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Categorial compositionality: a category theory explanation for the systematicity of human cognition.

ABSTRACT: Classical and Connectionist theories of cognitive architecture seek to explain systematicity (i.e., the property of human cognition whereby cognitive capacity comes in groups of related behaviours) as a consequence of syntactically and functionally compositional representations, respectively. However, both theories depend on ad hoc assumptions to exclude specific instances of these forms of compositionality (e.g. grammars, networks) that do not account for systematicity. By analogy with the Ptolemaic (i.e. geocentric) theory of planetary motion, although either theory can be made to be consistent with the data, both nonetheless fail to fully explain it. Category theory, a branch of mathematics, provides an alternative explanation based on the formal concept of adjunction, which relates a pair of structure-preserving maps, called functors. A functor generalizes the notion of a map between representational states to include a map between state transformations (or processes). In a formal sense, systematicity is a necessary consequence of a higher-order theory of cognitive architecture, in contrast to the first-order theories derived from Classicism or Connectionism. Category theory offers a re-conceptualization for cognitive science, analogous to the one that Copernicus provided for astronomy, where representational states are no longer the center of the cognitive universe--replaced by the relationships between the maps that transform them.

SUBMITTER: Phillips S

PROVIDER: S-EPMC2908697 | biostudies-literature | 2010 Jul

REPOSITORIES: biostudies-literature

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Categorial compositionality: a category theory explanation for the systematicity of human cognition.

Phillips Steven S Wilson William H WH

PLoS computational biology 20100722 7

Classical and Connectionist theories of cognitive architecture seek to explain systematicity (i.e., the property of human cognition whereby cognitive capacity comes in groups of related behaviours) as a consequence of syntactically and functionally compositional representations, respectively. However, both theories depend on ad hoc assumptions to exclude specific instances of these forms of compositionality (e.g. grammars, networks) that do not account for systematicity. By analogy with the Ptol ...[more]

PMID: 20661306

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Project description:Emotions are signaled by complex arrays of face and body actions. The main point of contention in contemporary treatments is whether these arrays are discrete, holistic constellations reflecting emotion categories, or whether they are compositional-comprised of smaller components, each of which contributes some aspect of emotion to the complex whole. We address this question by investigating spontaneous face and body displays of athletes and place it in the wider context of human communicative signals and, in particular, of language. A defining property of human language is compositionality-the ability to combine and recombine a relatively small number of elements to create a vast number of complex meaningful expressions, and to interpret them. We ask whether this property of language can be discerned in a more ancient communicative system: intense emotional displays. In an experiment, participants interpreted a range of emotions and their strengths in pictures of athletes who had just won or lost a competition. By matching participants' judgements with minutely coded features of face and body, we find evidence for compositionality. The distribution of participants' responses indicates that most of the athletes' face and body features contribute to displays of dominance or submission. More particular emotional components related, for example, to positive valence (e.g. happy) or goal obstruction (e.g. frustrated), were also found to significantly correlate with certain face and body features. We propose that the combination of features linked to broader components (i.e, dominant or submissive) and to more particular emotions (e.g, happy or frustrated) reflects more complex emotional states. In sum, we find that the corporeal expression of intense, unfiltered emotion has compositional properties, potentially providing an ancient scaffolding upon which, millions of years later, the abstract and constrained compositional system of human language could build.

Dataset Information

Categorial compositionality: a category theory explanation for the systematicity of human cognition.

Publications

Categorial compositionality: a category theory explanation for the systematicity of human cognition.

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