Computing minimal models by partial instantiation

Abstract

Unlike sets of definite Horn clauses, logic programs with disjunctions of atoms in clause heads are often interpreted in terms of minimal models. It is also well known that the minimal models of logic programs are closely related to the so-called stable models of logic programs with nonmonotonic negation in clause bodies, as well as to circumscription. Methods to compute minimal models of logic programs are becoming increasingly important as an intermediate step in the computation of structures associated with nonmonotonic logic programs. However, to date, all these techniques have been restricted to the case of propositional logic programs which means that an ordinary disjunctive logic program must be “grounded out” prior to computation. Grounding out in this manner leads to a combinatorial explosion in the number of clauses, and hence, is unacceptable. In this paper, we show how, given any method M which correctly computes the set of minimal models of a propositional logic program, we can develop a strategy to compute truth in a minimal model of a disjunctive logic program P. The novel feature of our method is that it works on an “instantiate-by-need” basis, and thus avoids unnecessary grounding.