Paraconsistent logic programs

Abstract

We propose a framework which extends Antitonic Logic Programs [2] to an arbitrary complete bilattice of truth-values, where belief and doubt are explicitly represented. Based on Fitting's ideas, this framework allows a precise definition of important operators found in logic programming such as explicit negation and the default negation. In particular, it leads to a natural integration of explicit negation with the default negation through the coherence principle [19]. According to this principle, the explicit negation entails the default negation. We then define Coherent Answer Sets, and the Paraconsistent Well-founded Model semantics, generalizing paraconsistent semantics for logic programs (for instance, WFSXp [4]). Our framework is an extension of important classes of Antitonic Logic Programs, and is general enough to capture Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs, and Fuzzy Logic Programming. Thus, we have a powerful mathematical formalism for dealing with default reasoning, paraconsistency, and uncertainty. © 2002 Springer-Verlag.