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

Studia Logica 60 (3):387-420 (1998)
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.
Keywords Modal Logic  Modal Deduction  Translation Methods  Second-Order Logic  Set Theory
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