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Preprints, Working Papers, ... Year : 2011

Orthogonality and Boolean Algebras for Deduction Modulo

Abstract

Originating from automated theorem proving, deduction modulo removes computational arguments from proofs by interleaving rewriting with the deduction process. From a proof-theoretic point of view, deduction modulo defines a generic notion of cut that applies to any first-order theory presented as a rewrite system. In such a setting, one can prove cut-elimination theorems that apply to many theories, provided they verify some generic criterion. Pre-Heyting algebras are a generalization of Heyting algebras which are used by Dowek to provide a semantic intuitionistic criterion called superconsistency for generic cut-elimination. This paper uses pre-Boolean algebras (generalizing Boolean algebras) and biorthogonality to prove a generic cut-elimination theorem for the classical sequent calculus modulo. It gives this way a novel application of reducibility candidates techniques, avoiding the use of proof-terms and simplifying the arguments.
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Dates and versions

inria-00563331 , version 1 (04-02-2011)

Identifiers

  • HAL Id : inria-00563331 , version 1

Cite

Alois Brunel, Olivier Hermant, Clement Houtmann. Orthogonality and Boolean Algebras for Deduction Modulo. 2011. ⟨inria-00563331⟩
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