General problem solving with category theory

TL;DR

This paper introduces a formal framework for problem solving using category theory, modeling states and transformations to unify cognitive processes, learning, and meta-cognition in AI systems.

Contribution

It presents a novel categorical model of cognition with unique constructs like cognitive categories and meta-cognition, linking AI methods to mathematical structures.

Findings

Cognitive problems are modeled as objects in a category with states and transformations.

Meta-cognition is represented through self-referenced sub-states within the category.

Examples demonstrate the application of the framework to basic AI methods.

Abstract

This paper proposes a formal cognitive framework for problem solving based on category theory. We introduce cognitive categories, which are categories with exactly one morphism between any two objects. Objects in these categories are interpreted as states and morphisms as transformations between states. Moreover, cognitive problems are reduced to the specification of two objects in a cognitive category: an outset (i.e. the current state of the system) and a goal (i.e. the desired state). Cognitive systems transform the target system by means of generators and evaluators. Generators realize cognitive operations over a system by grouping morphisms, whilst evaluators group objects as a way to generalize outsets and goals to partially defined states. Meta-cognition emerges when the whole cognitive system is self-referenced as sub-states in the cognitive category, whilst learning must always be considered as a meta-cognitive process to maintain consistency. Several examples grounded in basic AI methods are provided as well.