A Declarative Characterisation of Disjunctive Paraconsistent Answer Sets

In this work, paraconsistent answer sets for extended disjunctive logic programs are presented in terms of a fully declarative approach. In order to do that, we introduce a frame-based semantics. It is known 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 operation (like the program reduct) is employed in the process. Indeed, paraconsistent answer sets are defined simply by minimising models satisfying some particular conditions. Furthermore, considering that paraconsistent answer sets embed both answer sets and stable models, these semantics are also captured via frames.