An Extension of the Stable Semantics via Lukasiewicz Logic

Logic Programming and fuzzy logic are active areas of research, and their scopes in terms of applications are growing fast. Fuzzy logic is a branch of many-valued logic based on the paradigm of inference under vagueness. In this work we recall some of the interplay between three 3-valued logics that are relevant in these areas: The Lukasiewicz logic, the intermediate logic G3 and the paraconsistent logic G3′, and we present a contribution to the area of answer sets that consists in extending a definition of stable model based on proof theory in logic G3, to a more general definition that can be based on any of the more expressive logics G3′ or Lukasiewicz. Finally we present and explore a new 4-valued logic that bears relation to G3 and to Lukasiewicz 4-valued logic.