A declarative characterisation of disjunctive paraconsistent answer sets

Abstract

In this work, paraconsistent answer sets for extended disjunctive logic programs are presented as a fully declarative approach. In order to do so, we introduce a frame-based semantics. Frames are a powerful and elegant tool which have been used to characterise and study substructural logics. Unlike the original definition, no kind of syntactic transformation is employed. Indeed, paraconsistent answer sets are defined by minimising models satisfying some conditions. Considering that paraconsistent answer sets embed both answer sets and stable models, these semantics are also captured via frames.