Event Detail

Incompleteness of several modal logics was discovered in the 1970s, signaling a mismatch between what is valid in their relational frame semantics and what can be proved by the basic deductive engine of the logic. This has often been taken to be a serious limitation of Kripke semantics.

I will explain the phenomenon, and sketch a ‘reverse logic’ program of analyzing semantic arguments in terms of the proof strength they require. Next I will raise some broader issues such as the connection/tension between semantics and proof theory in logic, and what is the real content of completeness theorems.

My purpose is twofold: explain interesting technical issues at the interface of semantics and proof systems, and trigger some philosophical discussion of what all this means.

Ref. J. van Benthem, ‘Incompleteness, semantics and proof systems in modal logic’, Theoria, to appear.