Classical Natural Deduction for S4 Modal Logic

  • Daisuke Kimura
  • Yoshihiko Kakutani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5904)

Abstract

This paper proposes a natural deduction system CNDS4 for classical S4 modal logic with necessity and possibility modalities. This new system is an extension of Parigot’s Classical Natural Deduction with dual-context to formulate S4 modal logic. The modal λμ-calculus is also introduced as a computational extraction of CNDS4. It is an extension of both the λμ-calculus and the modal λ-calculus. Subject reduction, confluency, and strong normalization of the modal λμ-calculus are shown. Finally, the computational interpretation of the modal λμ-calculus, especially the computational meaning of the modal possibility operator, is discussed.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Daisuke Kimura
    • 1
  • Yoshihiko Kakutani
    • 1
  1. 1.Department of Computer ScienceUniversity of TokyoTokyoJapan

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