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A Tableau Calculus with Automaton-Labelled Formulae for Regular Grammar Logics

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3702))

Abstract

We present a sound and complete tableau calculus for the class of regular grammar logics. Our tableau rules use a special feature called automaton-labelled formulae, which are similar to formulae of automaton propositional dynamic logic. Our calculus is cut-free and has the analytic superformula property so it gives a decision procedure. We show that the known EXPTIME upper bound for regular grammar logics can be obtained using our tableau calculus. We also give an effective Craig interpolation lemma for regular grammar logics using our calculus.

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Author information

Authors and Affiliations

  1. The Australian National University and NICTA, Canberra, ACT, 0200, Australia

    Rajeev Goré

  2. Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Linh Anh Nguyen

Authors
  1. Rajeev Goré
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  2. Linh Anh Nguyen
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Koblenz-Landau,  

    Bernhard Beckert

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© 2005 Springer-Verlag Berlin Heidelberg

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Goré, R., Nguyen, L.A. (2005). A Tableau Calculus with Automaton-Labelled Formulae for Regular Grammar Logics. In: Beckert, B. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2005. Lecture Notes in Computer Science(), vol 3702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11554554_12

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  • DOI: https://doi.org/10.1007/11554554_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28931-9

  • Online ISBN: 978-3-540-31822-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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