A modal contrastive logic: The logic of ‘but’

Contrastive Logic

In this paper I introduce the notion of bilogics, namely logics interpreted over a pair of structures, in contrast to classical logic and many of its variations, the formulae of which are interpreted over one structure. In particular, I introduce and study Contrastive Logic, suitable for expressing contrast and conformity between the two structures involved. A major reason for this study is str...

Modal Logic As Dialogical Logic

The title reflects my conviction that, viewed semantically, modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy. Nonetheless, by making use of ideas which trace back to Arthur Prior (notab...

Modal Logic

The true modal logic

For Arthur Prior, the construction of a logic was a supremely philosophical task. As a logician, he could of course appreciate a finely crafted formal system for its own sake, independent of its " meaning " or philosophical significance. But a genuine logic-a good one, at least-lays bare the nature of those concepts that it purports to be a logic of: and this comes only by way of deep rellec-ti...

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...