Studia Logica

, Volume 60, Issue 3, pp 387–420

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


  • Johan van Benthem
    • ILLCUniversiteit van Amsterdam
  • Giovanna D'Agostino
    • Dipartimento di Matematica eInformatica Università
  • Angelo Montanari
  • Alberto Policriti

DOI: 10.1023/A:1005037512998

Cite this article as:
van Benthem, J., D'Agostino, G., Montanari, A. et al. Studia Logica (1998) 60: 387. doi:10.1023/A:1005037512998


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 LogicModal DeductionTranslation MethodsSecond-Order LogicSet Theory

Copyright information

© Kluwer Academic Publishers 1998