Fuzzy Propositional Formulas under the Stable Model Semantics

TL;DR

This paper introduces a stable model semantics for fuzzy propositional formulas, enabling nonmonotonic reasoning with graded truth degrees and extending classical stable model properties to a fuzzy, many-valued context.

Contribution

It defines a novel stable model semantics for fuzzy propositional logic, generalizing existing frameworks and enhancing reasoning in dynamic, graded-truth domains.

Findings

Properties of Boolean stable models extend to fuzzy setting

The semantics allows for configurable nonmonotonic reasoning

Connections to other fuzzy logic and stable model approaches are discussed

Abstract

We define a stable model semantics for fuzzy propositional formulas, which generalizes both fuzzy propositional logic and the stable model semantics of classical propositional formulas. The syntax of the language is the same as the syntax of fuzzy propositional logic, but its semantics distinguishes stable models from non-stable models. The generality of the language allows for highly configurable nonmonotonic reasoning for dynamic domains involving graded truth degrees. We show that several properties of Boolean stable models are naturally extended to this many-valued setting, and discuss how it is related to other approaches to combining fuzzy logic and the stable model semantics.