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Linear and UnitResulting Refutations for Horn Theories
 Journal of Automated Reasoning
, 1995
"... . 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 both linear (in the sense of Prologs SLDresolution) and unitresulting (i.e. the resolvents are unit clauses). This is not trivial since altho ..."
Abstract

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. 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 both linear (in the sense of Prologs SLDresolution) and unitresulting (i.e. the resolvents are unit clauses). This is not trivial since although both strategies alone are complete, their na ve combination is not. Completeness is recovered by our method through a completion procedure in the spirit of KnuthBendix 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 order clause logic over the given Horn theory. As an example application, our method discovers a generalization of the wellknown linear paramodulation calculus for the combined theory of equality and strict orderings. The met...