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1998 Technical Reports

On the Soundness and Completeness of Equational Predicate Logics

George Tourlakis

Technical Report CS-1998-08

York University

November 2, 1998


We present two different formalizations of Equational Predicate Logic, that is, first order logic that uses Leibniz's substitution of equals for equals as a primary rule of inference.

We prove that both versions are sound and complete. A by-product of this study is an alternative proof to that contained in [GS3], that the full Leibniz rule is strictly stronger than the no-capture Leibniz rule, this result obtained here for a complete Logic. We also show that under some reasonable conditions, propositional Leibniz, no-capture Leibniz, and a full-capture version are all equivalent, provided that the latter is restricted to act on universally valid premises whenever capture is allowed.

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