A Mechanically Verified, Sound and Complete Theorem Prover for First Order Logic

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...

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Bibliographic Details
Published inLecture notes in computer science pp. 294 - 309
Main Authors Ridge, Tom, Margetson, James
Format Book Chapter Conference Proceeding
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2005
Springer
SeriesLecture Notes in Computer Science
Subjects
Applied sciences
Automate Reasoning
Computer science; control theory; systems
Derivation Tree
Exact sciences and technology
Logical System
Logical, boolean and switching functions
Order Logic
Proof Theory
Theoretical computing
High order logic
OCaml language
Proof theory
First order logic
Theorem proving
Semantics
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ISBN3540283722
9783540283720
ISSN0302-9743
1611-3349
DOI10.1007/11541868_19

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Summary: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.
ISBN:3540283722
9783540283720
ISSN:0302-9743
1611-3349
DOI:10.1007/11541868_19