Paraconsistent Declarative Semantics for Extended Logic Programs

We introduce a fixpoint semantics for logic programs with two kinds of negation: an explicit negation and a negation-by-failure. The programs may also be prioritized, that is, their clauses may be arranged in a partial order that reflects preferences among the corresponding rules. This yields a robust framework for representing knowledge in logic programs with a considerable expressive power. The declarative semantics for such programs is particularly suitable for reasoning with uncertainty, in the sense that it pinpoints the incomplete and inconsistent parts of the data, and regards the remaining information as classically consistent. As such, this semantics allows to draw conclusions in a non-trivial way, even in cases that the logic programs under consideration are not consistent. Finally, we show that this formalism may be regarded as a simple and flexible process for belief revision.