# A Compositional Model of Consciousness Based on Consciousness-Only

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## Abstract

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## 1. Introduction

**other-dependent**, also called

**co-dependent**, i.e., the nature of existence arising from causes and conditions that are interdependent between each other. Without falling into idealism or dualism, we propose that consciousness should be treated as a primary process.

## 2. Category Theory and Process Theory

#### 2.1. Preliminaries

**Category**

- a class of objects $ob\left(\mathfrak{C}\right)$;
- for each pair of objects $A,B$, a set $\mathfrak{C}(A,B)$ of morphisms from A to B;
- for each triple of objects $A,B,C$, a composition map$$\begin{array}{ccc}\mathfrak{C}(B,C)\times \mathfrak{C}(A,B)& \u27f6& \mathfrak{C}(A,C)\\ (g,f)& \mapsto & g\circ f;\end{array}$$
- for each object A, an identity morphism ${1}_{A}\in \mathfrak{C}(A,A)$,

- associativity: for any $f\in \mathfrak{C}(A,B),g\in \mathfrak{C}(B,C),h\in \mathfrak{C}(C,D)$, there holds $(h\circ g)\circ f=h\circ (g\circ f)$;
- identity law: for any $f\in \mathfrak{C}(A,B),{1}_{B}\circ f=f=f\circ {1}_{A}$.

**Functor**

- a mapping$$\begin{array}{ccc}ob\left(\mathfrak{C}\right)& \u27f6& ob\left(\mathfrak{D}\right)\\ A& \mapsto & F\left(A\right);\end{array}$$
- for each pair of objects $A,B$ of $\mathfrak{C}$, a map$$\begin{array}{ccc}\mathfrak{C}(A,B)& \u27f6& \mathfrak{D}\left(F\right(A),F(B\left)\right)\\ f& \mapsto & F\left(f\right),\end{array}$$

- preserving composition: for any morphisms $f\in \mathfrak{C}(A,B),g\in \mathfrak{C}(B,C)$, there holds $F(g\circ f)=F\left(g\right)\circ F\left(f\right)$;
- preserving identity: for any object A of $\mathfrak{C}$, $F\left({1}_{A}\right)={1}_{F\left(A\right)}$.

**Natural Transformation**

**Strict Monoidal Category**

- a category $\mathfrak{C}$;
- a unit object $I\in ob\left(\mathfrak{C}\right)$;
- a bifunctor $-\otimes -:\mathfrak{C}\times \mathfrak{C}\u27f6\mathfrak{C}$,

- associativity: for each triple of objects $A,B,C$ of $\mathfrak{C}$, $A\otimes (B\otimes C)=(A\otimes B)\otimes C$; for each triple of morphisms $f,g,h$ of $\mathfrak{C}$, $f\otimes (g\otimes h)=(f\otimes g)\otimes h$;
- unit law: for each object A of $\mathfrak{C}$, $A\otimes I=A=I\otimes A$; for each morphism f of $\mathfrak{C}$, $f\otimes {1}_{I}=f={1}_{I}\otimes f$.

**Strict Symmetric Monoidal Category**

**Strict Monoidal Functor**

**Strict Compact Closed Category**

#### 2.2. Process Theory

**sequential composition**. As such, three things happening in sequence is seen as one process without any ambiguity, i.e., the sequential composition of processes is associative: $(f\circ g)\circ h=f\circ (g\circ h)$. We also assume that for each type A, there exists a process called the identity ${1}_{A}$, which does nothing at all to A. This is depicted as a straight line:

**parallel composition**of processes.

**swap**process:

**process theory**in the framework of a strict symmetric monoidal category (SMC). A much more detailed description of process theory can be found in [19].

**caps**and

**cups**, so that:

#### 2.3. Fine-Grained Version of Process Theory

**generators**, while specifying those generators in terms of equations of processes composed of generators. Below, we illustrate this idea by a typical example called ZX-calculus.

**rewriting rules**: one can rewrite each diagram into an equivalent one by replacing a part of the diagram which is on one side of an equation with the diagram on the other side of the equation. All the ZX diagrams modulo (modulo means using an equivalent relation) and the rewriting rules form a self-dual compact closed category [18]. To guarantee that there are no conflicts in this rewriting system, ZX-calculus needs a property called

**soundness**: there exists a

**standard interpretation**from the category of ZX diagrams to the category of matrices, i.e., a symmetric monoidal functor between them [18]. More general, a sound rewriting system means that there are not internal contradictions, while

**completeness**would mean that we can prove anything that is right about the phenomena in question with the chosen system. A sound and complete rewriting system defines a unique set of generators.

## 3. Compositional Approach For Consciousness-Only

#### 3.1. Process Theory for Consciousness

#### 3.2. Consciousness as Fundamental

#### 3.3. Yogacara Philosophy

**sense-consciousnesses**(eye or visual, ear or auditory, nose or olfactory, tongue or gustatory, body or tactile consciousnesses),

**mental consciousness**(the sixth consciousness),

**manas consciousness**(the seventh or thought-centre consciousness), and the eighth consciousness—

**alaya consciousness**(storehouse consciousness). These eight consciousnesses are not independent of each other: “... the Alaya consciousness and the first seven consciousnesses generate each in a steady process and are reciprocally cause and effect” [38]. A clarifying metaphor is to think about the eighth consciousness as the ocean, while the other consciousness are different types of waves in its surface. Neither of them are separated of the others and all consciousness are essentially one.

**potentialities**that would engender other complex types of experiences [5,39]. We will approach these potentialities only in relation with other seeds, leaving the types on our process theory for Alaya consciousness unspecified (a future approach may define the internal structure of Alaya taking six features in formal analogy with the seed metaphor from [39]). This might be an economical strategy, since, although this structure is considered the same for all living beings, the input and outputs types for those processes might be species dependent, or even specific to each individual.

**perceived division**and the perceiving faculty or

**perceiving division**(nimittabhaga and darsanabhaga)” [39]. The perceived is related to the object and the perceiving to the subject. In Husserlian phenomenology, this division is extrapolated to what is called Noema versus Noesis distinction [40]. The first division is mostly related to the sixth consciousness and the five perceptual consciousnesses, while the second one with the seventh manas consciousness.

## 4. Compositional Model for Consciousness-Only

#### 4.1. Process Theory for Alaya Consciousness

#### 4.1.1. Generators of Qufinite $Z{X}_{\Delta}$-Calculus

**Remark**

**1.**

#### 4.1.2. Rules of Qufinite $Z{X}_{\Delta}$-Calculus

#### 4.2. Standard Interpretation of Qufinite $Z{X}_{\Delta}$-Calculus

#### 4.3. The Perceived Division of Alaya Consciousness

#### 4.4. The Perceiving Division of Alaya Consciousness

## 5. The Unity of Experience

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Seth, A.K. Consciousness: The last 50 years (and the next). Brain Neurosci. Adv.
**2018**, 2. [Google Scholar] [CrossRef][Green Version] - Searle, J.R. Consciousness. Annu. Rev. Neurosci.
**2000**, 23, 557–578. [Google Scholar] [CrossRef] [PubMed] - Bayne, T.; Chalmers, D.J. What is the unity of consciousness? The Unity of Consciousness: Binding, Integration, and Dissociation; Oxford University Press: Oxford, UK, 2012; pp. 1–41. [Google Scholar] [CrossRef][Green Version]
- Crick, F.; Koch, C. Consciousness and neuroscience. Cereb. Cortex
**1998**, 8, 97–1007. [Google Scholar] [CrossRef] - Lusthaus, D. Buddhist Phenomenology, 1st ed.; Routledge Curzon: Oxfordshire, UK, 2002; p. 632. [Google Scholar] [CrossRef]
- Makeham, J. Introduction. In Transforming Consciousness: Yogacara Thought in Modern China; Makeham, J., Ed.; Oxford University Press: Oxford, UK, 2014. [Google Scholar] [CrossRef]
- Fields, C.; Hoffman, D.D.; Prakash, C.; Singh, M. Conscious agent networks: Formal analysis and application to cognition. Cogn. Syst. Res.
**2018**, 47, 186–213. [Google Scholar] [CrossRef][Green Version] - Thompson, E. Mind in Life; Harvard University Press: Cambridge, MA, USA, 2007. [Google Scholar]
- Varela, F.J. Neurophenomenology: A Methodological Remedy for the Hard Problem. J. Conscious. Stud.
**1996**, 3, 330–349. [Google Scholar] - Coecke, B. An Alternative Gospel of Structure: Order, Composition, Processes. In Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse; Heunen, C., Sadrzadeh, M., Grefenstette, E., Eds.; Oxford University Press: Oxford, UK, 2013. [Google Scholar] [CrossRef][Green Version]
- Coecke, B.; Duncan, R.; Kissinger, A.; Wang, Q. Generalised Compositional Theories and Diagrammatic Reasoning. In Quantum Theory: Informational Foundations and Foils. Fundamental Theories of Physics; Chiribella, G., Spekkens, R., Eds.; Springer: Berlin, Germany, 2016; Volume 181, pp. 309–366. [Google Scholar] [CrossRef][Green Version]
- Signorelli, C.M.; Meling, D. Towards new concepts for a biological neuroscience of consciousness. Cogn. Neurodynamics
**2021**. [Google Scholar] [CrossRef] - Prentner, R. Consciousness and topologically structured phenomenal spaces. Conscious. Cogn.
**2019**, 70, 25–38. [Google Scholar] [CrossRef] [PubMed][Green Version] - Yoshimi, J. Mathematizing phenomenology. Phenomenol. Cogn. Sci.
**2007**, 6, 271–291. [Google Scholar] [CrossRef] - Tsuchiya, N.; Saigo, H. Applying Yoneda’s lemma to consciousness research: Categories of level and contents of consciousness. Preprint
**2020**. [Google Scholar] [CrossRef] - Awodey, S. Category Theory, 1st ed.; Oxford University Press: Oxford, UK, 2006; p. 266. [Google Scholar]
- Maclane, S. Categorical Algebra. Bull. Am. Math. Soc.
**1965**, 71, 40–106. [Google Scholar] [CrossRef][Green Version] - Coecke, B.; Duncan, R. Interacting quantum observables: Categorical algebra and diagrammatics. New J. Phys.
**2011**, 13. [Google Scholar] [CrossRef] - Coecke, B.; Kissinger, A. Picturing Quantum Processes. A First Course in Diagrammatic Reasoning; Cambridge University Press: Cambridge, UK, 2017. [Google Scholar] [CrossRef]
- Coecke, B. (Ed.) New Structures for Physics; Lecture Notes in Physics; Springer: Berlin/Heidelberg, Germany, 2011; Volume 813, p. 1034. [Google Scholar] [CrossRef]
- Abramsky, S.; Coecke, B. A categorical semantics of quantum protocols. In Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS’04), Turku, Finland, 17 July 2004; pp. 415–425. [Google Scholar]
- Kissinger, A.; Uijlen, S. A categorical semantics for causal structure. In Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Reykjavik, Iceland, 20–23 June 2017; pp. 1–12. [Google Scholar] [CrossRef][Green Version]
- Pinzani, N.; Gogioso, S.; Coecke, B. Categorical Semantics for Time Travel. arXiv
**2019**, arXiv:1902.00032. [Google Scholar] - Kissinger, A.; Hoban, M.; Coecke, B. Equivalence of relativistic causal structure and process terminality. arXiv
**2017**, arXiv:1708.04118. [Google Scholar] - Coecke, B.; Sadrzadeh, M.; Clark, S. Mathematical Foundations for a Compositional Distributional Model of Meaning. Linguist. Anal.
**2010**, 36, 345–384. [Google Scholar] - Bolt, J.; Coecke, B.; Genovese, F.; Lewis, M.; Marsden, D.; Piedeleu, R. Interacting Conceptual Spaces I: Grammatical Composition of Concepts. arXiv
**2017**, arXiv:1708.04118. [Google Scholar] - Signorelli, C.M.; Dundar-Coecke, S.; Wang, V.; Coecke, B. Cognitive Structures of Space-Time. Front. Psychol.
**2020**. [Google Scholar] [CrossRef] - Signorelli, C.M. Can Computers become Conscious and overcome Humans? Front. Robot. Artif. Intell.
**2018**, 5. [Google Scholar] [CrossRef][Green Version] - Mulder, D.H. Objectivity. Available online: https://philpapers.org/rec/MULO (accessed on 26 February 2021).
- Searle, J.R. How to study consciousness scientifically. Philos. Trans. R. Soc. Biol. Sci.
**1998**, 353, 1935–1942. [Google Scholar] [CrossRef] - Anderson, P.W. More Is Different. Science
**1972**, 177, 393–396. [Google Scholar] [CrossRef][Green Version] - Mazzocchi, F. Complexity in biology. EMBO Rep.
**2008**, 9, 10–14. [Google Scholar] [CrossRef] [PubMed][Green Version] - beim Graben, P. Contextual Emergence in Neuroscience. Closed Loop Neuroscience; Academic Press: Cambridge, CA, USA, 2016; pp. 171–184. [Google Scholar] [CrossRef]
- Thomas Nagel. What is it like to be a bat? Philos. Rev.
**1974**, 83, 435–450. [Google Scholar] [CrossRef] - Chalmers, D. The puzzle of conscious experience. Sci. Am.
**1995**, 273, 80–86. [Google Scholar] [CrossRef] - LI, J. Buddhist Phenomenology and the Problem of Essence. Comp. Philos. Int. J. Constr. Engagem. Distinct Approaches Towar. World Philos.
**2015**, 7, 59–89. [Google Scholar] [CrossRef][Green Version] - Kern, I. The Structure of Consciousness According to Xuanzang. J. Br. Soc. Phenomenol.
**1988**. [Google Scholar] [CrossRef] - Xuanzang; Cook, F.H.; Vasubandhu. Three Texts on Consciousness Only; Numata Center for Buddhist Translation and Research: Berkeley, CA, USA, 1999. [Google Scholar]
- Xuanzang; TatWei; Vasubandhu. Cheng Wei Shi Lun; The Doctrine of Mere-Consciousness; Ch’eng Wei-shih Lun Publication Committee: Hong Kong, China, 1973. [Google Scholar]
- Husserl, E. General Introduction to a Pure Phenomenology; Martinus Nijhoff Publishers: Leiden, The Netherlands, 1983. [Google Scholar]
- Bruza, P.D.; Wang, Z.; Busemeyer, J.R. Quantum cognition: A new theoretical approach to psychology. Trends Cogn. Sci.
**2015**, 19, 383–393. [Google Scholar] [CrossRef][Green Version] - Cervantes, V.H.; Dzhafarov, E.N. Snow queen is evil and beautiful: Experimental evidence for probabilistic contextuality in human choices. Decision
**2018**, 5, 193–204. [Google Scholar] [CrossRef] - Golan, J.S. Semirings and their Applications; Springer: Dordrecht, The Netherlands, 1999. [Google Scholar] [CrossRef]
- Chalmers, D.J. Panpsychism and Panprotopsychism. Amherst Lect. Philos.
**2013**, 8. [Google Scholar] - Chalmers, D.J. The Combination Problem for Panpsychism; Brüntrup, G., Jaskolla, L., Eds.; Oxford University Press: Oxford, UK, 2016; pp. 179–214. [Google Scholar] [CrossRef][Green Version]
- Revonsuo, A.; Newman, J. Binding and consciousness. Conscious. Cogn.
**1999**, 8, 123–127. [Google Scholar] [CrossRef] - Hameroff, S.; Penrose, R. Consciousness in the universe: A review of the “Orch OR” theory. Phys. Life Rev.
**2014**, 11, 39–78. [Google Scholar] [CrossRef] [PubMed][Green Version] - Signorelli, C.M.; Wang, Q.; Coecke, B. Reasoning about conscious experience with axiomatic and graphical mathematics. Submitt. Conscious. Cogn.
**2021**. [Google Scholar] - Hoffman, D.D.; Prakash, C. Objects of consciousness. Front. Psychol.
**2014**, 5, 1–22. [Google Scholar] [CrossRef] [PubMed][Green Version] - Oizumi, M.; Albantakis, L.; Tononi, G. From the phenomenology to the mechanisms of consciousness: Integrated Information Theory 3.0. PLoS Comput. Biol.
**2014**, 10, e1003588. [Google Scholar] [CrossRef] [PubMed][Green Version]

**Figure 1.**Qufinite $Z{X}_{\Delta}$-calculus rules I, where $\overrightarrow{{\alpha}_{d}}=({a}_{1},\cdots ,{a}_{d-1});\overrightarrow{{\beta}_{d}}=({b}_{1},\cdots ,{b}_{d-1});\overrightarrow{{\alpha}_{d}{\beta}_{d}}=({a}_{1}{b}_{1},\cdots ,{a}_{d-1}{b}_{d-1});{a}_{k},{b}_{k}\in \mathcal{S};k\in \{1,\cdots ,d-1\};j\in \{0,1,\cdots ,d-1\};m\in \mathbb{N}.$

**Figure 2.**Qufinite $Z{X}_{\Delta}$-calculus rules II, where ${\overrightarrow{1}}_{d}=\stackrel{d-1}{\stackrel{\u23de}{(1,\cdots ,1)}};{\overrightarrow{0}}_{d}=\stackrel{d-1}{\stackrel{\u23de}{(0,\cdots ,0)}};\overrightarrow{{\alpha}_{d}}=({a}_{1},\cdots ,{a}_{d-1});\overrightarrow{{\beta}_{d}}=({b}_{1},\cdots ,{b}_{d-1});{a}_{k},{b}_{k}\in \mathcal{S};k\in \{1,\cdots ,d-1\};j\in \{1,\cdots ,d-1\};s,t,u\in \mathbb{N}\setminus \left\{0\right\}.$

**Table 1.**Generators of qufinite $Z{X}_{\Delta}$-calculus, where $m,n\in \mathbb{N};\overrightarrow{{\alpha}_{d}}=({a}_{1},\cdots ,{a}_{d-1});{a}_{i}\in \mathcal{S};i\in \{1,\cdots ,d-1\};j\in \{0,1,\cdots ,d-1\};s,t\in \mathbb{N}\setminus \left\{0\right\}$.

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Signorelli, C.M.; Wang, Q.; Khan, I. A Compositional Model of Consciousness Based on Consciousness-Only. *Entropy* **2021**, *23*, 308.
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Signorelli, Camilo Miguel, Quanlong Wang, and Ilyas Khan. 2021. "A Compositional Model of Consciousness Based on Consciousness-Only" *Entropy* 23, no. 3: 308.
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