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

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, deening a new set-theoretic function symbol for each new modal operator, we develop a general framework within which a number of extended modal logics can be dealt with. More precisely, we 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 deal with speciic cases of extended modal logics.