Studia Logica

, Volume 60, Issue 3, pp 387-420

First online:

Modal Deduction in Second-Order Logic and Set Theory - II

  • Johan van BenthemAffiliated withILLC, Universiteit van Amsterdam
  • , Giovanna D'AgostinoAffiliated withDipartimento di Matematica e, Informatica Università
  • , Angelo Montanari
  • , Alberto Policriti

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In this paper, we generalize the set-theoretic translation method for poly-modal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor such a translation to work with specific cases of extended modal logics.

Modal Logic Modal Deduction Translation Methods Second-Order Logic Set Theory