Deciding Horn classes by hyperresolution

Abstract

It is shown that positive hyperresolution can be used as decision procedure for solvable classes of Horn clause sets. Rather than by quantifier prefixes or by propositional features these classes are characterized by variable occurrence — and term depth properties. Special attention is given to a subclass of the Horn clause implication problem, which can be represented as consistency problem; to decide ∀C→∀D, ( ∀C denotes the universal closoure of C, C is a Horn clause, D is an arbitrary clause ) we apply hyperresolution to the clause form of ∀C∧⌍∀D. Special techniques can be used in handling such implication clause forms, because there is only one rule, ground unit facts and ground unit goals. The sharp boundary between solvable and unsolvable classes is illustrated, and a complexity analysis of some classes is given.