Abstract
This chapter focuses on logically possible worlds and counterpart semantics for modal logic. Originally conceived as the logic of necessity and possibility, philosophical roots of modal logic go back at least as far as Aristotle and the Stoic Diodorus Cronus. The most common semantics of modal logics introduce the notions of a world, a possibility, or a situation, and impose further structure by means of more or less complex relations, for example, by the notion of accessibility. Modal logic does not embody the commitment to possible worlds of any sort-rather the doctrines of modal realism and anti-realism are subject to considerable philosophical debate. The languages of modal predicate logic that is considered differs from the language of modal propositional logic as follows. First, there are neither propositional variables nor propositional constants. Second, first-order and second-order languages of modal predicate logic differ syntactically as well as with respect to the substitution principles assumed. This chapter discusses the notion of modal predicate logic, objects in counterpart frames, and the semantical impact of Haecceitism. Details of metaframes and status of the modal language are also presented in this chapter. © 2007 Elsevier B.V. All rights reserved.