Embedding Functions into Disjunctive Logic Programs

Abstract

We extend the notions of completion and loop formulas of normal logic programs with functions to a class of nested expressions that properly include disjunctive logic programs. We show that answer sets for such a logic program can be characterized as the models of its completion and loop formulas. These results provide a basis for computing answer sets of disjunctive programs with functions, by solvers for the Constraint Satisfaction Problem. The potential benefit in answer set computations for this approach has been demonstrated previously in the implementation called fasp. We also present a formulation of completion and loop formulas for disjunctive logic programs with variables. This paper focuses on the theoretical development of these extensions.