Reasoning about Quality and Fuzziness of Strategic Behaviors

Author:

Bouyer Patricia1ORCID,Kupferman Orna2ORCID,Markey Nicolas3ORCID,Maubert Bastien4ORCID,Murano Aniello4ORCID,Perelli Giuseppe5ORCID

Affiliation:

1. Université Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, Gif-sur-Yvette, France

2. Hebrew University, Jerusalem, Israel

3. Irisa, CNRS and Inria and Université de Rennes, Rennes, France

4. Università degli Studi di Napoli “Federico II”, Naples, Italy

5. Sapienza University of Rome, Rome, Italy

Abstract

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.

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science

Reference83 articles.

1. Natasha Alechina, Brian Logan, Nguyen Hoang Nga, and Abdur Rakib. 2010. Resource-bounded alternating-time temporal logic. In Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems.Wiebe van der Hoek, Gal A. Kaminka, Yves Lespérance, Michael Luck, and Sandeep Sen (Eds.), International Foundation for Autonomous Agents and Multiagent Systems, 481–488.

2. Discounting in LTL

3. Formally Reasoning About Quality

4. Latticed-LTL synthesis in the presence of noisy inputs

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1. Robust Alternating-Time Temporal Logic;Logics in Artificial Intelligence;2023

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