Modal Logic (1)

1 Modal Logic Meets Situation Calculus

1 Where are the differences? In 1965, my calvinist high school class was invited for a social evening at the home of a catholic family in Den Haag. After all those textbooks on our doctrinal differences, and all our gossip about the much warmer (though of course less studious and less reliable) temperament of the other faith, every step in that house was an adventure. From the corner of my eyes...

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...

Explicit Modal Logic

In 1933 Godel introduced a modal logic of provability (S4) and left open the problem of a formal provability semantics for this logic. Since then numerous attempts have been made to give an adequate provability semantics to Godel's provability logic with only partial success. In this paper we give the complete solution to this problem in the Logic of Proofs (LP). LP implements Godel's sugges...