An Alternative Definition of Stable Models Via Łukasiewicz Logic

Abstract

Extensions of G3 (3-valued Godel logic) were studied as tools for knowledge representation and nonmonotonic reasoning. One of these extensions was studied and baptized as G′ 3 by Osorio et al. as a tool to define semantics of logic programming. In this work, we will explore the possibility to use another fuzzy logic for knowledge representation. In particular, we show that Łukasiewicz 3-valued logic (for short, Ł3) can be used for knowledge representation based on logic programming. Firstly, we prove that the definition of stable model for Ł3 is equivalent to the obtained through G3 for augmented programs, but when we consider more general programs we obtain more answers for stable models on Ł3 than G3. Finally, we present and explore a new definition of stable model based on Lukasiewicz n-valued logic via the use of Monteiro-Baaz ∆ operator.