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Efficient loop-check for backward proof search in some non-classical propositional logics

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Theorem Proving with Analytic Tableaux and Related Methods (TABLEAUX 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1071))

Abstract

We consider the modal logics KT and S4, the tense logic Kt, and the fragment IPC(∧,→) of intuitionistic logic.

For these logics backward proof search in the standard sequent or tableau calculi does not terminate in general. In terms of the respective Kripke semantics, there are several kinds of non-termination: loops inside a world (KT), infinite resp. looping branches (S4, IPC(∧,→)), and infinite branching degree (Kt).

We give uniform sequent-based calculi that contain specifically tailored loop-checks such that the efficiency of proof search is not deteriorated. Moreover all these loop-checks are easy to implement and can be combined with optimizations.

Note that our calculus for S4 is not a pure contraction-free sequent calculus, but this (theoretical) defect does not hinder its application in practice.

Work supported by the Swiss National Science Foundation, SPP 5003-34279.

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Authors and Affiliations

  1. Institut für Informatik und angewandte Mathematik, Universität Bern, Switzerland

    Alain Heuerding, Michael Seyfried & Heinrich Zimmermann

Authors
  1. Alain Heuerding
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  2. Michael Seyfried
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  3. Heinrich Zimmermann
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Editor information

P. Miglioli U. Moscato D. Mundici M. Ornaghi

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© 1996 Springer-Verlag Berlin Heidelberg

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Heuerding, A., Seyfried, M., Zimmermann, H. (1996). Efficient loop-check for backward proof search in some non-classical propositional logics. In: Miglioli, P., Moscato, U., Mundici, D., Ornaghi, M. (eds) Theorem Proving with Analytic Tableaux and Related Methods. TABLEAUX 1996. Lecture Notes in Computer Science, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61208-4_14

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  • DOI: https://doi.org/10.1007/3-540-61208-4_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61208-7

  • Online ISBN: 978-3-540-68368-1

  • eBook Packages: Springer Book Archive

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