Reasoning about Quality and Fuzziness of Strategic Behaviours

Abstract

Temporal logics are extensively used for the specification of on-going behaviours 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 behaviours in multi-agent systems, and the transition of temporal logics to a quantitative setting, where different satisfaction values enable the specifier to formalise 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 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 ⋆ .

Strategic Reasoning in Automated Mechanism Design

“…SL has been extended to handle imperfect information and knowledge operators (Berthon et al 2021;Belardinelli et al 2020;Maubert and Murano 2018), but none of these logics can account for quantitative aspects. Recently, SL[F ] (Bouyer et al 2019a) was introduced as a quantitative extension of SL. By introducing quantitative values in the models and functions in the language, it enables the reasoning about all key concepts involved in auctions: utilities, payments, goods and quantities.…”

“…SL[F ] (Bouyer et al 2019a) introduces quantitative aspects in SL, but it lacks the ability to handle imperfect information inherent to the auction scenarios that we aim at modeling, where agents may ignore other agents' preferences for instance. We thus introduce SLK[F ], which extends SL[F ] with imperfect information and knowledge operators.…”

“…Remark 1. In (Bouyer et al 2019a), values are meant to represent degrees of truth value in [0, 1] where 0 corresponds to "false" and 1 corresponds to "true", as in Fuzzy Logics. In this setting, negation ¬ is the function x → 1 − x.…”

“…Unlike ATL, which it subsumes, it allows for explicit manipulation of strategies, and it can express important concepts in non-zero-sum games, such as Nash equilibria. Its recent quantitative extension SL[F ] (Bouyer et al 2019a) introduces values in models and functions in the language, enabling the reasoning about key game-theoretic concepts such as utilities and preferences. Several works have also considered extensions of SL with imperfect information, which is also an important feature in many systems of interest in mechanism design such as voting or auction systems.…”

Autonomics: In search of a foundation for next-generation autonomous systems

“…Also, not only is the behavioral specification of the system itself very hard, but it is no easier to specify the assertions that describe the behavior we want to verify in terms that are readily aligned with the expectations of the human users and engineers. This is further complicated by the fact that whether some behavior is desired or not may not by a binary decision but a quantitative one, spanning multiple scales (37).…”