On the semantics of negations in logic programming

Abstract

An extended logic program (ELP) is a logic program that allows for classical negation as well as for negation-as-failure. Previous proposals for ELP semantics can be divided into two classes. The first class avoids contradictions by means of an unnatural discrimination between positive literals and negative literals. In the second class, positive and negative literals have the same status, but contradictions may occur and therefor these semantics are not universally consistent (some programs have no consistent models). As both classes have their own specific shortcomings, we propose a new model-theoretic semantics for ELPs, called the pure semantics, based on the notions of unfounded set and assumption set. The pure semantics for ELPs resolves all contradictions while preserving the same status for positive and negative literals, thus overcoming the imperfections of previous semantics. This paper uses and extends the results obtained inLae92a where a simplification and unification of the semantics for general logic programs (i.e. ELPs that don't contain classical negation) was proposed.