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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 FO 2 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 FO 2 satisfiability is NE xp Time-complete. We indicate that the relation between L and FO 2 provides a general framework for comparing modal and temporal languages with first-order languages.

Keywords

Modal Logic Temporal Logic Modal Parameter Expressive Power Accessibility Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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