Modal Deduction in Second-Order Logic and Set Theory - II |
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Authors: | van Benthem Johan D'Agostino Giovanna Montanari Angelo Policriti Alberto |
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Affiliation: | (1) ILLC, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands;(2) Dipartimento di Matematica e, Informatica Università, di Udine Via delle Scienze 206, I-33100 Udine, Italy |
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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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Keywords: | Modal Logic Modal Deduction Translation Methods Second-Order Logic Set Theory |
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