Abstract
We introduce and study SL[F]—a quantitative extension of SL (Strategy Logic), one of the most natural and expressive logics describing strategic behaviours. 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?