An ambiguity in modal logic.

On an Intuitionistic Modal Logic

In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4—our formulation has several important metatheoretic properties. In addition, we study models of IS4, not in the framework of Kripke semantics, but in the more general framework of category theo...

Acyclic modal logic: an exercise in irreflexivization

Given a unimodal logic Λ extending the modal logic of reflexive frames T = K⊕2p→ p (the symbol ⊕ is used in the same way as in [3]), we can define several irreflexive or non-reflexive counterparts of Λ. Our first approach will be semantical. As usual, given a set W , define ∆W := {〈x, x〉 | x ∈W}. Definition 1.1 The irreflexivization of a frame F = 〈W,R〉 is 〈W,R〉• := 〈W,R − ∆W 〉. For X a class o...

Modal Logic, Autumn 2007 FIrst Steps in Modal Logic

Modal logic is sometimes characterized as the logic of necessity and possibility, of “must be” and “may be”. The aim of this book is to present both semantical and syntactical features of the subject and to illustrate gy detailed analysis of the three most popular modal systems S5,S4 and K. The text presupposes some knowledge of classical logic, although the necessary information is briefly rec...

Interpolation in Modal Logic

The interpolation property and Robinson's consistency property are important tools for applying logic to software engineering. We provide a uniform technique for proving the Interpolation Property, using the notion of bisimulation. For modal logics, this leads to simple, easy{ to{check conditions on the logic which imply interpolation. We apply this result to bering of modal logics and to modal...

Completeness in modal logic