Proof Procedures for Disjunctive Logic Programming

Abstract

Several proof procedures have been explicitly proposed for the pure (without nonmonotonic negation) Disjunctive Logic Programming (DLP) domain. These include SLO-resolution (Rajasekar, Minker), SLI-resolution (Minker, Zanon) and near-Horn Prolog in several variants (Loveland, Reed). Other procedures extend SLD-resolution to the full first-order predicate calculus and thus are also candidates for consideration as procedures for the DLP domain. Examples include variations of Model Elimination (which includes SLI-resolution) and SLWV-resolution (Pereira, Caires and Alferes). We introduce all of these procedures, all but SLO-resolution in a common sequent-style presentation that makes comparison of procedures more direct. It is seen that all have a goal-reduction rule equivalent to that of SLD-resolution, and also some type of ancestor invocation rule. The procedures differ in the use of contra-positives and use of restart rules. We argue that near-Horn Prolog has features that make it stand out in this crowd as a logic programming language for DLP.

To have some criterion by which to judge the worth of logic programming extensions to Horn-clause logic, Miller and Nadathur introduced the notion of abstract logic programming language (ALPL). In ALPLs logical symbols exhibit a duality between truth-function and search. The ALPL proof relation must correspond to a uniform proof relation, which is based on a constrained intuitionistic sequent calculus. These constraints and the duality provide an operational semantics for such languages. We discuss this notion of ALPL and uniform proof, then interpret Inheritance near-Horn Prolog as (a slight variant of) an ALPL.