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 $G_3^{\prime }$, 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 $G_3^{\prime }$ or Lukasiewicz. Finally we present and explore a new 4-valued logic that bears relation to G₃ and to Lukasiewicz 4-valued logic.