A Computational Interpretation of Modal Proofs

  • Simone Martini
  • Andrea Masini
Part of the Applied Logic Series book series (APLS, volume 2)


Proof theory of modal logics, though largely studied since the fifties, has always been a delicate subject, the main reason being the apparent impossibility to obtain elegant, natural systems for intensional operators (with the excellent exception of intuitionistic logic). For example Segerberg, not earlier than 1984 [5], observed that the Gentzen format, which works so well for truth functional and intuitionistic operators, cannot be a priori expected to remain valid for modal logics; carrying to the limit this observation one could even assert that ‘logics with no good proof theory are unnatural.’ In such a way we should mark as ‘unnatural’ all modal logics (with great delight of a large number of logicians!).


Modal Logic Accessibility Relation Intuitionistic Logic Natural Deduction Proof Theory 
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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Simone Martini
    • 1
  • Andrea Masini
    • 2
  1. 1.University of UdineItaly
  2. 2.University of PisaItaly

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