Volume 7: January - December 1997

Issue 2: 1997


Modal deduction in second-order logic and set theory - I

  • Modal deduction in second-order logic and set theory - I
  • J. van Benthem1, G. D'Agostino2, A. Montanari1,2 and A. Policriti2

    1ILLC, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands and 2Dipartimento di Matematica e Informatica, Unversita di Udine, Via delle Scienze 206, 33100 Udine, Italy


    We investigate modal deduction through translation into standard logic and set theory. In a previous paper, using a set-theoretic translation method, we proved that derivability in the minimal modal logicKs corresponds precisely to derivability in a weak, computationally attractive set theory [Omega]. In this paper, this approach is shown equivalent to working with standard first-order translations of modal formulae in a theory of general frames. The employed techniques are mainly model-theoretic and set-theoretic, and they admit extensions to richer languages and modal deductive systems than that of basic modal logic. Some of these extensions are discussed in the last part of the paper.

    Keywords: Modal logic, modal deduction, translation methods, set theory, second-order logic

    Pages: 251 - 265

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