Linear and unit-resulting refutations for Horn theories

Abstract

We present a new transformation method by which a given Horn theory is transformed in such a way that resolution derivations can be carried out which are bot h linear (in the sense of Prologs SLD-resolution) and unit-resulting (i.e. the resolvents are unit clauses). Thi s is not trivial since although both strategies alone are complete, their nacombination is not. Completeness is recovered by our method through a completion procedure in the spirit of Knuth-Bendix completion, however with different ordering criteria. A powerful redundancy criterion helps to find a finite system quite often . The transformed theory can be used in combination with linear calculi such as e.g. (theory) model elimination to yield sound, complete and efficient calculi for full first o rder clause logic over the given Horn theory. As an example application, our method discovers a generalization of the well-known linear paramodulation calculus for the combined theory of equality and strict orderings. The method has been implemented and has been tested in conjunction with a model elimination theorem prover.