Euclidean Hierarchy in Modal Logic

Euclidean Hierarchy in Modal Logic

For an Euclidean space Rn, let Ln denote the modal logic of chequered subsets of Rn. For every n ≥ 1, we characterize Ln using the more familiar Kripke semantics, thus implying that each Ln is a tabular logic over the well-known modal system Grz of Grzegorczyk. We show that the logics Ln form a decreasing chain converging to the logic L∞ of chequered subsets of R∞. As a result, we obtain that L...

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

Regression in Modal Logic

In this work we propose an encoding of Reiter’s Situation Calculus solution to the frame problem into the framework of a simple multimodal logic of actions. In particular we present the modal counterpart of the regression technique. This gives us a theorem proving method for a relevant fragment of our modal logic.