Modal Deduction in Second-Order Logic and Set Theory - II
- Cite this article as:
- van Benthem, J., D'Agostino, G., Montanari, A. et al. Studia Logica (1998) 60: 387. doi:10.1023/A:1005037512998
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In this paper, we generalize the set-theoretic translation method for poly-modal logic introduced in  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.