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Categorical Compositional Cognition

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Quantum Interaction (QI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10106))

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Abstract

We accommodate the Integrated Connectionist/Symbolic Architecture (ICS) of [32] within the categorical compositional semantics (CatCo) of [13], forming a model of categorical compositional cognition (CatCog). This resolves intrinsic problems with ICS such as the fact that representations inhabit an unbounded space and that sentences with differing tree structures cannot be directly compared. We do so in a way that makes the most of the grammatical structure available, in contrast to strategies like circular convolution. Using the CatCo model also allows us to make use of tools developed for CatCo such as the representation of ambiguity and logical reasoning via density matrices, structural meanings for words such as relative pronouns, and addressing over- and under-extension, all of which are present in cognitive processes. Moreover the CatCog framework is sufficiently flexible to allow for entirely different representations of meaning, such as conceptual spaces. Interestingly, since the CatCo model was largely inspired by categorical quantum mechanics, so is CatCog.

B. Coecke and M. Lewis—gratefully acknowledge AFSOR funding on grant ‘Algorithmic and Logical Aspects of Composing Meanings’.

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Authors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, UK

    Yaared Al-Mehairi, Bob Coecke & Martha Lewis

Authors
  1. Yaared Al-Mehairi
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  2. Bob Coecke
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  3. Martha Lewis
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Correspondence to Martha Lewis .

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Editors and Affiliations

  1. San Francisco State University, San Francisco, California, USA

    Jose Acacio de Barros

  2. University of Oxford, Oxford, United Kingdom

    Bob Coecke

  3. City University of London, London, United Kingdom

    Emmanuel Pothos

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Al-Mehairi, Y., Coecke, B., Lewis, M. (2017). Categorical Compositional Cognition. In: de Barros, J., Coecke, B., Pothos, E. (eds) Quantum Interaction. QI 2016. Lecture Notes in Computer Science(), vol 10106. Springer, Cham. https://doi.org/10.1007/978-3-319-52289-0_10

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  • DOI: https://doi.org/10.1007/978-3-319-52289-0_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-52288-3

  • Online ISBN: 978-3-319-52289-0

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