Theoretical Computer Science
Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic
Journal of Symbolic Logic
Phase semantic cut-elimination and normalization proofs of first- and higher-order linear logic
Theoretical Computer Science - Special issue on linear logic, 1
Theoretical Computer Science
Journal of Automated Reasoning
A simple proof that super-consistency implies cut elimination
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Truth values algebras and proof normalization
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
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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.