A mechanically verified, sound and complete theorem prover for first order logic

Authors:
Tom Ridge;James Margetson
Affiliations:
LFCS, Informatics, Edinburgh University, Scotland, UK;LFCS, Informatics, Edinburgh University, Scotland, UK
Venue:
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Year:
2005

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Abstract

We present a system of first order logic, together with soundness and completeness proofs wrt. standard first order semantics. Proofs are mechanised in Isabelle/HOL. Our definitions are computable, allowing us to derive an algorithm to test for first order validity. This algorithm may be executed in Isabelle/HOL using the rewrite engine. Alternatively the algorithm has been ported to OCaML.