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Outline

Title
Abstract
FAQs
Introduction
Herbelin's Calculus MJ in the Implicational Case
The Isomorphism (Typed Case)
Case MS = Apq(T, Mss)
Related Work
Conclusion and Future Work
References
All Topics
Philosophy
Logic

A permutation-free sequent calculus for intuitionistic logic

Profile image of Luis PintoLuis Pinto

1996, St Andrews University Computer Science Research Report CS/96/9 (August 1996)

Abstract

Abstract. We describe a sequent calculus MJ, based on work of Herbelin, of which the cutfree derivations are in 1-1 correspondence with the normal natural deduction proofs of intuitionistic logic. MJ (without cut) has the sub-formula property and is therefore convenient for automated proof search; it admits no permutations and therefore avoids some of the backtracking problems in LJ. We present a simple new proof of Herbelin's strong cut elimination theorem for this calculus.

FAQs

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What findings support MJ's suitability for proof search in intuitionistic logic?add

MJ demonstrates a 1-1 correspondence with dp-normal natural deduction proofs, leading to efficient proof searches. Its modification eliminates permutations, making it a permutation-free calculus compared to traditional approaches.

How does MJ's cut-elimination theorem diverge from previous research?add

MJ's approach provides a simplified proof of the strong cut-elimination theorem via recursive path ordering, differing from Herbelin's original method. This novel proof strategy enhances understanding of cut rules in sequent calculus.

In what ways does MJ tackle inefficiencies associated with permutations?add

MJ allows for direct representation of natural deductions while avoiding unwanted permutations inherent in sequent calculus. This results in a more efficient proof search process that is less prone to redundancies.

What methods are used to prove the strong normalisation property in MJ?add

The strong normalisation property is proven using an induction technique based on the SN-height of terms. Definitions and properties of cut rules align with established frameworks to ensure consistent results.

How does MJ compare with traditional sequent calculi in handling contractions?add

While MJ effectively avoids permutations, it does not simultaneously eliminate contraction issues that arise in traditional sequent calculus. Further research is required to explore completions addressing both aspects.

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