Extensional Superposition and Its Relation to Compositionality in Language and Thought

Thornton, Chris

doi:10.1111/cogs.12929

Cited by 3 publications

(2 citation statements)

References 93 publications

(119 reference statements)

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“…Also, it should have the explanatory import in showing how linguistic meanings that are embodied in sensory-motor systems come to simultaneously possess the formal-semantic properties that they do and also vice versa (see Arbib, 2012). Another promising approach towards this has been extensional superposition (Thornton, 2021), whereby concepts that can be mapped onto their referents or extensions are combined via the operation of superposition that is supposed to be independent of, or neutral with respect to, semantic composition in language and conceptual combination in thought (see, for details, the Appendix). This approach steers clear of the issue of how the ontological differences between cognitive representations and denotative set-theoretic structures can be reconciled and instead focuses on the procedure of meaning composition that can help get a handle on the expressive or combinatorial processes in both thought and language.…”

Section: Current Progress and Promisesmentioning

confidence: 99%

“…A.1 Extensional superposition (Thornton, 2021) Extensional superposition operates on extensional meanings that link to, but are not in themselves, concepts. If BOX and CONTAINER are such extensional meanings, (BOX) will be the extension of the concept attached to BOX, and (CONTAINER) will be the extension of the concept attached to CONTAINER ( has been used here instead of Thornton's ξ in order to avoid confusion with the form normalizing function in (1)).…”

Section: Appendixmentioning

confidence: 99%

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The Puzzling Chasm Between Cognitive Representations and Formal Structures of Linguistic Meanings

Mondal

2022

Cognitive Science

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Natural language meaning has properties of both (embodied) cognitive representations and formal/mathematical structures. But it is not clear how they actually relate to one another. This article argues that how properties of cognitive representations and formal/mathematical structures of natural language meaning can be united remains one of the puzzles in cognitive science. That is primarily because formal/mathematical structures of natural language meaning are abstract, logical, and truthconditional properties, whereas cognitive/conceptual representations are embodied and grounded in sensory-motor systems. After reviewing the current progress, this work offers, in outline, the general formulations that show how these two different kinds of representations for semantic structures can (potentially) be unified and also proposes three desiderata for testing, in brain dynamics, the mathematical equivalence between formal symbolic representations (and their transitions), and neuronal population codes (and their transitions).

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Section: Current Progress and Promisesmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

The Puzzling Chasm Between Cognitive Representations and Formal Structures of Linguistic Meanings

Mondal

2022

Cognitive Science

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On the ability of standard and brain-constrained deep neural networks to support cognitive superposition: a position paper

Garagnani

2024

Cogn Neurodyn

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The ability to coactivate (or “superpose”) multiple conceptual representations is a fundamental function that we constantly rely upon; this is crucial in complex cognitive tasks requiring multi-item working memory, such as mental arithmetic, abstract reasoning, and language comprehension. As such, an artificial system aspiring to implement any of these aspects of general intelligence should be able to support this operation. I argue here that standard, feed-forward deep neural networks (DNNs) are unable to implement this function, whereas an alternative, fully brain-constrained class of neural architectures spontaneously exhibits it. On the basis of novel simulations, this proof-of-concept article shows that deep, brain-like networks trained with biologically realistic Hebbian learning mechanisms display the spontaneous emergence of internal circuits (cell assemblies) having features that make them natural candidates for supporting superposition. Building on previous computational modelling results, I also argue that, and offer an explanation as to why, in contrast, modern DNNs trained with gradient descent are generally unable to co-activate their internal representations. While deep brain-constrained neural architectures spontaneously develop the ability to support superposition as a result of (1) neurophysiologically accurate learning and (2) cortically realistic between-area connections, backpropagation-trained DNNs appear to be unsuited to implement this basic cognitive operation, arguably necessary for abstract thinking and general intelligence. The implications of this observation are briefly discussed in the larger context of existing and future artificial intelligence systems and neuro-realistic computational models.

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Towards a unified representation of linguistic meaning

Mondal

2023

Open Linguistics

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Natural language meaning has properties of both cognitive representations and formal/mathematical structures. But it is not clear how they actually relate to one another. The central aim of this article is to show that properties of cognitive representations and formal/mathematical structures of natural language meaning, albeit apparently divergent, can be united, as far as the basic properties of semantic structures are concerned. Thus, this article will formulate the form of unified representations for semantic structures. With this goal, this article takes into account standard formal-semantic representations and also Discourse Representation Theory (DRT) representations on the one hand and semantic representations in different versions of Conceptual/Cognitive Semantics (Jackendoff’s, Langacker’s and Talmy’s approaches to Conceptual/Cognitive Semantics) and representations of Mental Spaces (Fauconnier’s approach) on the other hand. The rationale behind the selection of these approaches is that the representations of semantic structures under these approaches are all amenable to unification. It must be emphasized that showing that the representations of semantic structures under these approaches can be unified does not simply amount to unifying these theories/approaches in toto. Rather, it is to demonstrate that cognitive representations and formal/mathematical structures can be shown to be inter-translatable for at least some accounts of linguistic meaning.

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Extensional Superposition and Its Relation to Compositionality in Language and Thought

Cited by 3 publications

References 93 publications

The Puzzling Chasm Between Cognitive Representations and Formal Structures of Linguistic Meanings

The Puzzling Chasm Between Cognitive Representations and Formal Structures of Linguistic Meanings

On the ability of standard and brain-constrained deep neural networks to support cognitive superposition: a position paper

Towards a unified representation of linguistic meaning

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