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Some pitfalls of LK-to-LJ translations and how to avoid them

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Automated Deduction—CADE-14 (CADE 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1249))

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Abstract

In this paper, we investigate translations from a classical cut-free sequent calculus LK into an intuitionistic cut-free sequent calculus LJ. Translations known from the literature rest on permutations of inferences in classical proofs. We show that, for some classes of first-order formulae, all minimal LJ-proofs are non-elementary but there exist short LK-proofs of the same formula. Similar results are obtained even if some fragments of intuitionistic first-order logic are considered. The size of the corresponding minimal search spaces for LK and LJ are also non-elementarily related. We show that we can overcome these difficulties by extending LJ with an analytic cut rule.

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  1. Abt. Wissensbasierte Systeme 184/3, TU Wien, Treitlstraße 3, A-1040, Wien, Austria

    Uwe Egly

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  1. Uwe Egly
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William McCune

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© 1997 Springer-Verlag Berlin Heidelberg

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Egly, U. (1997). Some pitfalls of LK-to-LJ translations and how to avoid them. In: McCune, W. (eds) Automated Deduction—CADE-14. CADE 1997. Lecture Notes in Computer Science, vol 1249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63104-6_14

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  • DOI: https://doi.org/10.1007/3-540-63104-6_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63104-0

  • Online ISBN: 978-3-540-69140-2

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