Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics (Extended Version)

TL;DR

This paper demonstrates that approximation fixpoint theory can unify and extend classical semantics to fuzzy logic programming, enabling broader analysis and new semantics variants.

Contribution

It shows how stable model and well-founded semantics are reconstructed within AFT, broadening its applicability to fuzzy logic programming.

Findings

Unified classical and fuzzy semantics via AFT

Generalized stratification for fuzzy programs

Developed more precise fuzzy semantics variants

Abstract

Fuzzy logic programming is an established approach for reasoning under uncertainty. Several semantics from classical, two-valued logic programming have been generalized to the case of fuzzy logic programs. In this paper, we show that two of the most prominent classical semantics, namely the stable model and the well-founded semantics, can be reconstructed within the general framework of approximation fixpoint theory (AFT). This not only widens the scope of AFT from two- to many-valued logics, but allows a wide range of existing AFT results to be applied to fuzzy logic programming. As first examples of such applications, we clarify the formal relationship between existing semantics, generalize the notion of stratification from classical to fuzzy logic programs, and devise "more precise" variants of the semantics.