Safe beliefs for propositional theories

Abstract

We propose an extension of answer sets, that we call safe beliefs, that can be used to study several properties and notions of answer sets and logic programming from a more general point of view. Our definition, based on intuitionistic logic and following ideas from D. Pearce [Stable inference as intuitionistic validity, Logic Programming 38 (1999) 79–91], also provides a general approach to define several semantics based on different logics or inference systems. We prove that, in particular, intuitionistic logic can be replaced with any other proper intermediate logic without modifying the resulting semantics. We also show that the answer set semantics satisfies an important property, the “extension by definition”, that can be used to construct program translations. As a result we are able to provide a polynomial translation from propositional theories into the class of disjunctive programs.