Topics in Dynamic Epistemic Logic 2011-2012

TOPICS IN DYNAMIC EPISTEMIC LOGIC

(Spring 2011, ILLC, University of Amsterdam)

Instructor

ALEXANDRU BALTAG

Objectives of Course

First, to present to students the main concepts and formalism of Dynamic Epistemic Logic (DEL), including recent developments on connections to other fields (from Epistemology and Learning Theory to Game Theory, Social Software, Pragmatics, Quantum Information etc). Second, to enable students to acquire some research experience, by discussing some of the outstanding conceptual challenges in the field, as well as more technical open questions, and giving them guidance and encouragement to tackle some of these issues in their final projects.

Contents

This course is addressed to students and researchers interested in logics for reasoning about multi-agent belief revision, belief updates and knowledge updates induced by various forms of communication or interaction. We start by presenting the main concepts of "standard DEL" (as covered e.g. in the book ``Dynamic Epistemic Logic" and in several ESSLLI courses with the same name): multi-agent epistemic Kripke models, public announcements, epistemic event models, product update, and the corresponding dynamic logics. Then we present the more recent "belief-revision-friendly" version of DEL and its main concepts (plausibility models, the Action-Priority Update), by combining the techniques of Dynamic Epistemic Logic with the insights and models from Belief Revision theory. We formalize various types of doxastic attitudes (belief, strong belief, safe belief, conditional belief, degrees of belief, group belief), notions of defeasible "knowledge", belief upgrades and belief-revision policies etc. We give some axiomatizations and apply these notions to communication strategies and the pragmatics of Natural Language, to rationality and strategic reasoning in Game Theory, to the formalization of key concepts in modern Epistemology, and to the analysis of various epistemic-doxastic paradoxes and puzzles (Fitch's knowability paradox, the Puzzle of the Perfect Believer, the Muddy Children, the Surprise Examination etc). Further, we present various extensions of this setting (to dynamics of probabilistic beliefs, dynamics of evidence and justification etc), as well as recent work at the interface of DEL with Learning Theory, Epistemology, Social Choice theory, Quantum Information, Secure Communication etc. We discuss some of the on-going conceptual challenges and the open technical questions encountered in the field, and we encourage and guide students to start tackling some of these problems.

Recommended prior knowledge

We presuppose some (but very little) background knowledge in Logic: basically, the syntax and semantics of modal logic. This should be enough for understanding the course, though obviously having more prior knowledge can only lead to better final projects. Having some more advanced technical knowledge of Modal Logic theory would be very useful for tackling some of the open questions, but it is not required. Some familiarity with, or at least some interest in, any of the above-mentioned areas of intended application (Epistemology, Pragmatics, Game Theory, Multi-Agent Systems etc) would also be very welcome, and particularly useful for tackling some of the more conceptual challenges. More importantly, we assume that participants in the course possess both some degree of mathematical maturity (as can be expected from students in logic at a MSc level) and a live interest in interdisciplinary connections and applications of Logic.

Format

Lectures and office hours.

Study materials

There is no main textbook for this course. The principal material consists in slides of lectures, which will be regularly made available after each lecture. In addition, I will refer to a number of textbooks and materials, among which the most important are:

A. Baltag, H. P. van Ditmarsch and L.S. Moss, Epistemic logic and information update, in the Handbook of Philosophy of Information (Editors: P. Adriaans and J. van Benthem), part of the series Handbook of Philosophy of Science, vol. 8, pp. 361-455, Elsevier, 2008. Electronically available HERE

J. van Benthem, Logical Dynamics of Information and Interaction, Cambridge Univ Press, 2011.

H. P. van Ditmarsch, W. van der Hoek and B. Kooi , Dynamic Epistemic Logic, Springer, 2007.

R. Fagin, J.Y. Halpern, Y. Moses and M.Y. Vardi, Reasoning about Knowledge, MIT Press, Cambridge MA 1995.