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Temporal logics are extensively used for the specification of on-goingbehaviours of reactive systems. Two significant developments in this area arethe extension of traditional temporal logics with modalities that enable thespecification of on-going strategic behaviours in multi-agent systems, and thetransition of temporal logics to a quantitative setting, where differentsatisfaction values enable the specifier to formalise concepts such ascertainty or quality. We introduce and study FSL---a quantitative extension ofSL (Strategy Logic), one of the most natural and expressive logics describingstrategic behaviours. The satisfaction value of an FSL formula is a real valuein [0,1], reflecting `how much' or `how well' the strategic on-going objectivesof the underlying agents are satisfied. We demonstrate the applications of FSLin quantitative reasoning about multi-agent systems, by showing how it canexpress concepts of stability in multi-agent systems, and how it generalisessome fuzzy temporal logics. We also provide a model-checking algorithm for ourlogic, based on a quantitative extension of Quantified CTL*.

Reasoning about Quality and Fuzziness of Strategic Behaviours