Abstract
This chapter discusses maximal models and refutation completeness. The chapter also discusses resolution, factoring, and paramodulation. It is desirable that the underlying set of inference rules have certain logical properties related to semidecidability. The key property is that of R-refutation completeness. A refutation is a proof of contradiction. The chapter provides definitions of a number of concepts such as interpretation and model. The chapter proves the maximal model theorem that states that given a particular interpretation for a given satisfiable set of disjunctions, there is a model for that set of disjunctions whose set–theoretic intersection with the particular interpretation is as small as it can be without losing the property of modelhood. Although many classic inference systems have the property of refutation completeness, they are also deduction complete and not conservative.
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