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 S5n (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. In this paper, we examine what an geometric analysis of the model may tell us of the MAS. Also the analogous notion of path will be analysed for interpreted systems and S5n-Kripke models, and is compared to the notion of ‘run’ as used with MASs. Further progress may need adaptions to handle S4n rather than S5n and to use directed homotopy rather than standard ‘reversible’ homotopy. Geometric Aspects of Multiagent Systems