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Article Dans Une Revue ACM Transactions on Computational Logic Année : 2023

Reasoning about Quality and Fuzziness of Strategic Behaviors

Résumé

Temporal logics are extensively used for the specification of on-going behaviors of computer 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. In the first class, SL ( Strategy Logic ) is one of the most natural and expressive logics describing strategic behaviors. In the second class, a notable logic is LTL[ℱ] , which extends LTL with quality operators . In this work, we introduce and study SL[ℱ] , which enables the specification of quantitative 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, showing how it can express and measure concepts like stability in multi-agent systems, and how it generalizes some fuzzy temporal logics. We also provide a model-checking algorithm for SL[ℱ] , based on a quantitative extension of Quantified CTL ⋆ . Our algorithm provides the first decidability result for a quantitative extension of Strategy Logic. In addition, it can be used for synthesizing strategies that maximize the quality of the systems’ behavior.
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hal-04219131 , version 1 (26-09-2023)

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Patricia Bouyer, Orna Kupferman, Nicolas Markey, Bastien Maubert, Aniello Murano, et al.. Reasoning about Quality and Fuzziness of Strategic Behaviors. ACM Transactions on Computational Logic, 2023, 24 (3), pp.1-38. ⟨10.1145/3582498⟩. ⟨hal-04219131⟩
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