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International Joint Conference on Automated Reasoning

IJCAR 2006: Automated Reasoning pp 541–556Cite as

Presburger Modal Logic Is PSPACE-Complete

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4130))

Abstract

We introduce a Presburger modal logic PML with regularity constraints and full Presburger constraints on the number of children that generalize graded modalities, also known as number restrictions in description logics. We show that PML satisfiability is only pspace-complete by designing a Ladner-like algorithm that can be turned into an analytic proof system. algorithm. This extends a well-known and non-trivial pspace upper bound for graded modal logic. Furthermore, we provide a detailed comparison with logics that contain Presburger constraints and that are dedicated to query XML documents. As an application, we show that satisfiability for Sheaves Logic SL is pspace-complete, improving significantly its best known upper bound.

The second author has been supported by the research program ACI ”Masse de données”.

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Author information

Authors and Affiliations

  1. Laboratoire Spécification et Vérification CNRS & INRIA Futurs projet SECSI & ENS Cachan,  

    Stéphane Demri

  2. Laboratoire d’Informatique Fondamentale, Marseille UMR 6166 CNRS-Université de Provence,  

    Denis Lugiez

Authors
  1. Stéphane Demri
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  2. Denis Lugiez
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Artificial Intelligence Research Group, University of Koblenz-Landau, Universitätsstr. 1, 56070, Koblenz

    Ulrich Furbach

  2. SRI International, MS EL256,, 333 Ravenswood Avenue, 94025-3493, Menlo Park, CA, USA

    Natarajan Shankar

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Demri, S., Lugiez, D. (2006). Presburger Modal Logic Is PSPACE-Complete. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_44

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  • DOI: https://doi.org/10.1007/11814771_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37187-8

  • Online ISBN: 978-3-540-37188-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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