Abstract
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.
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van Benthem, J., D'Agostino, G., Montanari, A. et al. Modal Deduction in Second-Order Logic and Set Theory - II. Studia Logica 60, 387–420 (1998). https://doi.org/10.1023/A:1005037512998
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DOI: https://doi.org/10.1023/A:1005037512998