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Extended Modal Dependence Logic \(\mathcal{EMDL}\)

  • Johannes Ebbing
  • Lauri Hella
  • Arne Meier
  • Julian-Steffen Müller
  • Jonni Virtema
  • Heribert Vollmer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8071)

Abstract

In this paper we extend modal dependence logic \(\mathcal{MDL}\) by allowing dependence atoms of the form dep(ϕ 1,…,ϕ n ) where ϕ i , 1 ≤ i ≤ n, are modal formulas (in \(\mathcal{MDL}\), only propositional variables are allowed in dependence atoms). The reasoning behind this extension is that it introduces a temporal component into modal dependence logic. E.g., it allows us to express that truth of propositions in some world of a Kripke structure depends only on a certain part of its past. We show that \(\mathcal{EMDL}\) strictly extends \(\mathcal{MDL}\), i.e., there exist \(\mathcal{EMDL}\)-formulas which are not expressible in \(\mathcal{MDL}\). However, from an algorithmic point of view we do not have to pay for this since we prove that the complexity of satisfiability and model checking of \(\mathcal{EMDL}\) and \(\mathcal{MDL}\) coincide. In addition we show that \(\mathcal{EMDL}\) is equivalent to \(\mathcal{ML}\) extended by a certain propositional connective.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Johannes Ebbing
    • 1
  • Lauri Hella
    • 2
  • Arne Meier
    • 1
  • Julian-Steffen Müller
    • 1
  • Jonni Virtema
    • 2
  • Heribert Vollmer
    • 1
  1. 1.Institut für Theoretische InformatikLeibniz Universität HannoverHannoverGermany
  2. 2.School of Information SciencesUniversity of TampereTampereFinland

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