Speaker: Johan van Benthem (ILLC, University of Amsterdam & Department of Philosophy, Stanford University & Department of Philosophy, Tsinghua University)
Date and Time: Thursday, March 19th 2026, 16:30-18:00
Venue: ILLC Seminar Room F1.15, Science Park 107 and online.
Title: Incompleteness for modal logics: What is at stake?
Abstract. Incompleteness of several modal logics was discovered in the 1970s, signalling a mismatch between what is valid in their relational frame semantics and what can be proved by the basic deductive engine of the logic.
I will explain the phenomenon, and sketch a research 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.
In doing so, my purpose is twofold: explain interesting technicalities and trigger some philosophical discussion.
You may think the risks of incompleteness occur far away from the area of agent logics or DEL. But I will present one recent candidate for incompleteness which is relatively close to the LIRa world.
Reference: J. van Benthem, ‘Incompleteness, semantics and proof systems in modal logic’, Theoria, to appear.