A Category-Theoretic Perspective on Approximation Fixpoint Theory

TL;DR

This paper explores how category theory can extend Approximation Fixpoint Theory (AFT), a framework for non-monotonic logic semantics, aiming to unify and generalize its application in computer science.

Contribution

It introduces a category-theoretic perspective to AFT, proposing a more general framework for constructive knowledge and semantic structures in non-monotonic reasoning.

Findings

Category theory provides new insights into AFT.

AFT can be extended to broader semantic frameworks.

Potential applications in database theory and argumentation.

Abstract

Approximation Fixpoint Theory (AFT) was founded in the early 2000s by Denecker, Marek, and Truszczy\'nski as an abstract algebraic framework to study the semantics of non-monotonic logics. Since its early successes, the potential of AFT as a unifying semantic framework has become widely recognised, and the interest in AFT has gradually increased, with applications now ranging from foundations of database theory to abstract argumentation. The non-monotonic constructive processes that occur in many more areas of computer science, together with their associated semantic structures, can be successfully studied using AFT, which greatly simplifies their characterizations. The goal of my research is to take a step towards the lifting of AFT into a more general framework for constructive knowledge.