A Category-Theoretic Perspective on Approximation Fixpoint Theory

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.