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

Johan van Benthem, Giovanna D'Agostino, Angelo Montanari and Alberto Policriti
Studia Logica: An International Journal for Symbolic Logic
Vol. 60, No. 3 (May, 1998), pp. 387-420
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015978
Page Count: 34
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Modal Deduction in Second-Order Logic and Set Theory: II
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Abstract

In this paper, we generalize the set-theoretic translation method for polymodal 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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