Johan van Bentham
University of Amsterdam and Stanford University

"Logical Dynamics Today: merging update, revision, and interaction"

Abstract:

Modern 'logical dynamics' is all about putting multi-agent activities of communication, conversation, and general interaction at center stage in logic - in addition to the standard one- (or zero-) agent themes of proof or truth. In recent years, ideas from dynamic logics of action and computation have come together with epistemic/doxastic logics from philosophy to form powerful calculi for analyzing communication - and indeed, information flow triggered by any type of event. Right now, we seem to have reached a stage where these systems can be integrated with mechanisms of belief revision to form new logics beyond the traditional scope of belief revision theories. But the full story of update, revision, and communication plays in a much larger temporal setting of long-term behavior, where also ideas from game theory become relevant. In this talk, we discuss the current state of the art in the area, with a special emphasis on new types of logical question arising in societies of communicating and interacting agents.

References

J. van Benthem, 2002, 'One is a Lonely Number', Tech Report, ILLC Amsterdam. To appear in P. Koepke et al., eds., 2005, "Colloquium Logicum", AMS Publications, Providence.

J. van Benthem, 2005A, 'Open Problems in Logic and Games', manuscript, ILLC Amsterdam, http://www.illc.uva.nl/glc/

J. van Benthem, 2005B, 'Open Problems in Update Logics', to appear in T. Rozhkovskaya, ed., "Mathematical Problems from Applied Logic", Russian Academy of Sciences, Novosibirsk & Plenum Press.

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