Abstract

The paper contains an exposition of standard ND-formalizations for modal logics. For the sake of simplicity, it is limited to propositional monomodal logics because focus is on methods not on logics. Some of the discussed approaches, however, may be easily extended to first order modal logics of different sorts or to multimodal logics . Natural Deduction is understood in the strict sense, explained below; neither Gentzen Sequent Calculus, nor Tableau Systems belong to that group. Moreover, some ND-systems with generalized apparatus, like [2] or [3] are also omitted in this survey. There are four basic approaches to modality via NDformalization, which are compared and evaluated with respect to their generality: modalization of assumptions, modalization of reiteration rule, modalization of rules, application of modal assumptions. We focus on practical matters, especially on the applicability of discussed approaches, the only exception is the discussion of independent rules for necessity and possibility in the last section