Towards Alternating-Time Temporal Logic with Uncertainty and Fuzziness

Alternating-time temporal logic (ATL or more generally, ATL*) is a logic for reasoning about computational models of multi-agent decision-making. It mainly deals with strategic capabilities of agent coalitions in multi-player games. Whilst ATL* is useful for the specification and verification of multi-agent systems, it needs further extensions for modeling human players because they usually have to make decisions with uncertain and vague information. As probability calculus is the standard approach to model uncertain information, there have been some probabilistic extensions of ATL. However, in real-world situations, forms of incomplete information are diverse. Hence, in this paper, we propose another two extensions of ATL* to accommodate incomplete information. On one hand, the possibilistic ATL* can represent and reason about uncertainty arising from imprecise predictions of outcomes caused by agents' actions in terms of possibility theory. On the other hand, the many-valued ATL* facilitates the representation and reasoning of fuzzy events. In both extensions, we introduce the syntax and formal semantics of the proposed logics.