This course is addressed both to students interested in the logical study of information flow in multi-agent systems and to the ones interested in the informational aspects of  the semantics and pragmatics of dialogues in natural language. It explores models and languages for reasoning about information exchanges leading to mutual knowledge updates and belief revisions among a group of communicating agents. A fundamental distinction underlying the course is the one between ``static" belief revision (formalized as a form of conditional doxastic logic, and thought of as a ``pre-encoding" of possible belief changes) and ``dynamic" belief revisions induced by real actions (learning or communication) that change the epistemic-doxastic structure. I argue that this distinction is essential in solving the well-known dillemas (such as the impossibility results concerning the ``Ramsey test") arising from a conditional understanding of belief revision. The same distinction can be used to elucidate the status of Moore sentences and to solve the so-called ``knowability paradox".

In the first hour, I present various models and logics for ``static" knowledge and conditional beliefs:  epistemic plausibility models, conditional doxastic models, conditional probabilistic models etc. I present a logic of conditional beliefs, and show its relations to the standard AGM theory of belief revision. I distinguish between two notions of ``knowledge": on one hand, ``Aumann-knowledge", stated as usual in terms of information partitions (or equivalence relations), is an ``absolutely unrevisable belief", fully introspective and thus satisfying the standard S5 axioms; on the other hand, ``Stalnaker-knowledge" (which I  will also call  ``safe belief")  is defined  as ``defeasible belief" (unrevisable by any learning of new truthful information), and satisfies only the S4 axioms. I show the importance of this distinction using examples from game theory, and show how it can be used to solve another classical epistemic-doxastic paradox. Finally, I show that the above two forms of knowledge are enough to define belief and conditional beliefs, and give a complete axiomatization of the underlying logic.

In the second hour, I move on to ``dynamic" belief revision. Following in the steps of J. van Benthem, G. Aucher, H. van Ditmarsch, B. Kooi and others who worked on extending the so-called BMS approach to incorporate belief revision, I show how each of the above-mentioned static models of knowledge and belief can be made into ``action models"; and how the BMS ``product update" operation can be naturally extended to these models, in a way that keeps close to the main principles and intuitions of the AGM theory. I show through examples how various types of ``belief updates" discussed in the literature can be recovered as special cases of this operation, simply by varying the action model; and how the epistemic-doxastic effects of various kinds of communication acts (lying, secret exchanges of messages, wiretapping or other forms of message interception, as well as various forms of cheating and suspicion) can be computed using these models. I present ``Reduction axioms" that completely axiomatize the dynamic logic of belief-revising actions, and that can be used to predict the agents' beliefs after successive communication acts in terms of their initial beliefs (and knowledge). I give an example of applying this logic to the analysis of a cryptographic communication protocol. Finally, I present some open problems.

PREREQUISITES: The only prerequisite for this course is some familiarity with Kripke models, modal languages and the standard S5, S4 and KD45 systems. But some previous acquaintance (however brief) with the AGM postulates for belief revision would be most welcome.

There is a sizeable literature on the epistemic foundations of solution concepts in non-cooperative game theory. These two lectures will provide a brief overview of the literature, focusing on conceptual issues and methodology. The first lecture will be devoted to solution concepts for strategic-form games, namely rationalizability (and refinements such as Stalnaker's notion of strong rationalizability), Nash equilibrium and correlated equilibrium.  The second will focus on solution concepts for extensive-form games, in particular backward induction and extensive form rationalizability.

PREREQUISITES. There are no prerequisites for this class. However, familiarity with Kripke structures and basic game theory would be useful.

PREPARATION. The following reading is required: Pierpaolo Battigalli and Giacomo Bonanno, "Recent results on belief, knowledge and the epistemic foundations of game theory", Research in Economics, 53 (2), June 1999, pp. 149-225. (In particular pages 149-194.)

The aim of this tutorial is to introduce the fundamentals on infinite games in the automata theoretic framework. This theory started from two motivations: algorithmic synthesis of finite-state programs with infinite behaviour (Church's Problem), and the analysis of monadic second-order logic over infinite trees (complementation via determinacy). The solution of infinite games is explained for several versions, in increasing complexity: reachability games, recurrence games, parity games, and more general types of games with complex winning conditions. The application of these results in program synthesis and in logic is outlined. Special emphasis is given to the algorithmic aspects of the theory.

As a preparation, it is recommended to get acquainted with the basic models of automata over infinite words and trees (see. e.g., W. Thomas, Languages, Automata, and Logic, in: Handbook of Formal Languages (G. Rozenberg, A. Salomaa, eds.), Vol 3, Springer 1997, Sections 5 and 6.1).