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Tractable Transformations from Modal Provability Logics into First-Order Logic

  • Stéephane Demri
  • Rajeev Goré
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1632)

Abstract

We define a class of modal logics LF by uniformly extending a class of modal logics L. Each logic L is characterised by a class of first-order definable frames, but the corresponding logic LF is sometimes characterised by classes of modal frames that are not first-order definable. The class LF includes provability logics with deep arithmetical interpretations. Using Belnap’s proof-theoretical framework Display Logic we characterise the “pseudo-displayable” subclass of LF and show how to define polynomial-time transformations from each such LF into the corresponding L, and hence into first-order classical logic. Theorem provers for classical first-order logic can then be used to mechanise deduction in these “psuedo-displayable second order” modal logics.

Keywords

Modal Logic Structural Connective Atomic Proposition Axiom Scheme Tractable Transformation 
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 1999

Authors and Affiliations

  • Stéephane Demri
    • 1
  • Rajeev Goré
    • 2
  1. 1.Laboratoire LEIBNIZ — C.N.R.S.GrenobleFrance
  2. 2.Automated Reasoning Project and Dept. of Computer ScienceAustralian National UniversityCanberraAustralia

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