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International Tbilisi Symposium on Logic, Language, and Computation

TbiLLC 2011: Logic, Language, and Computation pp 231–256Cite as

Model Checking for Modal Intuitionistic Dependence Logic

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7758)

Abstract

Modal intuitionistic dependence logic (\(\mathcal MIDL \)) incorporates the notion of “dependence” between propositions into the usual modal logic and has connectives which correspond to intuitionistic connectives in a certain sense. It is the modal version of a variant of first-order dependence logic (Väänänen 2007) considered by Abramsky and Väänänen (2009) basing on Hodges’ team semantics (1997).

In this paper, we study the computational complexity of the model checking problem for \(\mathcal MIDL\) and its fragments built by restricting the operators allowed in the logics. In particular, we show that the model checking problem for \(\mathcal MIDL\) in general is PSPACE-complete and that for propositional intuitionistic dependence logic is coNP-complete.

ACMSubject Classifiers

  • F.2.2 Complexity of proof procedures
  • F.4.1 Modal logic
  • D.2.4 Model checking

Keywords

  • dependence logic
  • intuitionistic logic
  • modal logic
  • model checking
  • computational complexity

This work was supported by DAAD grant 50740539 and by grant 138163 of the Academy of Finland. It was also partially supported by the EUROCORES LogICCC LINT programme and the NTH Focused Research School for IT Ecosystems.

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  • DOI: 10.1007/978-3-642-36976-6_15
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Author information

Authors and Affiliations

  1. Theoretical Computer Science, Leibniz University Hannover, Appelstr. 4, 30167, Hannover, Germany

    Johannes Ebbing & Peter Lohmann

  2. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, Gustaf Hällströmin katu 2b, FIN-00014, Finland

    Fan Yang

Authors
  1. Johannes Ebbing
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  2. Peter Lohmann
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  3. Fan Yang
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, 88003, Las Cruces, NM, USA

    Guram Bezhanishvili

  2. Department of Language and Information, Heinrich Heine Universität, Kruppstrasse 108, 40227, Düsseldorf, Germany

    Sebastian Löbner

  3. Dipartimento di Matematica "Fredigo Enriques", Università degli Studi di Milano, via Cesare Saldini, 50, 20133, Milan, Italy

    Vincenzo Marra

  4. Seminar für Sprachwissenschaft, Universität Tübingen, Wilhelmstraße 19, 72074, Tübingen, Germany

    Frank Richter

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Ebbing, J., Lohmann, P., Yang, F. (2013). Model Checking for Modal Intuitionistic Dependence Logic. In: Bezhanishvili, G., Löbner, S., Marra, V., Richter, F. (eds) Logic, Language, and Computation. TbiLLC 2011. Lecture Notes in Computer Science, vol 7758. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36976-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-36976-6_15

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