Uniform proofs and disjunctive logic programming

One formulation of the concept of logic programming is the notion of Abstract Logic Programming Language, introduced in [8]. Central to that definition is uniform proof, which enforces the requirements of inference direction, including goal-directedness, and the duality of readings, declarative and procedural. We use this technology to investigate Disjunctive Logic Programming (DLP), an extension of traditional logic programming that permits disjunctive program clauses. This extension has been considered by some to be inappropriately identified with logic programming because the indefinite reasoning introduced by disjunction violates the goal-oriented search directionality central to logic programming. We overcome this criticism by showing that the requirement of uniform provability can be realized in a logic more general than that of DLP under a modest, sound, modification of programs. We use this observation to derive inference rules that capture the essential proof structure of InH-Prolog, a known proof procedure for DLP.