A Double-Categorical Framework for Constructive Cognitive Architectures

Explore a double-categorical framework for constructive cognitive architectures in this 12-minute conference talk from the Models of Consciousness Conferences. Delve into the mathematical foundations of computational cognitive architectures, examining an approach based on virtual equipments, double-pushout rewriting, and profunctor optics. Investigate the categorification of cognitive systems and consider intriguing questions that arise, including the potential explanation for the utility of quantum probability theory in cognitive science. Cover topics such as symbolic cognitive architectures, rewriting categorically, virtual double categories, recognition of rewrite rules in free categories, dynamics from a functor of possible worlds, and various perspectives on cognition including change-of-base, learner models, and internal quiver theory.

Intro
Symbolic cognitive architectures
Rewriting categorically
Virtual double categories
The basics: Vertical arrows, horizontal arrows and 2-cells
Recognition of rewrite rules in free categories
Dynamics from a functor of possible worlds
Cognition as change-of-base
Cognition as a learner
Cognition as internal quiver theory
Quantum probability in cognitive science