Abstract. We present an approach to the problem of verification of epistemic properties in multi-agent systems by means of symbolic model checking. In particular, it is shown how to extend the technique of unbounded model checking from a purely temporal setting to a temporalepistemic one. In order to achieve this, we base our discussion on interpreted systems semantics, a popular semantics used in multi-agent systems literature. We give details of the technique and show how it can be applied to the well known train, gate and controller problem.

This paper deals with the problem of verification of game-like structures by means of symbolic model checking. Alternating-time Temporal Epistemic Logic (ATEL) is used for expressing properties of multi-agent systems represented by alternating epistemic temporal systems as well as concurrent epistemic game structures. Unbounded model checking (a SAT based technique) is applied for the first time to verification of ATEL. An example is given to show an application of the technique.

Alternating-time Temporal Logic (ATL) is typically applied for specifying properties of multiagent systems modelled by game-like structures. This paper deals with verification of ATL by means of a fully symbolic model checking. Unbounded model checking (a SAT-based technique) is applied for the first time to verification of AT. Several examples are given in order to present an application of the technique.

Ordered fuzzy numbers (OFN) invented by the second author and his two coworkers in 2002 make possible to utilize the fuzzy arithmetic and to construct the Abelian group of fuzzy numbers and then an ordered ring. The definition of OFN uses the extension of the parametric representation of convex fuzzy numbers. Fuzzy implication is proposed with the help of algebraic operations and a lattice structure defined on OFN.

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