific question limiting our abilities to investigate the representation and communication of semantics via intrinsic causal correlation.In the paradigm presented here, the states of agents bear intrinsic correlation with the semantic content of information of the context, which is not decodable by an external agent.However, the coherence in the semantic elements of a context reflects in coherence in the active states of agents that causally correlate with them.A coherence among their active states presents an opportunity to capture and represent structured semantics in terms of disjunction and conjunction of elemental values.
As noted above, the construction and referability of an object are based on the constancy of its structural and functional relations in the dynamics of change.This basic principle serves well to create and represent all objects (relations, processes) in a context via mapping.One may recall that a correlation profile is specified by the limits of positive, negative, and null correlation with range of values in specific spaces of semantics (see Fig. 3).Therefore, greater the coherence based conjunction, greater the specificity of the represented object in the context.The active coherence must be further sustained to follow continued relevance in evolving context.Now, if each of the modules in a system carries out the same task of representing the constancy of structural relation among elemental objects of lower level modules and functional relation with objects of higher level modules, then one has a universal mechanism to construct all semantics (objects) in hierarchy, which includes their function in the domain of representation.
A specification represented by the predominant coherence among agents with varying correlations in a context in opposition to other such possible coherence must be the most likely an object in its neighborhood.For instance, in presence of a right angle in a context, coherence in the neural activity representing the right angle in contrast to other angles is likely to be predominant based on feed forward and feedback signals from a multitude of parametric spaces.That is, only the reality can be consistent when observed multiply!Greater the specificity of the relative description, more specific the action possible towards a goal.A goal directed action may require certain degree of specificity, where a greater specificity may not serve a purpose.For example, the need to displace a physical object by a few centimeters with a precision of a centimeter does not require greater resources to be recruited to move by a millimeter precision.As suggested by the population coding mechanism presented in Fig. 3 and Section.7 of [1], finer resolution (precision) may require a greater coherence and conjunction among larger number of agents, and greater loopback processing.
Similarly, in the dynamics of change, the specification of a temporal object, such as a rate of change or a sequence of events, that continues to stay relevant for the duration of the context in contrast to other objects or processes in the neighborhood must be the most suitable specification of the object or process.For instance, consider swinging of a branch in the wind that one attempts to hold.A prediction of movement with greater precision may not hold for long, and a long range prediction may not be accurate.As the approach closes, the specificity of prediction must improve.In the dynamics of change, greater specificity may be relevant only for shorter times, while lower specificity may not suffice for goal oriented action.Such a relevancy contrast requires a dominant coherence among the active states of agents to stay relevant and dominant with time in a re-entrant system.Since the coherence relation is captured from the temporal dynamics, configuration of active states of agents at one moment must loop back to strengthen the configuration at the next [33], (Eqn.5).Therefore, if a dominant coherence of a moment is looped back and stays in coherence with the incoming signals at the next moment, it represents the most relevant constancy of temporal process within the modular space.Hence, a continued competitive coherence in the re-entrant network becomes a requirement of the function in modular organization.The constructor expression serves well to represent temporal coherence among agents with discrete signaling, such as action potential.Recall that a conjunction of events at contiguous steps in time represents the structured temporal object as referred to in Fig. 4(b), depicted in Fig. 6, and expressed in Eqn.10, where the conjunction builds via loopback mechanism.Moreover, a disjunction of variations of events at each instance allows a class of process specifications to be represented.Since all observations are necessarily temporal even when the objects do not change, the mechanism of temporal coherence (synchronization) among the transient states of agents remains general to represent relations in the dynamics of objects (variables) as observed in neural systems.The continuity of time and space, uniform function of their intervals, and the speed of signal propagation are a few of the fundamental constancies of relation that provide a robust basis to observe other structured constancies in natural phenomena.
The process of population coded competitive coherence over time has a few immediate implications.First, the evolved mapping based on the population coded constructor expression functions as the causal predictor and effector of the semantics of the next moment (See Eqn.5,7).Second, since the function of an object is dependent on all causally relevant objects in a context, the context relative functional relations of each object get represented, where each object also plays a part of the context for other objects.The function of a structured object is also defined by the function of its components, hence, relevance of each component in a context increases the relevance of the structured object.Third, in this process a powerful mechanism emerges from the fact that in a given context the system makes available even those causally correlated semantics from past experiences (memory) that are relevant but not part of current observation [34].In common parlance this is often referred to as understanding of an object in opposition to the single threaded semantic dependence and processing in artificial technologies of the present times.
Fourth, it also enables a system to recall element wise correlations in a new context to build coherence and to generate the most probable prediction, which has the power of graceful degradation even in novel contexts.Larger the number of elements in a context, lower the probability of a bad prediction.
A prediction is necessarily based on the constancy of causal function.A contextual state in the environment naturally evolves to the next state as per the causal function of the elements in the context.Temporal evolution of objects follows their causal dependence on objects of context, which can be used to create a population coded re-entrant mapping system, where a configuration of active states of agents representing the elements of the context at one moment enhances the coherence of the configuration representing the context at the next moment as expressed in Eqn.7.An idealized mapping system is illustrated in Fig. 5(b).For a dynamically evolving mapping system, instances of active mapping from one moment to the next capture instances of causal function of the objects.A disjunctive relation among such mappings represents the semantics of the causal function specific to the object space as per Eqn.5.For example, when bringing together two groups of elements into one yields the sum of elements in the resultant group, the disjunction of such mappings within observable limits represents the semantics of function of joining groups or summing.Moreover, since such causal relations are representable in multiple relatively higher level modules for their relevance, a disjunctive relation among such space dependent causal functions would then represent a space independent referable semantics of causal function (causality) itself in yet higher level module where it may be relevant for higher semantic structure.This mechanism of abstraction exemplifies how arbitrary semantics of conceptual entities emerge without a dependence on specific object types.
Since there is no mechanism of coding and decoding of information by signal structure, how could a system construct a representation of structured semantics in modular hierarchy based on the constancy of causal relation?The only way useful functions of objects may get represented is by the measure of success of action / behavior towards certain evolving goals in line with the selection pressure from the prevailing context.This in turn requires that the predictions from learning via multiple sensory modes find conformance with each other and with action.Therefore, the evolutionary processes favor the self organizing functional architecture that models the environment based on the constancy of relations to select self-sustaining action.The same mechanism can be used to develop artificial systems of processing without specific coding for learning.In a modular system, specific states of agents in certain set of modules, M, may evolve to represent the physical states of the holding body (the body that sustains the system of processing) that are in accord or conformity with the requirements of selection.For biologically evolved systems such modules may represent the conditions of well being of the body consequential to the sustenance of the system of processing.In mammalian brains, these modules are located in old sub-cortical regions [35,36].For an artificial system under arbitrary causal function, such states may even be externally coded.For the consideration here, it is immaterial how the processing system represents the states of suitability.The conditions of suitability may be multi-dimensional and graded.Net effect of the active states of agents in modules in M on rest of the processing system, S, is to select specific processing and action that are aligned with the suitability conditions [37,38,39].Now, given the abilities to represent higher level abstract semantics in S, the descriptions of suitability of function and states of the system may emerge in S (say in cortical brain, for instance [40,37]), which may bidirectionally map to modules in M [37,38,39] and evolve in tandem such that M's function is based on higher level semantics rather than on just the physical states.Modules in S may represent higher level referable semantics, together serving to select specific processing and action [35,41,38,42].That is, these referable semantic values serve as preferential biases (goals), such that their activation serves to modulate, strengthen (promote) or weaken (demote), the competing processes of relevance for action (behavior) in different modules.The satisfaction of the biases may depend on what is observed on the holding body and within the system of representation itself.Since the biases are referable, a causal relation between the biases and the behavior is further representable as per Eqn.7.Furthermore, the semantics of biases may express even explicit negation of other semantic values allowing the classes of semantics of likes / wants and dislikes / unwants to emerge when these semantics relate to the representation of self as shown in the next section.Such classes of preferences in relation to the represented self function as guiding principles or emotions [41,38,42], and serve to enhance the self preservation.Moreover, the process of promotion and demotion may proliferate the semantic classes of likes and dislikes in every module that has an effect on action to the extent that every external action depends on the convergence of such choices.Furthermore, S and M may produce physiological effects and arousal [43,44,45] that are either fed back into S internally or observed on the body and related with the semantics of emotions -another pathway to control function and behavior.Such semantics of biases (goals) are a product of evolution, which plays a critical role in the development of systems with abilities to represent arbitrary semantics with causal powers of selection and action.The biases emerge in response to varying selection pressures arising from diverse but specific environmental contexts; they are not expected to be functionally and optimally consistent in all possible contexts.It is not important here whether such modulations of competing coherence are effected via chemical means in a biological system or via strict signaling mechanism.
In summary, representing the semantics of structured relation among objects gets translated into capturing the optimally probable dynamics among agents in a re-entrant network via coherence building mechanism in opposition to other probable dynamics in input states of agents as historically observed.As per the observation above, a goal directed action requires merely a sufficiency of relative specification among competing descriptions, not necessarily the one with sharpest specification.A sharper specification of a relation in the context, may require a larger number of elemental agents to form a coherence, and multiple looping back of signals to achieve greater synchrony as suggested in Section.7 of [1].Therefore, there exists a trade off between greater specificity and the amount of resources required for functionally optimal behavior.The representation of causal relation as presented here (Eqn.7)forms a central mechanism at all levels.In addition, it is noted here how the referable biases and goals may emerge in such a system of processing that control function and behavior.
It is not the purpose here to identify specific physiology, function, and types of neurons in the brain and their connectivity, rather to lay down the specific mechanism of information processing leading to the representation of semantics of self and its relation with the objects, of which the brain is an instance.The specific mechanics of constructing object description provides sufficient ground to construct semantic components of self.

The semantics of self as an element of represented objects
The correct identification of the object of a scientific investigation is as important as the construction of its objective formulation.In an expression like, "I see the blue sky", what does the 'I' refer to?The representation of self is an object like any other, even though in common reference to consciousness either it is ignored or it holds an asymmetric status with other objects as if there is a fundamental qualitative difference between the two [13].

Spatial relative placement of the observing system
As first, we construct a representation of spatial placement and temporal movement of an observing system in relation to other physical objects observed in space and time.Consider a system capable of correlating or mapping relative times of signal propagation to relative constancies in natural function such as mutual distances and angles of placement of objects with respect to the system's direction of movement in a 2-dimensional Euclidean space (field).Further consider a few objects scattered in the field at (r i , θ i , s i , i = a, b, c, ...) with respect to the observing system at a given time.Here, r i is a measure of distance, θ i a measure of angle with respect to the direction of movement, and s i the side of placement of objects, Left, Right, or Inline.We may label the placement of the objects independent of a coordinate system symbolically as (x i , y i , i = a, b, c, ...).For the moment, these labels merely serve as symbolic names for different points without any reference to a coordinate system.The idea here is that if points in space and time, and distance and duration, play any causal role in the function of the universe such that events at different points in space and time cause mutually relative differential consequences, then these labels serve to identify and relate the points by their mutual relation in the consequence.For instance, if a short pulsed narrow frequency signal of an event originates at the system and travels in space as per the reality of natural function, then the signal traverses through all objects.If the objects served as signal reflectors, then the system at the origin of the event would receive back the reflected signals in certain temporal order.Measures of relative time of signal travel form the measures of spatial distance to these objects by virtue of the constancy of speed of signal propagation as shown in Fig. 5. dimensional spatial field, where system X serves as an observing and mapping system to represent the relative placements.A signal originating from X at location X 0 is reflected by {A, B, C} and received back by X at relative times (t a 0 , t b 0 , t c 0 ) respectively that further map to respective distances (r a 0 , r b 0 , r c 0 ) in one-toone mapping as shown on the right, where the index in alphabet represents the object and in numeral the measurement number.For instance, the placement of object A can be anywhere on the circle in red centered at X 0 .As the system X moves to a new location X 1 , it regenerates a new signal with a different pulse duration or frequency and receives the reflected signals back at relative times (t a 1 , t b 1 , t c 1 ).Now, the locus of object A is shown with a circle in blue centered at X 1 .The cross section points of red and blue circles fix the location of A with respect to both points X 0 and X 1 , before and after the movement; the symmetric placement of A about the line of movement is shown with dashed lines leading to A .The second movement of system X to X 2 at an angle α with respect to the first movement and a new set of measurements of reflected signals fixes the location of all objects in the field uniquely as analyzed in the text and shown graphically with three circles for object A. The angles θ a 0 and θ a 1 are values of correlation for object A relative to two ends of first movement, while θ a 1 − α and θ a 2 are to the second.(b) Labeled parametric spaces are shown as black horizontal lines, whereas labeled nodes shown as big dots on them represent discrete values.Colored lines converging on a node from below represent incoming projections from lower parametric spaces.Similarly, the lines emerging upward from a node designate forward projection, which bear no color correlation with incoming lines.The lines shown in the same color converging on a node from below represent a conjunction of values represented by the projecting nodes, whereas, a convergence of multiple such conjunctions in different colors on the same node represent a disjunctive relation.The angle space is marked with L and R to indicate Left or Right of movement, or the sign of angle.(r 2 , θ 2 , s 2 ) labels the composite space of distance and angle for different objects.The node in the top parametric space represents a disjunctive convergence of conjunctions of relative placement of any three objects observed in the field at all times, only one conjunction is shown in the figure.This node represents the placement of observing system X itself relative to objects in space at all times, and forms a component of the system's identity.
In Fig. 5, the perspective of the parametric mapping is based on system X.It is assumed here that signal travel speed is much greater than the speed of X.As first approximation we take displacement of X to be negligible while reflected signals are received back from nearby objects.Since the active state of an agent in an array is said to represent the time interval since signal generation, which causally depends on the speed of signal travel, the state directly correlates with distance.Moreover, the distance traveled by X between two signal generations is also assumed to be relatively small with respect to the inter-object separation in the field.This implies that the two closely spaced measures of time from two consecutive signal generations are from the same reflector, hence, conjugated together.This places a limit to spatial resolution.These approximations are not required when number of objects in the field is larger than three or prediction from past observations is used as shown below.For one-to-one correlation with distance, the relative times of signal travel are mapped to distance space on one-to-one basis in Fig. 5(b).Eqn.8 expresses the displacements of the system X by d 1 and d 2 at intervals of signal generation and angular displacement α.
Here, the indices in alphabet identify the object and in numerals the measurement number.The same equations hold for all reflecting objects.The values r a 0,1,2 are known at respective points of measurement.The sine is an odd and cosine is an even function, hence, a sign inversion in the argument angle is a degenerate solution as shown with dashed lines for object A in the figure .A set of four equations for each object adds three unknown angles θ i , where α = nπ/2, d 1 , and d 2 remain common among all objects requiring at least three objects to match the equations to parameters.A conjunction of two relative times or distances from two consecutive measurements for each object not only correlates with the angles at each point of measurement, but also with the measure of movement of X common to all objects.A conjunction of three distance measures for an object correlates with all parameters of relevance here, Eqn.9.
Where, ⇒ stands for 'correlates with'.Here, conjunction on LHS serves as a multi-valued function, where the values in conjunction can be thought of as arguments to the function.The conjunction on the RHS is consistent with the sign (L,R selection) for θ a 1 for non-zero value of α.Sufficient information exists in the system to create modules for parametric spaces shown in Fig. 5(b).The inputs received by a module fix the parametric space represented by the module.The process of competitive coherence building under population coding scheme, as discussed above, among modules of these parametric spaces, would converge to unique values for all correlated measures of angles and movements.It is evident that greater the number of objects followed, greater the accuracy and precision achieved under the scheme.The values for d 1 and d 2 are common to all objects in Eqn.8, they are shown as a product of a disjunctive relation as per Eqn.6 in a bottom-up mapping in Fig. 5(b) for simplicity.The conjunction of two measures of distance and the respective movement of X correlates with unique magnitudes for the angles at both ends.
First two distance measures of objects correlate positively with respective θ x i as well, but the third measure correlates negatively with it.Therefore, the conjunction of three measures for each object correlate negatively with all angles except θ x i .To avoid clutter in the figure, the mapping is shown only for the object A.
A relation that is very relevant for action in nearly all placement contexts is a conjunction of measures of (r 2 , θ 2 , s 2 ), where s 2 denotes the sign or the (L, R) value for θ, for it uniquely specifies or represents the placement of the system itself with respect to any three objects as shown in the diagram.While the values (r 2 , θ 2 , s 2 ) may continuously change for each object as the system moves in space and time, a conjunction of three continues to cohere with the placement of the observing system itself.If there are n reflecting objects in the field, then there are n C 3 combinations that ideally represent the same common information.Given the redundancy, a system may build or select greater coherence based conjunction to gain specificity.If a system has multiple measures for the same quantity, each with independent resolution limit, then a larger conjunction of such measures significantly improves the resolution as shown in Fig. 3.Even though the distances and angles of other objects are represented in system X, the same angles and distances are mapped to a modular space that represents the placement of the observing system itself, making it referable within the system, which forms a part of its own identity defining relation.
A few points are noteworthy.In real systems, a number of agents represent overlapping limits of values in the population coding scheme presented here to cover a semantic space, but here, nodes represent discrete ranges of values covering the space, which makes it convenient to show a relational feed forward mapping among nodes with lines.Moreover, in a hierarchical re-entrant system these mappings are dynamically constructed from competitive coherence relation among signals received to capture relevant constancy in observed phenomena as discussed in previous section.But here, it suffices to show how relations describable by conjunction and disjunction correlate with values in different semantic spaces.A space gets defined by a mapping given by the constructor expression on the values from different spaces.Lower level elemental objects define structure, and higher level contextual objects define the limits of relevance as implied in Fig. 4(d).
It is apparent that the same mechanism remains applicable to all measures in observed phenomena if they are relevant in contexts.In the example discussed above, measures such as spatial and angular displacements of system X, d 1 , d 2 , α, are represented.If the signal generations are periodic at constant intervals, then the same measures also serve as (or map to) rates of their respective changes, for the divisor remains a constant.In fact, each measure of distance arising from consistency of feed forward and feedback coherence and relative time may also map to the measure of speed of signal travel as it is relevant for prediction.If the number of objects in the field is much larger than three, then the population coding method not only achieves higher resolution or precision of specifics as per the need, but also provides resolution to the combinatorial problem while allowing incremental changes at all times based on statistical coherence without undergoing complete reset of the mapping system.Such a system is robust against a degree of deviations and errors because the system of processing is based on competitive coherence.Forward and feedback mapping from related parametric spaces along with the previous measures in each of these spaces correlate with the new measures sustaining coherence in a re-entrant system.For instance, conjunction of rates of displacement of observing system in space and in angle along with the previous measures of distance and angle of objects' placement in periodic sampling correlates with the next values of objects' placement.In fact, inter-signal interval need not be a constant if it is represented in a parametric space of its own and forms a factor in conjunction.
In a hierarchical organization of processing, higher order derivatives of change are representable with variations in lower order derivatives if relevant enough for competitive coherence for successful predictions.With the availability of parametric rates of change in measures resulting in forward predictions of measures, neither of the two approximations stated above are required.Moreover, sustainable deviations from prediction correlate with the external changes in the context.For example, when the objects in the field move, the displacement is captured via difference relation from coherent prediction for all objects, and the derivatives of change are mapped and represented, which then become part of the next prediction, and so on.A noteworthy point is that the observing system may continue to follow the movement of objects in relation with other objects and map onto the same node in a parametric space that serves as the space of identities for respective objects as shown for the system X in Fig. 5

(b).
We note from Eqn.8 that cosine expression gives the same result for all objects and respective sine expression yields a value zero for all.It is natural to expect that these constants relative to the movement of system may form parametric spaces of their own.We also note that a given displacement of an object irrespective of its current location merely corresponds to a constant addition of values in these parametric spaces that cosine and sine expressions yield.Now, the labels (x i , y i ) are meaningful as measures of distance along axes that define the Cartesian coordinate system.There is no necessity to begin with a reference frame, a relative frame emerges from correlations.Since relations are constructible with respect to any arbitrary point or direction in space depending on its relevance in coherence building and prediction, all such frames are equivalent.A third person perspective is merely an arbitrary fixation of a frame.Therefore, it is always possible to choose one arbitrary but convenient reference frame to place all objects with respect to it to draw certain specific inferences, which is often the case in scientific analyses.
While this specific example serves as a simplified illustration of a mapping system, it also serves as an idealized system of echo location.In fact, the mechanism stays true for all parametric (object) spaces, making available an uniform mechanism of object description.For echo location, distances are observed that correlate with angles, whereas for vision, angles are observed that correlate with distances.Since the constancy of relation is the basis of representing an object, and every relation is captured via the interaction among physical substratum quantified by the constructor expression, all represented objects have causal consequence.

Representing a system as an actor, observer, and controller
When a physical system interacts with other systems it undergoes a transition in its state in response to the causal states of the interacting systems, Fig. 2. Hence all physical systems function as a sensor and effector.A neuron functions as an elemental agent that receives discrete action potentials (APs) as input from a large number of other neurons and generates an AP which is then distributed to a large number of other neurons as per the dynamically evolved connectivity.A neuron turns active when there is a sufficient coherence in the input signals, where a signal coherence is based on the coherence in the semantics of elements of the context represented by the active states of presynaptic (projecting) neurons.An inhibitory input serves to raise the requirement of even greater coherence (conjunction) of excitatory signals in number and in temporal synchrony for activation as part of a competitive organization, effectively narrowing the limits of positive correlation while widening that of negative correlation (see Fig. 3).If inhibition succeeds, then there is no further communication from a neuron in the network.Naturally the mechanism applies to all sensory domains and their integration.The problem then reduces to representing the semantics of function of being an observer of objects and an effector of change to the objects, as they are rather dominant correlations for their suitability for behavior.
We recapitulate the basis of construction of all semantics.An element of semantic value specifies a profile of range of values with positive and negative correlation.A conjunction of such semantic values evaluates to greater specificity in the range where the profiles overlap among the operands, and extend the profile or composition where they do not, i.e., when for a given range or domain one of the operands has null correlation.A disjunction expresses the generality of a class that includes a range of instances, or a relation as a descriptor of the class, an abstract value.Structural integration occurs when a conjunction binds components together [22] into a composite, and the disjunction generalizes the variations into a class of structure (see also [1,46,47,48,49] on binding).A structure or a class at one level relates as an element at the next higher level.Function of an object is defined by its relation with other objects that determines the consequence in a context.Functional relations constitute elements of a structure in modular hierarchy.The constancy of structural and functional relations forms the basis of all descriptions, their referability, and a general mechanism to construct all object specifications uniformly (systems, relations, processes).In addition, the mechanism of population coding enables a self organizing system to evolve with incremental changes based on observations of statistical correlations, and to represent a large dimensional object space with greater specificity with far fewer agents and their intrinsic states.These correlations form the basis of functional and temporal prediction in re-entrant systems allowing continuous correction to achieve goal oriented sufficiency of accuracy.Since there is no limit to higher order complexity of structure formation and abstraction of semantics, a system like human brain has evolved deep layers of hierarchy and wide modular object spaces to represent very complex and abstract semantics and their causal relations.Moreover, there is no unique pathway of constructing the representation of self and its relation with other objects as is evident from the existence of multitude of species with different modular neural organizations.Hence, the idea here is to construct a description that resolves only the essential issues in representing the self and its relation with other objects.
Active states of agents of inter-modular communication may represent gradually more complex (structured) semantics in hierarchy.For instance, from pixelized points in the field of view to line segments, from lines to specific contours, and from contours to specific shapes may emerge that are independent of space, time, color, contrast, and other qualities that may additionally be associated with them.Similarly, the semantics of inter-object relations, such as relative time, location, orientation, size, motion, and visual contrast may emerge.Similarly, inter-modal structures may emerge from different sensory systems.Similarly, the relative rates of change in different object spaces may form elements of structures.Similarly, the representation of temporal processes (episodes) may form elements of the observed dynamics.A conjunction of events at regular intervals of time in a temporal sequence binds together the events to form a temporal event or a process as depicted by Eqn.10 and shown in Fig. 6.Then, the subsequent active state of agents that depends on this conjunction in a re-entrant system would represent the semantic value of the prior sequence or process including temporal relation among the events ( [50]).As the semantic structure of events at each interval includes certain limits of variation within the parametric spaces of description equivalent to a disjunctive relation, the conjunction of events represents the process as a class with diminishing (less specific) correlation with events in the past.
First two lines in Eqn.10 establish the symbolic convention used here.E i (t i ) denotes the i th event in the sequence bounded within relative time t i , which is a disjunction of conjunctions of values from parametric spaces of relevance.Last equation expresses that a conjunction of semantics of such events in temporal sequence is a temporal event, a process.One of the variable parameters of correlation is time relative to the neighboring events which positively overlaps with them minimally, and bears negative correlation with the rest of space as depicted in Fig. 6.That is, t i carries positive correlation only with the range t i−1 < t i < t i+1 .A simple mechanism to enforce a temporal order is the dependence on prior coherence among active agents in each module, and the subsequent activation being aligned with the next coherence at regular intervals.Then the continued conjunction of such events maintains temporal order among events as well as their continuity without a hole as one continuous process over the entire duration.This constitutes a general mechanism to represent continuity in a parametric space of observation as also exemplified by the representation of a line segment by overlapping points (Section.4 in [1]).Here, an episode merely refers to a sequence of events temporally bound together, without any reference to external source of time keeping [51].

Conjunction
Representation of a temporal process t 1 t 2 t 3 t 4 Time Figure 6: Graphical illustration of representation of a temporal event.Events E i occur in temporal sequence.A colored bar shows the limits of correlation in relative time space for respective events; the range in green represents positive correlation, while in blue the negative correlation.The green ranges are marked with t i that represent relative times with respect to the neighboring events.Conjunction of such E i (t i ) is represented by a bar below the dashed line.This bar expresses the whole episode, a specific conjunction of events at their respective relative times.
Systems that evolve with time or with reproducible generations under certain selection pressure must possess physical structure and specific function of action appropriate for the causal function in the environment as per the demands of selection.Such a system may have broadly three subsystems, sensing (observing), correlating + inference drawing, and action execution subsystems, even if not neatly divided with well defined boundaries or interfaces, in addition to the subsystem that represents the evolved biases (goals).This can then evolve into a formalized and specialized information processing system with ability to observe and represent the structure and function of the holding body in congruence with the causal function in the environment to select action.This may significantly improve sustenance [52].As noted earlier, the selection of action may evolve to optimally satisfy semantics of certain preferential biases.
A system capable of visual and tactile observation of its own physical extents (limbs of the holding body) in constant structural relation within limits of variation may construct a representation of the structure in hierarchy as suggested above (see Neuropsychologia, vol.48, issue.3,2010).Similarly, the constancy of functional relations, such as relative movements of limbs and their causal consequence, allows the representation of structure of functional relations among limbs.As noted above, the components and their inter-relations are integrated at each step in hierarchy extending to the multi-modal representation of a unified descriptor, U, as a class of all representable specific physical structure and function at the lower levels.Similarly, the objects not bearing a constant relation (i.e., not bound) to the unified object U may get classified in contrast to the class of objects associated with U.This is a class of external objects, E, in the context.In fact, for the integration of action and its effect, U and E may constitute a domain of all observable objects, O. Similarly, the semantics of temporal dynamics of motor functions bound to the unified object U having a causal effect in the context O form a class, say A. It is apparent that A is a class of actions, and it may connect where actions are relatable.Referable relations of correlation among U, O, A, and the changes C in the context O are representable as causal relations among U, O, A, and C as shown in Eqn.11 (context Eqn.7).Actions are representable first in the system as intended actions before translating to motor functions.Ability to represent the temporal dynamics may easily extend to intended actions with continued modifications.
R U OA expresses a causal relation that maps instances of states of U and O to the instances of intended action A. Similarly, R ref −U OA is a referential mapping that shows how the relation R U OA is referably represented as per Eqn.5.R U OAC expresses a causal relation that maps a combination of the three classes to the class of changes C in the context O.We may ask, "What does a referable disjunction of instances (states) of the unified object U in conjunction with the instances of the class O as causal precursor to the instances of class A in turn resulting in the instances of change C in O may semantically correspond to?"One may recall that the perspective of observed objects is always centered at the constancy of unified object U as shown in Fig. 5.It is apparent that the causal and contextual distinctions among the classes semantically relate them in different contexts.For instance, instances of class U may relate or connect where the semantics of an observer and / or an actor is relevant, instances of O where the observed class is in context, and instances of A where the actions are relatable.Moreover, top-down functional relations (specification) from higher level contexts [20] fixate the semantics of an observer and actor on U. The disjunction of instances in different classes forms their respective class descriptors, labeled here as U for observer, O for observed, A for action, and C for consequence, which may relate as referable elements in higher levels of semantic structure.
At this stage, we note that a system based on the organization discussed above with network of agents in modular hierarchy bears mechanisms to model and construct referable representation of arbitrary objects in relation to the object U, and their structural and functional inter-relations as well as causal relation between actions associated with U and their consequence.Function of such a system satisfies first order definition of consciousness.All objects of relevance for action, including the causal relations in the environment and between action and consequence are mapped to the object U. A component of U refers to the structure and function of the system itself at a level of abstraction that semantically qualifies the system as an observer and actor of action.Yet, the qualification does not include the observer (knower) of being an observer.That is, the semantics of observer-observed relation is not yet referably represented in the system and mapped to U having a functional (causal) role in action as shown in the next subsection.Such a system can make selection of actions towards certain goals without the knowledge of being a selector, or an actor, or the possessor of goals.Such a system may even sequence the actions suitable for stepwise approach without the knowledge of being a planner.Such a system may evade processes that are in opposition to the embedded goals -e.g., evading approaching objects with suitable movements taking into account the limits of its physical structure and function, without the knowledge of being a controller.Such a system is capable of learning and acquiring knowledge in each of the domains noted above without the knowledge of being a learner.Indeed, it differs from a system like thermostat in many ways that needs no elaboration here.Such a system also differs from unicellular organisms at least in one respect.Unicellular organisms do not have states that represent the semantics of its own structure and function unified into one abstract notion, semantics of its relation with external systems as being embedded in the environment, semantics of a cause-effect relation between action and consequence positing it as an observer, actor, or selector of action, even though behaviorally, and from a third person perspective within limited contexts, there may not be a discernible qualitative difference.Now, given the nature of evolution under selection pressure, it is reasonable to expect that the structured biases and goals and abilities of action may evolve in line with the sustenance of represented unified object.One of the purposes such goals may serve is that the action pathways may be selected based on the context of the system (organism) while the goals evolve at evolutionary time scales (of species).Moreover, in order for dynamic development of action pathways, goals must be referable or observable.

Representing self referential semantics of actor, observer, and controller
In a way it is easy to infer that the mechanisms used so far to construct a system that performs actions based on observed context including the unified system and evolved goals extends in scope via yet higher level organization to include the actor and observer functions of the unified system as part of the observed context itself to generate action.That is, at the next higher level of abstraction an agency emerges, whose components include the causal functions of the observing, acting, and controlling self in relation with the environment and the goals; the causal functions include actions and their outcomes.In short, R U OA and R U OAC in Eqn.11 form parts of observed dynamics, which in turn form the causal factors for superseding action.We refer to this agency as r-self and examine how it satisfies the second order definition of a self aware system.
A clarification is needed here before proceeding.Commonly, we refer to a conscious agent as a subject in the act of experiencing or as an experiencer.In the text below the agent is referred to as an object of representation.Subject matter of this article is to deal with the semantics as objects of discussion; therefore, it may lead to a confusion whether a term is used to convey the linguistic meaning to a reader, or to refer to the object represented by a state of the system.Therefore, a method is devised to indicate the correct identification of the meaning of a term where there is a possibility of a confusion.A prefix, 'r-' is used to designate the terms that refer to the represented objects; 'r-' stands for 'representation of '.
Here, we trace a path to construct semantics of self that includes being an observer of self, effector (actor) of change, comparator of predicted outcome of intended action with the goals, hence, selector or controller of action.It is by no means an assertion that the mechanism presented here is in anyway unique for creating a self observing system, for the mechanism is generic to support multitude of pathways to create the semantics of r-self; at best, it constitutes an instance of such a possibility.
In line with the Eqn.11, we consider causal, referential, and compositional relations (mappings) that encapsulate emergence of r-self.
The above expressions are indicative or suggestive of the steps in mapping of classes of objects.R U OAC is a mapping from the three classes, U, O, A, to the class of C, representing a causal relation.This leads to a referential mapping R ref −U OAC to the relation R U OAC that creates a reference to the semantics of U in the observed context O as a precursor to action A, which in turn forms a causal precursor to change C as stated above.A compositional mapping R comp−self is constituted of U and the relational mapping R U OAC , that includes U in the reference to R U OAC , and maps to the second order definition of R self or r-self, a self observing self.As we noted above, right hand side of a map forms a referable object.This r-self may be further enriched or related to other functions of self as discussed below.Thus, there exists a path to represent 'r-self r-observing r-objects', where the r-objects include the composite of U and R U OAC or the observing and acting unified system.In a re-entrant system, such a referable representation of self may even be recursive representing an r-self n that observes an observing and acting r-self n−1 for as long as the layered observation of r-self remains relevant in the evolving context.Any expression based on this observation refers to r-self n−1 as an observing and acting agency overriding the previous r-selves within a continued episode.That is, a report may include only a referable observed relation involving r-self in the previous iteration.
Similarly, when the class of action is conjugated with the observer class, the composite class may connect in contexts where the act of observing or making an observation is relevant.Similarly, the observer class may be conjugated with any sub-classes if relevant, for instance, with visual observation, a seer; with aural sounds, a listener; with tactile senses, a touch / pressure / heat sensing agent; with thought chains, a thinker, and so on.Each of these classes are referably representable.We ask, "What may the class of disjunction of a seer, a listener, a touch sensor, etc., of objects semantically correspond to?"It is apparent that such an emergent class as a referable object may relate well in contexts where the generic semantics of an experiencer, or the self in the act of experiencing serves as an element.That is, mapping of such sub-classes of semantics of agency to the object r-self serves as qualifier sub-classes of r-self as a unified agency.It is apparent that the process of constructing an experiencer sub-class is not limited only to the three domains of senses, but applies to all that can be classified under classes of observed or sensed, such as goals, wants, thoughts, actions to match goals, or any other referable objects.It is instructive to label such classes of agency in linguistic terms to understand the variety of abstract qualifiers we use to qualify ourselves.The steps suggested above may get realized in the following manner.From repeated observations of causal correlation between elemental actions and their internal and external consequences, a map for this relation may emerge under population coding scheme, as discussed above, for its relevancy [53].It is possible then that the specifics of an action and its result in the observed context is communicated to modules that relate to r-self before it is acted upon (see maps R ref −U OAC , R comp−self , and R pred in Eqn.12).With respect to r-self the referable class of such actions bears a semantics of intended actions, which when applied to the current context O yields a new context O new .It then becomes possible to relate the result of the intended action, O new , to expected outcomes or r-wants (map R dif f ).The choices of action become competitively selectable based on the alignment of O dif f with the optimal realization of the active r-wants by the same process of competitive dominance of coherence.The classes of intended actions, their outcomes, and comparator relations are referably representable via mapping for their relevance in selection of action.Again, a conjunction of r-actor with context specific selection of action creates rselector class, another sub-class of r-self.Moreover, since the system described here has the ability to select an action and predict the consequence, it can be applied in a series of steps with evolving outcomes to represent the temporal process as a whole and to evaluate the comparator function at each step with r-wants.Furthermore, by tracing such paths repeatedly in different contexts, a store of useful elemental paths may emerge for different classes of elemental contexts in different modules, which may then be competitively traced in parallel discovering paths for a structured problem, corresponding to a plan.A few of them may even be acted upon simultaneously as we observe from our behavior.Parallel evaluation does not necessarily relate to r-self at each step, remaining subliminal.Moreover, trial and error and observing other systems carrying out a task at conscious level may help organize a sequence of action towards specific goals.
The mechanism places no limits on how many competing considerations may participate with differing relative weights of satisfaction of goals in the selection of an action; limit arises from sharing of resources.All of these processes form elements of observed context that map to r-self creating referable semantics of selector of actions, controller, or decision maker.Moreover, if a system develops a representation of a pseudo-random selection of action for it may satisfy certain goals, then that may also constitute one of the competing r-wants in determining the action.Therefore, the 'freedom of will' [54,55] is a representation of abstraction of observed phenomena of evaluation of selection based on the consequence of r-choices satisfying r-wants related to r-self.Once this abstraction of freedom of selection is referably represented, it can also become one of the overriding r-wants in selection.'Freedom of selection' manifests less at the moment of activation (evaluation) of wants against options, but more in the formation of such competing wants.The wants may undergo a non-linear evolution via extended context of their realization, or lack of it, in accordance with the requirements of more basic emotions within evolved limitation of diminishing returns and their inherent incompatibility to avoid run-away processes.The fuzzy terms 'less' and 'more' are used to take into account a limit of randomness in neural function and non-linear dynamic evolution.
It may be noted that if specific selection is a deterministic outcome of prior state at all times then 'free will' is a notional representation, but if it does not depend on the prior state at all, then it is random.Due to an inherent limit in randomness, an outcome of limited indeterminism [1], and non-linear evolution of wants, the reality is in between the two making the 'freedom of selection' a relevant semantic value.
In an extended temporal event, r-wants causally affect the decisions and actions towards specific rgoals as observed by r-self over the duration.But to report on a decision to act at a sharply defined moment (say, on observation of a stimulus), referable memory of the selection must form, then the report constructed referring to the selection as in the present resulting in a short time lag between the two.The point is that the context based decision to act by the agency of r-self must be related to or mapped to the next iteration (level) of r-self as having been observed to have a causal effect of the conscious act.In fact, a system can report an event only when a memory is formed, where the tense of the report is expressed by the temporal semantic value represented, not what an external device can determine (see [56,57]).Soon after, when the time lapse is represented, the report may refer to the past.A real time system developer knows well, even while reading, evaluating, and recording the time of an event (say, GPS signal), the time is elapsing which must be modeled.Even in the brain, a perception (report) of simultaneity is created between visual and aural receptions of an event tens of milliseconds apart.
In summary, we may note that any such endeavor that aims to describe the minimalist central mechanism of emergence of semantics of r-self as an r-observer, r-actor, r-experiencer, and r-controller can not be particular to a specific real system; however, the mechanics presented here are observable in such systems.The human brain has evolved extremely rich set of semantic values that relate to the identity of r-self, e.g., specifics of senses, thoughts, memories, relations, knowledge, memes, values, desires, abilities, and so on, all by the same mechanics presented here.This work does not attempt to identify human brain areas that may represent different classes of objects discussed here.Thus, it is concluded that the semantics of 'r-self r-experiencing r-object', or 'r-self r-controlling raction', are entirely constructible with any contextually required level of specification, structure, and abstraction.Here, r-experience is the semantic value that qualifies what the experience is to the r-self, or r-self 's relation to r-object as a part of R U OAC .For instance, r-experience may include the semantics of reference to r-object, or action by r-self upon r-object, and so on.To emphasize, when one refers to oneself as the experiencer subject in a thought, that subject is the object r-self in the semantic representation of the thought.The abstraction of consciousness then becomes a referable semantics of r-self 's relation R with r-objects having a causal effect as in the definition proposed; consciousness is a perspective from the viewpoint of an observer r-self at subsequent iteration in a re-entrant processing as shown in Eqn.12.This further provides a robust rationality as to why consciousness ought to be subjective.It is of particular importance to note that if an object is represented in a system but does not relate to the r-self, then the r-object does not form a part of the relatable conscious event.That is, an experience is necessarily relative to an experiencing agency.
In general, the objects of representation have a life time for as long as the states of agents are preserved; the transient nature of active states of neurons makes the objects of experience transient too.However, the re-entrant activation in a loop preserves the continued semantics of objects, where active state of an agent represents the continued process or the relevant historical perspective.Since the idea of controlling action and temporal processing of causally connected events is to sustain the experience in the present even during the recalls of memories, the objects of experience ought to be transient.Moreover, the function of consciousness is inextricably linked with the function of action, internal (as generator of thought chain) or external (brain, body, environment), which can be continuously generated even for no action, transience is a norm.

The control of action, central to the emergence of consciousness
First, the consciousness requires the representation of semantic structure that includes the self and its relation with the objects.As we noted, it requires deeper levels of abstraction from the primitive sensory information.Such an organized system is unlikely to come into existence by random processes alone without the mechanism of selection requiring evolution of modeling and acting subsystems to meet the varying requirements.
The complexity of organization of systems evolving over generations or over the lifetimes of their function with the ability to adapt to the dynamical environmental contexts for their sustenance is markedly different from those that arise from a large number of elemental parts forming a complex pattern, function, and structure under certain rules or relations [58,59,60].While the evolved organization of the former acquires functions to meet certain specific purposes even in dynamically changing contexts including those that have never been encountered before, the latter does not.While the former may not emerge spontaneously as the paths of evolution is based on variable external selection, the latter may.Therefore, the former must possess a capacity to self reorganize in order to model (learn) the dynamically evolving context to control or select appropriate action to meet the evolved goals and to enhance the sustenance.Different subsystems that sustain the internal environment in a relatively stable (constant) state within limits, such as homeostasis, may evolve to be autonomous, but the same is not true for external contexts, which can not be comprehensively controlled.Therefore, a highly evolved system like human brain must be able to select and follow a coherent action avoiding different subsystems to function at cross purposes detrimental to the very sustenance of the system as a whole [61].Creation of a singular abstract notion of self enables an evolutionary process to support function and organization with single objective to optimize, enhance, and preserve the unified r-self that includes critical features of body and mind, rather than conflicting multiples.Even for multi-headed systems, a protocol of messaging must exist to decide precedence, which effectively amounts to a unified system.The corpus callosum in human brain also seems to perform the same function.Hence, an organism's sustenance may critically depend on a centralized system of decision making with overriding control.Such a need leads to a representation of a unified self, to which all wants, desires, and contextual details are mapped for the evaluation and selection of a suitable course of action for the sustenance of self.In addition, with the abilities to follow different action pathways internally, as part of a selection of most dominant coherence, satisfying optimally the r-wants associated with the r-self, the abstraction of 'self as a controller of action' emerges.In a modular system, the components of r-self are distributed among different functional spaces.It is indeed likely that actions, even in minimal (first order) consciousness, may arise from any of these components, and only in cases requiring wider scope of relations, comparisons, analysis, planning, thoughts, etc., that the higher level self referential r-self acts like a controller.If the r-self is the sole agency in control of the system for action, then only those r-objects that relate to the unified r-self may constitute parts of reportable or actionable conscious event.When a conscious system refers to itself in a physical expression (verbal or otherwise), only the r-self in control of the physical system can do that.It may be noted that the active state of a neuron intrinsically may correlate with extended information as per the law rather than just the relation of self with the objects, but they do not form parts of conscious experience.The conjunction of a population restricts the information to the semantic value of relation the r-self has with r-objects, which map to a population in another module for action.Therefore, in order for the semantics of specific relation of r-self to have a definite causal influence a single neuron can rarely be the cause of an action.
In fact, a system may even construct representations of other agents, their functional relation with objects, their goals, their actions, and outcomes, which may or may not relate to r-self in a given moment to form a part of a conscious event.Objective functions of r-self may also form association with other agents (recall mirror neurons [62,63]), but such r-agents are rarely mapped (with probable exceptions such as hypnosis) to bear r-controller element of the unified system.Thus, functionally represented semantics of a 'unified system as an observer and controller of body, action, and thoughts' serves as an all encompassing conscious agency in all references to the self.

Interpretation and conclusion
For the first time a framework for the emergence of consciousness is constructed with semantics of information of causal correlation of state of physical systems leaving no insurmountable conceptual gaps and voids.A reference to the semantics of 'unified system' functions as an abstract identity for the self in a context.This does not lead to infinite recursion, for a reference to the product of disjunction is not reducible to an instance in every context, whereas a bottom-up construct relates the self in a limited domain.Given the quantitative methods of information processing and construction of structured and abstract semantics, dynamically evolving artificial systems are constructible without limitation.

The critical role of language
The role of language in the emergence of consciousness is deliberately left out of consideration while dealing with the mechanics of emergence of self and its relation with the rest, for language also emerges in the same process.That is, language does not form the basis of emergence of consciousness, even though language plays a critical role in advancing the abilities to construct higher order abstract semantics in general and self awareness in particular [64].
As we noted above, a semantic value becomes accessible when active states represent the value in a context where it relates well and stays relevant.That is, beyond a degree of limited fluctuations, there is no mechanism of accessing a semantic value without the presence of relevant context.But we also noted that the active state of groups of agents in a module represent specific values, which may arbitrarily connect to other modules that are coherently active based on relevance or proximity in any parametric space forming significant correlations (e.g., Gestalt principles).A modular structure covering the space of verbal or visual symbolic expressions may evolve connections with arbitrary modules in the system bearing repeatable association.That is, it is possible to associate or relate arbitrary semantic spaces by virtue of their co-activation or by any other mechanisms that the mapping system uses to create connections.Therefore, specific graphic symbols (graphemes) and the aural or visual forms / terms may be arbitrarily connected to referable semantic values if such terms and forms are co-activated during accesses to such values.In fact, such association of terms with semantics is natural to expect if all semantics / objects are constructed of relations, where relations can be arbitrarily set.As discussed in Section.8.4 of [1], linguistic terms and forms are constructible along with their syntactical schema with pre-assigned semantics, where an expression with such terms is evaluated in terms of disjunction and conjunction of semantics that the terms and forms refer to.
Armed with such association of formal terms and expressions with referable semantics, it becomes possible to connect terms with r-self, r-experience, r-action, r-causation, r-object along with their functional variations to be able to express, 'I see the blue sky'.Commonality of functional variations in robjects enables common linguistic variations (syntactical forms) to emerge in respective terms for objects (nouns), actions (verbs), relations (prepositions), qualifications (adjectives), etc.Moreover, the terms having definite context dependent specific relations with other terms, when used within a linguistic structure, limit the expressed semantics with far greater specificity and concreteness than the fuzzy semantics of active relations with multitude of wide ranged correlations.Furthermore, by mere expression of terms in certain order or proximity as per the semantics of syntactical forms / structure, it becomes possible to combine or relate semantic values in ways that have never been related / mapped naturally in the contexts encountered by a system.For this reason, the learning and communicating potentials become unlimited.For instance, the term 'right angle' may have been initially associated with a relation between two lines, but now linguistically they can be used to relate two vectors or planes, further helping to create semantics of orthogonality.If one organism of a species with common brain structure expresses certain semantic structure with such terms, then the referenced structure readily gets communicated to other organisms within the limits of variations in semantics associated with the terms.Such expressions may even be recorded in a medium and re-accessed in arbitrary forms providing continuity of concepts to future generations.For systems without such modules for symbolic mapping to represent higher level abstract semantics, it must evolve modules that represent the specific relations expressing the semantics.
Given the mechanism of integration at each step in hierarchy and back propagation to the specifics in respective modules, a new concept expressing a relation may get represented by the connections within the modular hierarchy of language rather than among the r-objects in different modules, such that an activation of relation among the terms within the linguistic structure activates the referenced semantics in different modules.While most linguistic expressions are instances of this phenomenon, consider an extreme example, "X hammered her idea into Y's head!".We may have specific semantic representation of object hammer, the repeated action of hammering, and the class of physical objects that are usual targets of the action.In this expression, a non-physical class object (idea) substitutes a class of physical targets, and head substitutes the brain which in turn is a substitute for mind, yet we form a rather concrete semantics of the expression on its first encounter.A language provides a means to substitute objects with other objects where the homomorphism (analogy) between their respective structure or function bears a relevance in the context.
Once a term, such as 'consciousness' is created to refer to the disjunction of instances of r-self 's relation with r-objects, then such an abstract semantics may further relate with objects in relevant contexts.For example, expressions like, 'What is consciousness?', 'How am I conscious?',and, 'There is a hard problem of consciousness', become constructible.That is, with the advent and evolution of language, the term gets much sharper meaning and richness with variety of connections due to the definite relations in which it can be conjugated with other semantics.It is apparent then that the diversity and specificity of sense and awareness of consciousness may have evolved with the evolution of language [64].

Relative nature of representation
One of the important properties of such a representational system is that descriptions of all objects are only relational including even those that are directly acquired from the external worlds, such as pixels, temporal variations of vibrations, pressure profiles in pixelized form etc. Consider for example, a two dimensional pixelized array of sensory organ, as a retina.A specific configuration of on-or off-center [65] contrast relative regions (points) forming a line segment may be represented by a dynamical system of representation based on its statistical relevance.A point to note is that given a set of objects what relation gets represented depends on its relevance; mapping system shown in Fig. 5 is independent of any particular relation.
Similarly, if the two dimensional pixelized array is constituted of three types of light sensors, sensitive to different ranges of wavelengths, similar to the cone cells in the retina, then any arbitrary relation among these can be represented based on their relevance to the system's function.Since surfaces of physical objects exhibit constancy in their light reflectivity or transmission properties, it allows an observing system to represent such a relation.Moreover lighting conditions, shades, depth or distance, motion, etc., do not change the reflectivity, the system would be able to construct a disjunctive mapping to represent constancy of reflectivity of a surface under all variations observed.Naturally, such a mapping requires inter-dependent modules to represent objects (relations) in each of these domains.For evolving systems under selection pressure, the specific relations of contrast and similarities relevant for behavior are most likely relations to find representation.Since the area of space is integral to the relation of reflectivity with the surrounding, it forms a structured relation as it further relates to r-self, hence, an area of space is an inseparable component of color perception.Moreover, since lighting conditions alter the measures of light in different wavelengths reaching the retina, the relation is not specific to particular wavelengths.In fact, different combinations of wavelengths in varying context map to the same class object, hence creating the same percept.Here, we noted the semantics of color perception of surfaces that relate to r-self, such as the blueness of sky, not the semantics of blue.The same perception may have an association with a number of objects in different contexts, such as blue sky, blue wall, blue paper, blue reflection, etc.A referable abstract semantics may emerge from a disjunctive relation among such descriptions to label the reference as blue.In other words, semantic relation of blueness is primary for the abstraction of blue.It is fallacious to trust that blue is an inherent property of physical objects in nature and then wonder how blueness may arise.It forms a conceptual error to look for manifestation of blueness in the physical world other than in relation to r-self in the domain of representation.Blue as a label serves as an abstract qualifier to an object, but it does not cause a perception of blueness unless it is instantiated on a spatial extent of the object in a top-down activation, similar to the way a specific right angle may get instantiated in context of a reference to 'right angle'.Since all descriptions are built from relations, even the blueness of sky, it is entirely possible to have the same vivid experience, even without the sky if the retinal neurons, or the LGN neurons, or even the cortical neurons in the visual system of the brain are activated in specific pattern.All the blueness and depth perception in relation to r-self would reappear.A subjective dream event constitutes sufficient evidence of that.A sense perception in a phantom limb can only be a semantic attribution.That is, what the r-self is r-conscious of is not the quality of reality of the external world, but rather the relation constructed by the organization of the neural connectivity and the relation among the activation pattern of the neurons in that organization.The physical systems like sky and other objects bearing constancy in their reflectivity or transmission simply enable the neural system to self-organize to represent the relation.The sensory neurons serve to keep the relations in conformance with the behaviorally useful relations in the external world.When a system predicts and takes appropriate action, the system observes conformed results, which is used to reinforce the mechanism of prediction [66,67,68].

Comparison with a bat's system
Projection network of modules determine what structure and abstraction the recipient modules may represent via conjunction and disjunction.Given the stark difference between the sensory systems and the projection network of modules in a bat's brain and the human brain, the abstractions of irreducible emergent semantics between the systems are not comparable, which creates a non-bridgeable gap in the subjective r-experiences of the r-selves of the two systems.The represented self in the human brain has no mechanism to relate with the abstractions represented in a bat's brain [69].This provides a natural explanation to incompatibility of subjective experiences represented by two species even though the mechanism of forming such experiences is objectively common.That is, the mechanism of emergence of consciousness is such that it limits a conscious agency to a set of specific abstractions, which undergo continuous change with every experience.A subjective sense of empathy with other humans and commonality of reporting the same are only possible due to near identical modular projections in hierarchy resulting in very closely related abstraction of semantics of objects and terms.This inference of continuous proximity relation stands against the idea of Inverted Spectrum [70].

Attention and its role in differentiated action
The mechanics of top-down mapping at each step in hierarchy that provides more global context to each module allowing them to select more relevant processing suggests the mechanism of attention rather naturally.At any given moment, a large number of elemental processing takes place within the physical brain, but the ones that integrate through hierarchy and relate with the r-self having stronger relevance in the context are back referable via top-down mapping [71,72].As shown in Eqn.3 and in Fig. 4, the same expression serves both ways in construction of semantic values.Therefore, formation of a high level context relating to r-self in conjunction with the specific r-goals or r-wants of the moment enhances the relevance of certain r-objects distributed over the object spaces.The top-down propagation of relevance strengthens the competitive edge for such r-objects at respective modules enabling enhanced specification via greater synchronization, larger conjunction of elements, and recurrent looping.This enhanced specification integrates bottom-up through hierarchy to form a part of a new context relating to r-self enabling much sharper specification for further processing or action.This top-down and bottomup process of enhancement of specification for certain r-objects functionally defines attention.Unless the specification relates back to r-self it could not form a part of consciousness.Second, in line with the emergence of semantics of actor element, the causal dependence of enhancement of r-objects on r-wants associated with r-self creates the semantics of r-self being the director of attention.Third, the same topdown process of referencing holds the potential to create mental imagery [73] with vivid low level specifics when bottom-up processes from sensory modules are absent or overridden.
There is yet another primary function of mental attention that requires our attention.At top level modules that represent integrated classes of r-self, each agent (neuron) projecting to motor areas represents highly integrated context, which does not provide differentiated detail for specific action.Therefore, it is expected that the attended r-objects in different modules must also map to the motor areas to make object specific differentiated details available for precision control of action in accord with the attended r-goals at high level integration.This is empirically verifiable.

Active vs. passive representation of functional objects
The active states of neurons have real time direct causal consequence in the network, therefore, it constitutes an instance of active representation.Memories form via active connections and their strengths forming associative mapping with related objects.When reactivated, the associative relations to objects turn active functionally serving as memory recall.That is, all three elements of processing, namely, the object specification, the memory, and the action as per the function of the object are inbuilt into the neural process.This is unlike von Neumann architecture, where an independent processor fetches instructions and coded memories from passive addressable storage and carries out the instructed function without any regard to the semantics of the coded information -an instance of passive processing.This necessarily requires interpretation of the resultant states / values.The neural activation pattern carries out the function of the objects within the domain of representation via causal correlation.It is possible because the function of objects is specifiable by a uniform expression in terms of conjunction and disjunction operators, which is also the mechanism how the neurons carry out processing via coherent activation.Therefore, objects with arbitrary function may be created in the domain of representation without any correspondence in the physical world.Moreover, the representation can be dynamic, because a neural state only represents the semantics expressed by the said expression on the values represented by the active presynaptic neurons.Furthermore, the connectivity with other neurons and their weights may change gradually with time changing the semantic space represented without resetting the system.Such a system can have a dynamic control on the external world.

The power of associative recall of contextual elements
One of the most powerful consequences of associative recall by active agents in a population coded system is that a related context is made available that helps comprehend the current observation or interaction with the environment.At any given moment, a system observes a limited set of elements in a context, but the ability to access elementally associated information at all levels in hierarchy [74] to carry out competitive coherence over all accessed space creates a suitable convergence of applicable context.For instance, in the ionization chamber experiment, as shown in Fig. 3 of [1], the current generated by the coherent convergence of electrons on the anode is observed by the experimenter.But the recall of the spatial isolation of the chamber, the electric field, and the models of ejection of electrons from argon atoms by a heavy ion process, enables the associative brain processes to immediately relate the measure of current above threshold to a heavy ion process.Without such an associative recall to a list of relations, a physical system must observe specific causal correlations with each of these semantics at once to form a conjunctive relation among them to correlate with the heavy ion process.An organism's survival and performance critically depend on the power of such associative recalls.In fact associative mapping based on limited observation of relations is also the cause of so called intuition in our thoughts [1].That is, the intuitions are not a product of formal logic.The leaps in interpretations are also the cause of most perceptual illusions [75,76].

Consciousness vis-a-vis causal powers
This work shows how causal function of physical substrate and experiential content are inextricably connected.It offers an explanation to why and how an experiential state have physical consequence (also see [77,78,79,80,70]).As part of the integrated semantics, r-self relates to r-objects as an agency with motive and causal power to effect change.The semantics of experience attributed to r-self is a part of causal correlation of a coherent state of a group of neurons resulting from processing organized in modular hierarchy.So, does the represented semantics of willfulness to act have a causal power?Naturally so, as it requires the group of neurons to functionally connect in specific relational structure to effect a definite coherent state among the recipient neurons in order to correlate with the causal consequence of the function of willfulness to act, as we also observe in our thoughts.Without the causal correlation with willfulness to act, there cannot exist the specific coherence of states in exactly the same context to have the same causal effect.In other words, a representation of semantics emerging from causal relations can not be separated from its causal function.Any statement to the contrary is in logical and natural contradiction to existential reality.Therefore, every semantic value represented in a system, conscious (relating to r-self) or otherwise, have causal function; some may even have a function to negate others.
Information of causal correlation, has an existential reality in natural universe, but information is not directly observable with a probe.Moreover, since information arises from the constancy of causal function in nature, there is no existential reality of information that is not a part of causal correlate of a physical state.Every bit of information that we construe, including the ones that we attribute to other systems as having, such as a DNA strand, are constructed in the brain based on such causal correlation as presented in part (ii) of the law.Due to the function of disjunction in causal correlation, the objects referred to by information may not have an external existential reality, but the information itself remains undeniable.Information serves as a medium to all knowability, whereas information itself does not require any medium, i.e., this is the only reality of nature that we have direct access to in a definite sense, all other descriptions of natural phenomena remain subject to interpretation, hence subject to change with time!With the advancement of knowledge, notions of charge, mass, and fields may transition into different objective models, but the information of correlation, hence the represented perceptions of the moment remain unmodifiable, non-revisitable, even though memories can be modified.As also asserted in [1], time reversal has no basis in reality.The reality of perception is in direct contrast to what several authors call illusion [81,82,83,52].Whether it is an illusion about the mind or about external world [83], either way it is constructed of semantic values.If one takes illusion to mean a false perception, then perception is still there.Besides, (nearly) all objects of perception are non-physical.Consider a specific book in the field of view that one has a perception about.A range of values in nearly all apparent features of the book, such as shape, size, color, texture, relative dynamics, etc., are non differentiable.Hence, the perception encompasses a class of indistinguishable variations, which is not the reality of the given book.Therefore, one's perception of the specific book is an illusion.In fact, this is coded in the statement of the law itself, which expresses the causal correlate in terms of a disjunction of conjunctions of states.
Following the natural causal relations, that which needs no interpretation, if an autonomously evolved system, such as a human, expresses a reference to itself, it must certainly have a causal representation of the self and the objects that it relates to.A reference to causally represented semantics of self unambiguously establishes the existential reality of the referrer self -'I think, therefore I am', has a robust basis, causally so well founded that even a well represented assertion, 'I do not exist', cannot falsify the existence.Similarly, the represented semantics of the referrer as the referent establishes self aware consciousness of the second order.This conclusion stands against the very idea of zombiehood [84].
The mechanics presented here deviates from established processing schemes where a resultant state at each step is arrived at by a conjunctive mapping (think of a one-to-one function), which continues to bear dependence on the coded objects.The result may only be interpreted by an external agent with the scheme of coding and specific processing (mapping) as indicated by John Searle [85,86], who holds that any processing based on syntactical rules cannot ever capture the meaning (semantic values) necessary for a conscious system.But if the causal function in the rules allows for disjunction of arbitrary conjunctions, where specific conjunctions hold instances of a relation covering the space, then the disjunction represents the relation as a class object without a dependence on the underlying objects as discussed in Section.3.Meaning still emerges.Arbitrarily assigned values are absolutes, require interpretation, a frame of reference, but relations do not.Searle's arguments fail to encompass the mechanism of emergence.An artificial system too may self organize, as detailed above, under a devised causal scheme and arbitrarily set biases (goals); the representation of self may emerge from the observations of self as an actor, as an observer (experiencer), and as a controller to have causal function within the realm of devised scheme.But if the system is required to have a function in the natural world of time, space, and other causal functions, then the emerging r-self is also bounded by the same constraints of the natural world.Since all causal functions are expressible in terms of conjunction and disjunction and organized in population coded modular hierarchy, there is no particular dependence on biological systems (in contrast to [87]).

Blueness of sky and the light of consciousness
We consider here a few common fallacies to compare and contrast with the emergence of consciousness from causal information (ECCI).In our articulations, we often tend to place the experiencing entity and the objects experienced into two distinct categories.The experiencing self is taken as putative and we seek to discover the reality of qualitative or 'phenomenal' experience in nature, either in the form of qualia or corporal senses, which immediately runs into a problem with the existing scientific knowledge and the closure of causal function.One tends to hypothesize new laws that directly or indirectly include such senses.ECCI stands in contrast to such ideas by virtue of the intrinsic causal correlation of a state with semantic values and the quantitative foundation to evaluate and build semantic structure represented by active state of neurons bridging the explanatory gap [88].It also provides an objective causal basis to subjective consciousness enabling the implementation of such systems.
Color perception such as blueness is often cited [13] as a qualitative character to emphasize category difference from objective reality.It is noted above that the character of blueness is an abstract semantics in relation to 'r-self as observer' emerging via a disjunction of relations, such as contrast relations in shading, lighting, reflectance or transmission of light in different wavelengths etc., spread over an area of space, in addition to functional relations with other objects.It is not reducible to a specific conjunction of physically manifestable objects except the part of space.The question is, "How should this abstract semantic value relate to observer r-self such that a response based on this value conforms to external context?"First, it is no different than asking the question, "How should an abstract notion of 'right angle' feel?"Second, via top-down mapping the structure of contrast relations spread over an area is referable and paid attention to.Third, in different contexts, experiences of blueness may get associated with certain abstractions such as likes and dislikes, or states of emotion; therefore, the perception of blueness includes functional relation with such abstract objects and states.Fourth, the paradigm of population coding readily suggests why different contrast relations can be judged as close or distant with arbitrary precision.Fifth, it is possible to construct expressions within the framework of a language that requires a response in terms that is not satisfiable (see Russell Paradox [89]).For example, 'what it is like to be experiencing blue?', formed as a query, can be satisfied either by accepting its irreducibility without objectivity or by providing a communicable reductive description enabling one to evaluate how it should or should not feel, either way it excludes an objective account of subjectivity as shown here.Only for the reason of creating an instance of a right angle in terms of two visible specific lines, one develops a sense of satisfaction as if one has a description to know how the relation feels.When it comes to communicating the same, one merely draws multiple instances of right angle in relation to acute and obtuse angles, and relies on the ability of the observer to form a referable irreducible semantics of right angle via disjunction.But when the level of abstraction becomes deep and multi-dimensional, where components themselves are constituted of abstract elements without any physically manifestable instances, it creates a gap in communication.The question is not why the blueness feels or relates to r-self the way it does, the right way to express the reference to the relation the observer r-self has with the specific class of irreducible conjugation of conditions of lighting, reflectance, area of space, and abstract liking, is that we have come to refer to the relation as the 'feel of blue' or blueness.
Recognition of first person subjective experience as qualitatively different in category from third person informational data in physical sciences led some [84] to propose quale as primitive of subjective sensory datum.One asks [84] -why cannot the information processing be non conscious, or in dark and in silence?Though the question is metaphorical with respect to the light of consciousness, but it directly manifests into our perceptions of seeing light and hearing sounds.A short answer is that the information processing is indeed taking place in the 'darkness of neural senses', neurons and the brain neither sense nor are aware of the information, but the value represented by their states happens to express semantics of a 4.π steradian (sr) space extending in depth around the r-self, where the points, lines, curves, shapes and surfaces over 4.π sr bear specific mutual relations and with the r-self.Such descriptions may also include brightness, color, temporal dynamics etc.For a moving observer, the r-self is always posited at the point of observer, as shown in Fig. 5, enabling the semantics of perception of unification.The embedding of r-self in r-context bears a causal function, which in turn is represented by active states of neurons in a network resulting in action.Similarly, the information happens to express semantics of certain disturbance in temporally continuous signal space embedded in the same 4.π sr space around rself.That is, a structured information is represented by the neural state that expresses the semantics of an r-observer r-observing the r-lights and r-sounds and r-causing an r-action.In this representation, the integrated component, r-observer + r-actor, stands for a conscious agency.
In fact, extending the metaphor to physical domain it can be asserted that there is no light and sound in the space around, but the semantics represented by the neural state objectify a self and the illumination in a 3-D space, where the objects are constructed from physical function of electromagnetic and acoustic disturbances as reflected from the objects.Consider entering into an optically dark space (room), which has objects in space radiating and reflecting in microwaves or x-rays.That is, even for r-self bearing the 'light of consciousness', there is no light and sound in the environment if it is not represented and related to r-self.But by virtue of having the semantic representation of lights and sounds, the r-self may relate to them, where the structured semantics of this relation expresses the system being the seer of darkness and hearer of the silence.Such a representation does not require an actual space, objects, lights and sounds, only the specific relations in modular hierarchy, as is evident from the dream events, but the relations (models) are constructed from the interactions of sensory systems with the physical environment around.The way color is considered synthetic, so are the senses of space, time, and physical objects; they just happen to bear a degree of consistency in system's interaction with them as much as the color over an area does.
Alternative thought experiment to Mary's color vision [90]: Consider a person who has a fully developed color vision, but by some accident or disease she loses all color sensitive cone cells leaving only the rod cells intact, a variant of achromatopsia post brain development.In each of the visual experiments, she is unable to report color, but reports only the shades of gray similar to the way Knut Nordby reports [91].But the connections in the visual areas of color processing are intact.When asked, if she can see colors in her dreams, she may report affirmatively.Inheriting this cortical organization but without the cone cells in retina, Mary may know the feel of colors without ever observing them.

Who or what is a conscious agent?
If we ask this question on a conceptual level seeking to identify a physical system as a possessor of 'phenomenal qualities' of consciousness, we face an immediate difficulty.The difficulty arises from multiple perspectives.First, causal function in nature does not include reality of phenomenal quale or corporal senses.Second, even from the natural information processing point of view, a represented semantics does not entail any conscious perception.Instead, a part of the structured information arising from second order causal dependence carries the semantics of the self as the bearer of the characteristic qualities that we have come to associate with consciousness.That is, there is a reference to an object within the semantic structure, which includes a persistent dynamic model of the body as the bearer of the senses and the experiencer and controller of actions.The semantic structure entails a perspective that is always centered at this object (as in Fig. 5) forming an identity between the body, the experiences, the memories, and the control of action.
It implies that even the perception of color, taste, smell, pain, pleasure, and emotions, are constructed semantic values in relation to the constructed self having causal function as shown above.That is, the semantics of perceptions are inextricably bound to that of the perceiver.It may be noted that the question, "How is the computed semantics accompanied by a conscious sense?", creates a blind spot for thinkers from examining how the reality of structured semantics itself expresses the semantics of self as undergoing the semantics of senses.One must not lose sight of the facts that semantics arises from natural causal correlation, semantics captures the qualitative character as well, and the semantics of senses is a perspective from the semantics of self.Third, semantics arising from causal correlation is associated with a state of a system rather than with the system itself, and a system's state has a definite functional reality upon observation, for the qualities observed depends on what the observing system is sensitive to.Though the active state of a neuron is uniquely discrete, yet the information is not attributable to the neuron itself, for its function is limited to the time of activity.Every time a neuron loses its active state it loses its association with exclusive semantic value, yet we continue to relate the identity of the neuron as before.There is no surprise then that during sleep or anesthesia consciousness ceases, even though the system remains the same.Hence a physical system cannot be said to be conscious in a fundamental sense of the causal function.It is worthy of recall that as observed in phantom limb experiments [92,93], the semantics of senses are attributed even to the missing limbs or to the out of body images [94].Therefore, one may continue to express, "I am conscious", but the correctness of the expression lies in the understanding that this attribution to the 'self ' is a semantic value of correlation of a definite state of a group of neurons causally in control of action at the moment.The integrated identity among the unified system and the observer, actor, and the controller elements is observed as a datum leading to the abstraction of causal inference (Eqn.7) of ownership of the senses and consciousness by the unified system.Yet such unification is seen divided in pathological conditions, where the constructed self disowns parts or whole of the unified system [95].

The observables
Every mechanism, process, and feature discussed in the text towards ECCI construes a prediction, and where the correspondence is already observed in real systems, an explanation.Since this work deals with the fundamental basis of reality of information, and the hallmark of the brain function is information processing, it must set the basis to determine physiology and function of neurons and their organization.
By virtue of being intrinsic, the information of causal correlation of an observable state cannot be measured with a device, though the correlates of states of neurons can be observed; the real challenge lies in large number of neurons involved in population coding and in the dynamic change in their correlation profile.Three basic mechanisms, namely, 1. information processing via conjunction and disjunction, 2. reentrant coherence building to capture constancy of competitively dominant relations, and 3. population coding, function together to dynamically represent the context.Each of these can be empirically tested as sufficient quantitative specificity is presented here.A correlation may also be tested for negative range of semantics.Modular and hierarchical organization is now well established already.All neurons are capable of implementing the first mechanism, but the other two are a product of network function.For instance, if several objects in a field of view have the same rate of linear or angular displacement, the projection from active neurons representing the respective objects in motion will cause the build up of coherence among the recipient neurons via feedforward mechanism resulting in the binding of the objects via conjunction.Hence, the active coherence among the recipient neurons must correlate with each element in constancy of relation, but not with others.Moreover, it is likely that the neurons in mammalian cortical layer-IV largely capture conjunction among projecting neurons to represent composition of features, and layer-III their disjunction (the variation in composition).If so, then as the represented objects / features in projecting modules undergo change, the coherent population by frequency and phase in layer-IV may shift.But if the structure is kept fixed, the population in layer-III may remain stable.For instance, line segments may change in orientation, but the relation is kept fixed at right angle.And when this relation is also dynamically changed the population shift should be observed in layer-III.The top-down projection via layer-I may also modulate layers II and III the same way, but by keeping the overall context reasonably unchanged one may observe the said effect.
Given the detailed specification of the mechanics of processing, many different functional properties can be identified for observation.Of course, the simplest test is to simulate the mechanisms on artificial devices, then compute as well as observe the correlation.In fact, this mechanism of computing the values can also be used at sensory interfaces where the local mapping and temporal signals of first sensory neurons are known, e.g., the response function of cells in retina.The technique is also applicable to deep learning systems enabling the evaluation of values of correlation of intermediate nodes.
Now, since all elements of consciousness are constructed of semantic values of information, Neural Correlates of Consciousness (NCC) [96] comes back into sharp focus in a different form.A correlate is not specific to neurons, but to information.Ingenious experiments may be devised to observe neural correlates of semantic values of 'an object' being the observer or referrer of the objects in a context, the sensor of the senses, the actor of the actions or the controller of change, and so on.That is, one observes correlates of the relation R in the definition of consciousness and the term R U OAC in Eqn.12.These correlates are not required to be exclusive, yet satisfy sufficiency.It can be further established that the references to the self in expressions by subjects correlate with 'the object' in consideration as per the second order definition of consciousness.In fact, observations of neural correlates of references to 'other subjects' (individuals) [97,98] in relation to their appearance, acts, motives, functions, causal powers, etc., constitute a strong evidence for a similar correlation of an active population of neurons for the self.One may note, there is no perception without a mapped perceiver in the semantic structure, for a perception is only relative to the perceiver; a disjunction of relations to perceptions itself defines the perceiver.Also, the senses need to be attributed to a common object within a semantic structure for centralized control of behavior.Care must be exercised to require that the neural correlates are not interpreted based on any artificial causal constraints of processing in the system, which also eliminates any correlation based on assigned values.Most scientific experiments are analyzed based on interpreted causal constraints making them a third person perspective.This method of NCC differs from the so called Turing Test [99], in that it is based on direct correlates rather than on the observed function or behavior of a system and their interpretation from a presumed causal basis.

Consciousness vs. material existence
The intent here is to examine ontology vs. epistemology of existence in light of the finding that the apparent reality of consciousness is emergent from more basic causal information.We noted earlier that a correlation of an observable state with semantic value is based on the constancy of causal function in nature.Therefore, a causal correlation must naturally include the semantic value of whatever qualities of elements of reality responsible for the change; a quality also includes the quantity.For instance, in the example discussed in the context of Eqn.1 and Fig. 2, the correlation with 'mass state' encapsulates both the quality of whatever it is that we refer to as 'mass' and its relative quantity that caused a relative transition in the interacting system.Does this imply that the quality of mass is the most fundamental element in nature?Not necessarily.As noted in [1], an interaction proceeds over time and space, and the result of the interaction correlates with the coherent property that emerges from such an interaction.That is, 'mass' itself can be an emergent property observable (bearing a causal function) in nature.An emergent property is an abstraction of reality, such as momentum, energy, brightness, color, temperature, heat, etc.We know that the object observed is relative to the quality that an observing system responds to [1].Without such an observation (interaction), there is no correlation with the respective qualities and their quantities.That is, an interaction leading to a specific observable transition in the observing system, causes this quality and its measure to bear an existential reality to be referable.It is inferred then that all known or knowable objects have existential reality only in terms of the causal correlation of observable states.
This understanding provides a robust resolution to the age old debate on what exists.As noted in [1], a decoherence completes the interaction creating a record of the observed states and their correlation in turn.Given the reality of limited indeterminism [1], once a relative state description resulted in an observed consequence, it cannot be undone from the perspective of the totality of the state of the universe.That is, the ontology of an object is dependent on the causal correlation.Since all our notable observations entail consciousness, some may hold a view that consciousness is the basis of all existence, but that limits the semantics of correlation relative to an observing self.The information of correlation may not create a physical substratum (see also [100]), but it projects the causal relation in underlying substratum into a knowable substance.This inference is consistent with the view that the ultimate substratum may only have relations as observables.If the epistemology is extended beyond the knowability by a conscious agency to the correlation of all observable states, then, in that limit, ontology and epistemology express the same notion.

An Overarching Remark
In addition to laying down the basis and mechanism of the emergence of consciousness from causal information (ECCI), this work also provides a resolution to several outstanding fundamental problems related to information processing and consciousness.For instance, 1. semantic content of information is grounded in natural causal function; 2. mechanics of semantic processing directly applicable to neural systems and implementable on artificial devices is founded; 3. a principle based on constancy of relations in arbitrary space of semantics is introduced as a uniform mechanism to construct object description via structural and functional relations; 4. mechanism of abstraction and emergence is computably formulated; 5. specification of process of integration and binding is laid down; 6. population coding of semantic values is expressed quantitatively; 7. objective basis of subjectivity is derived from causal correlation; 8. a definition of consciousness relating to causal function is proposed; 9. what constitutes a conscious agency is identified; 10. mechanics of attention and freedom of will are presented in the new light; 11. the role of language in acute sense of consciousness is re-examined; 12. the process of evolution via selection is identified as the sole causal function responsible for the emergence of consciousness in an otherwise value absent (neutral) physical universe.In addition, this work deals with the directly accessible or knowable reality of nature, whereas, all physically observable properties are subject to interpretation and modification.This work does not include, 1. specific function and physiology of agents in a network; 2. specification of networking; 3. specification of competitive coherence; 4. specifics of modular organization for a given species; 5. possible sources of instabilities in computing; 6. analysis of complexity; 7. entropy and energy considerations of physical systems, and such.This work makes use of certain self evident first principles.Information as causal correlate of a physical state is based on the constancy of causal dependence; interpretation of the result of every experiment is an evidence.Conjunction and disjunction function as generic operators enabling expressions of structured and abstract semantics.Abstraction via disjunction causes emergence of classes and relations, and enables a mechanism of referencing such objects.Moreover, since all specifications are based on relations, and a relation is uniformly expressible in terms of conjunction and disjunction, what physical entities and function constitute the elements and mechanisms are immaterial.Similarly, the constancy principle is based on the fact that an object is referable only due to certain constancy in its structure and function, which forms a robust mechanism to construct its specification.The population coding method based on the constructor expression enables the process of competitive coherence building to capture relevant constancy in observed context and to represent practically unlimited variations in object description.Re-entrant modular and hierarchical network is an organizational principle to allow constructing self-referential arbitrarily deep structure and abstraction.
The objectivity of the intrinsic correlation of a physically observable state to the information of its causal dependence, computable in terms of conjunction and disjunction bridges the 'explanatory gap' [88] between the objective reality of physical function and the subjective reality of consciousness.If the causal function in a universe has sufficient complexity to organize processing in modular hierarchy, then the universe is sufficiently potent to allow the emergence of consciousness.

Figure 4 :
Figure 4: A graphical illustration of methods of conjunction and disjunction on semantic values; conjunction captures the composition, while disjunction gives rise to an abstraction of a class or a relation.Each of the panels a, b, c, and d is organized horizontally.(a) A conjunction of 4 line segments appropriately placed form a rectangle.On the right, features in specific relation form composites. (b) One of the composites in (a) undergoes a regular transformation sustaining an internal relation among its components.A conjunction of events in temporal sequence forms a temporal event or a process.(c) When a rectangle undergoes a rotation about one of its vertices or a rigid displacement, the neighboring two sides (line segments) maintain a relation of right angle as shown on the right.A mapping of each conjunction of two lines on the orientation space (displayed vertically) is shown as horizontal bars in the same color.A disjunction of all such combinations that covers the orientation space gives rise to an emergent semantics of 'right angle', an abstract semantic value with no physical counterpart.The same mapping is also shown as a network of connectivity from a set of agents (such as neurons) that represent line segments at specific orientation to a higher level agent A, such that each active conjunction in the map, shown in the same color, may activate the agent A. The active state of A then represents the irreducible semantics of right angle that emerges from a bottom up mapping here.(d) A series of composite (structured) objects may share a common feature; a disjunctive relation among such objects evaluates to the common feature as a base class as expressed in Eqn.3 and 6, without any particular dependence on another feature in each conjunction.

Figure 5 :
Figure5: A graphical illustration of a mapping scheme.(a) Objects {A, B, C} are shown in a two dimensional spatial field, where system X serves as an observing and mapping system to represent the relative placements.A signal originating from X at location X 0 is reflected by {A, B, C} and received back by X at relative times (t a 0 , t b 0 , t c 0 ) respectively that further map to respective distances (r a 0 , r b 0 , r c 0 ) in one-toone mapping as shown on the right, where the index in alphabet represents the object and in numeral the measurement number.For instance, the placement of object A can be anywhere on the circle in red centered at X 0 .As the system X moves to a new location X 1 , it regenerates a new signal with a different pulse duration or frequency and receives the reflected signals back at relative times (t a 1 , t b 1 , t c 1 ).Now, the locus of object A is shown with a circle in blue centered at X 1 .The cross section points of red and blue circles fix the location of A with respect to both points X 0 and X 1 , before and after the movement; the symmetric placement of A about the line of movement is shown with dashed lines leading to A .The second movement of system X to X 2 at an angle α with respect to the first movement and a new set of measurements of reflected signals fixes the location of all objects in the field uniquely as analyzed in the text and shown graphically with three circles for object A. The angles θ a 0 and θ a 1 are values of correlation for object A relative to two ends of first movement, while θ a 1 − α and θ a 2 are to the second.(b) Labeled parametric spaces are shown as black horizontal lines, whereas labeled nodes shown as big dots on them represent discrete values.Colored lines converging on a node from below represent incoming projections from lower parametric spaces.Similarly, the lines emerging upward from a node designate forward projection, which bear no color correlation with incoming lines.The lines shown in the same color converging on a node from below represent a conjunction of values represented by the projecting nodes, whereas, a convergence of multiple such conjunctions in different colors on the same node represent a disjunctive relation.The angle space is marked with L and R to indicate Left or Right of movement, or the sign of angle.(r 2 , θ 2 , s 2 ) labels the composite space of distance and angle for different objects.The node in the top parametric space represents a disjunctive convergence of conjunctions of relative placement of any three objects observed in the field at all times, only one conjunction is shown in the figure.This node represents the placement of observing system X itself relative to objects in space at all times, and forms a component of the system's identity.

Table 1 :
Table.1 and Fig.3.The table specifies the result of conjunction and disjunction on correlation values.