Modal independence logic:

Modal Independence Logic

This paper introduces modal independence logic MIL, a modal logic that can explicitly talk about independence among propositional variables. Formulas of MIL are not evaluated in worlds but in sets of worlds, so called teams. In this vein, MIL can be seen as a variant of Väänänen’s modal dependence logic MDL. We show that MIL embeds MDL and is strictly more expressive. However, on singleton team...

Approaches to Independence Friendly Modal Logic

The aim of the present paper is to discuss two different approaches for formulating independence friendly (IF) modal logic. In one of them, the language of basic modal logic is enriched with the slash notation familiar from IF first-order logics, and the resulting logic is interpreted in terms of games and uniform strategies. A different approach is formulated in the present paper: an IF modal ...

Modal Logic

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, 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...