AAAI Publications, 2009 AAAI Fall Symposium Series

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To Cognize Is to Categorize Revisited: Category Theory Is where Mathematics Meets Biology
Jaime Gomez, Ricardo Sanz

Last modified: 2009-10-31

Abstract


This paper claims for a shift towards "the formal sciences" in the cognitive sciences. In order to explain the phenomenon of cognition, including aspects such as learning and intelligence, it is necessary to explore the concepts and methodologies offered by the formal sciences. In particular, category theory is proposed as the most fitting tool for the building of an unified theory of cognition. This paper proposes a radically new view based in category theory is provided. A cognitive model is informally defined as a mapping between two different structures, while a structure is the set of components of a system and their relationships. Put formally in categorical terms, a model is a functor between categories that reflects the structural invariance between them. In the paper, the theory of categories is presented as the best possible framework to deal with complex system modeling -ie: biologically inspired systems that transcend and offer a much more powerful tool kit to deal with the phenomenon of cognition that other purely verbal tools like the psychological categories that Rosch or Harnad refer.

Keywords


category theory; formal models of cognition; functor; isomoprphism

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