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A Tableau Calculus for Regular Grammar Logics with Converse

  • Conference paper
Automated Deduction – CADE-22 (CADE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5663))

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Abstract

We give a sound and complete tableau calculus for deciding the general satisfiability problem of regular grammar logics with converse (REG c logics). Tableaux of our calculus are defined as “and-or” graphs with global caching. Our calculus extends the tableau calculus for regular grammar logics given by Goré and Nguyen [11] by using a cut rule and existential automaton-modal operators to deal with converse. We use it to develop an ExpTime (optimal) tableau decision procedure for the general satisfiability problem of REG c logics. We also briefly discuss optimizations for the procedure.

Supported by the MNiSW grants N N206 3982 33 and N N206 399334.

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Authors and Affiliations

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

    Linh Anh Nguyen & Andrzej Szałas

  2. Department of Computer and Information Science, Linköping University, SE-581 83, Linköping, Sweden

    Andrzej Szałas

Authors
  1. Linh Anh Nguyen
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  2. Andrzej Szałas
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Editors and Affiliations

  1. School of Computer Science, The University of Manchester, Manchester, UK

    Renate A. Schmidt

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Nguyen, L.A., Szałas, A. (2009). A Tableau Calculus for Regular Grammar Logics with Converse. In: Schmidt, R.A. (eds) Automated Deduction – CADE-22. CADE 2009. Lecture Notes in Computer Science(), vol 5663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02959-2_31

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  • DOI: https://doi.org/10.1007/978-3-642-02959-2_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02958-5

  • Online ISBN: 978-3-642-02959-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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