Modal Logic and the Two-Variable Fragment

  • Carsten Lutz
  • Ulrike Sattler
  • Frank Wolter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2142)

Abstract

We introduce a modal language L which is obtained from standard modal logic by adding the difference operator and modal operators interpreted by boolean combinations and the converse of accessibility relations. It is proved that L has the same expressive power as the two-variable fragment FO2 of first-order logic but speaks less succinctly about relational structures: if the number of relations is bounded, then L- satisfiability is ExpTime-complete but FO2satisfiability is NExpTime-complete. We indicate that the relation between L and FO2 provides a general framework for comparing modal and temporal languages with first-order languages.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Carsten Lutz
    • 1
  • Ulrike Sattler
    • 1
  • Frank Wolter
    • 2
  1. 1.LuFG Theoretical Computer ScienceRWTH AachenAachenGermany
  2. 2.Institut für InformatikUniversität LeipzigLeipzigGermany

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