Geometric Aspects of Multiagent Systems

Recent advances in Multiagent Systems (MAS) and Epistemic Logic within Distributed Systems Theory, have used various combinatorial structures that model both the geometry of the systems and the Kripke model structure of models for the logic. Examining one of the simpler versions of these models, interpreted systems, and the related Kripke semantics of the logic $S5_n$ (an epistemic logic with $n$-agents), the similarities with the geometric / homotopy theoretic structure of groupoid atlases is striking. These latter objects arise in problems within algebraic K-theory, an area of algebra linked to the study of decomposition and normal form theorems in linear algebra. They have a natural well structured notion of path and constructions of path objects, etc., that yield a rich homotopy theory.Comment: 14 pages, 1 eps figure, prepared for GETCO200

Using Counterfactuals in Knowledge-Based Programming

: We show how counterfactuals can be added to the framework of knowledgebased programs of Fagin, Halpern, Moses, and Vardi [1995, 1997]. We show that counterfactuals allow us to capture in a natural way notions like minimizing the number of messages that are sent, whereas attempts to formalize these notions without counterfactuals lead to some rather counterintuitive behavior. We also show how knowledge-based programs with counterfactuals can capture subgame-perfect equilibria in games of perfect information. 1 Introduction Knowledge-based programs, first introduced in [Halpern and Fagin 1989] and further developed by Fagin, Halpern, Moses, and Vardi [1995, 1997], are intended to provide a high-level framework for the design and specification of protocols. Their key feature is that of allowing explicit tests for knowledge. Thus, a knowledge-based program might have the form if K(x = 0) then y := y + 1 else skip; where K(x = 0) should be read as "you know x = 0" and skip is the actio..