Fuzzy Propositional Formulas under the Stable Model Semantics
This work provides a configurable nonmonotonic reasoning framework for dynamic domains with graded truth, but it is incremental as it builds on existing fuzzy and stable model semantics.
The paper tackles the problem of extending stable model semantics to fuzzy propositional formulas, generalizing both fuzzy logic and classical stable models, and shows that key properties from Boolean stable models extend to this many-valued setting.
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.