Many-Sorted Inferences in Automated Theorem Proving

A brief account of the basic ideas and advantages of many-sorted first-order logic is given. Based on this survey, a many-sorted version of a resolution calculus is proposed. The advantages of such a calculus and the problems related to its definition are illustrated with several examples. We also discuss the problems, which arise when extending this calculus with equality reasoning and present a many-sorted version of the paramodulation rule. We show how the structure of a sort hierarchy influences the inferences of our many-sorted calculus and discuss the ways to state certain axioms of a theorem proving problem by an adequate definition of a sort hierarchy. We conclude with a brief survey on related work.

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