Superdeduction in Lambda-Bar-Mu-Mu-Tilde

Clément Houtmann
(INRIA Saclay Ile de France)

Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way.

A proof-term language and a cut-elimination reduction already exist for superdeduction, both based on Christian Urban's work on classical sequent calculus. However the computational content of Christian Urban's calculus is not directly related to the (lambda-calculus based) Curry-Howard correspondence. In contrast the Lambda bar mu mu tilde calculus is a lambda-calculus for classical sequent calculus.

This short paper is a first step towards a further exploration of the computational content of superdeduction proofs, for we extend the Lambda bar mu mu tilde calculus in order to obtain a proofterm langage together with a cut-elimination reduction for superdeduction. We also prove strong normalisation for this extension of the Lambda bar mu mu tilde calculus.

In Steffen van Bakel, Stefano Berardi and Ulrich Berger: Proceedings Third International Workshop on Classical Logic and Computation (CL&C 2010), Brno, Czech Republic, 21-22 August 2010, Electronic Proceedings in Theoretical Computer Science 47, pp. 34–43.
Published: 27th January 2011.

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