A computable semantics for general logic programs

Abstract

Semantics for positive programs have been thoroughly explored in the context of Herbrand models through the immediate consequence function T. For general logic programs, i.e. programs whose clauses may contain negative literals in their body, parallel semantics have been developed using three-valued logic and a new immediate consequence function Φ. However, over Herbrand models this semantics is not in general computable. A computable subclass is introduced in this paper, termed the canonical general programs. Our main result is to show, constructively, that thislatter class is in some sense representative of all general logic programs, thus extending to general logic programs a result proven recently by Jaffar and Stuckey for positive logic programs. The new result is obtained by providing a transformation which, given any general logic program GP, produces a canonical general logic program CGP “semantically equivalent” to GP in the sense that it has the same success set and finite failure set. It intuitively means that the declarative semantics of CGP captures exactly the set of answer computable from GP.