Courses

Chitta Baral, Arizona State University, USA.
Knowledge Representation, Reasoning and Declarative Problem Solving using Answer Sets

In this course we will start with discussing the importance of knowledge representation and reasoning in the building of intelligent systems and efforts to develop a "calculus" of Knowledge and Reasoning. We will explore one of the best developed "calculus" of Knowledge and Reasoning called Answer Set Programming (ASP). Starting with the formal syntax and semantics of this logic and language we will go on to illustrate how ASP can be used to express various kinds of knowledge; how it can be used in doing various reasoning and problem solving tasks such as hypothetical reasoning, reasoning about actions and narratives, planning, diagnosis and ontological reasoning; and how it can be used in multi-agent reasoning. In these we will use available ASP solvers to write the specifications, which are also executable programs.
Rohit Parikh, CUNY, USA.
Epistemic Logic and Game Theory

Epistemic Logic and Game Theory are young fields but have acquired a great deal of importance over the last few decades. Epistemic Logic is the logical analysis of states of knowledge, not only what an agent knows about the world but also what the agent knows about what other agents know. Epistemic logic not only has applications in computer science, but also in economics, in literature, and in understanding certain aspects of animal behavior.
Game theory is a little older, going back to the major work of von Neumann and Morgenstern in the forties, as well as Nash, Aumann and others. Several Nobel prizes in economics have been given to game theorists including the latest one to Roth and Shapley. It has a strong mathematical aspect, but also has a behavioral aspect having to do with the fact that actual behavior often departs from theoretical predictions.
Famous examples of simple games include the Prisoners dilemma and the Ultimatum game. The work of Grice, Crawford and Sobel shows how game theory enters into communication.
We will give an introduction to both fields and hope that some of the audience is impelled to progress further, towards contributing to the fields.
Johann A. Makowsky, Technion - Israel Instt. of Tech., Israel.
Determinism vs non-determinism in algebraic structures: P vs NP

The lectures will be:
1. The Blum-Shub-Smale (BSS) model of computation: Register machines over algebraic structures $A$. $P_A = NP_A$ implies quantifier elimination for the first order theory of $A$.
2. The case of the reals as a real closed field with order $RCF$ and extensions by additional functions.
3. The case of the reals as an abelian group (orderd abelian group).
4. Infinite abelian groups, infinite boolean algebras, and matrix rings.
5. The ring of integers and the field of rational numbers.
More details here.

Courses

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