Reasoning about Quality and Fuzziness of Strategic Behaviours
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Temporal logics are extensively used for the specification of on-going behaviors of reactive systems. Two significant developments in this area are the extension of traditional temporal logics with modalities that enable the specification of on-going strategic behaviors in multi-agent systems, and the transition of temporal logics to a quantitative setting, where different satisfaction values enable the specifier to formalize concepts such as certainty or quality. We introduce and study SL[F], a quantitative extension of SL (Strategy Logic), one of the most natural and expressive logics describing strategic behaviors. The satisfaction value of an SL[F] formula is a real value in [0,1], reflecting ``how much'' or ``how well'' the strategic on-going objectives of the underlying agents are satisfied. We demonstrate the applications of SL[F] in quantitative reasoning about multi-agent systems, by showing how it can express concepts of stability in multi-agent systems, and how it generalises some fuzzy temporal logics. We also provide a model-checking algorithm for our logic, based on a quantitative extension of Quantified CTL*.