Theory and Practice of Quantitative ATL

Angelo Ferrando, Giulia Luongo, Vadim Malvone, Aniello Murano

Abstract: In multi-agent system design and reasoning, strategy logics and formal verification play pivotal roles. Numerous logic formalisms have been introduced alongside the implementation of formal verification tools. Recently, also spurred by applications in neuro-symbolic AI, there has been a growing interest in modelling and reasoning about quantitative aspects of multi-agent systems as well. This paper introduces a quantitative strategic logic called \({\textsf {ATL}\,}{[\mathcal {F}]}\), which extends the well known Alternating-time Temporal Logic with fuzzy functions. We have developed an algorithm to model check a multi-agent system with respect to an \({\textsf {ATL}\,}{[\mathcal {F}]}\) formula, and implemented it within the VITAMIN tool. The paper also provides execution examples to show how the tool behaves and scales in practice.