{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T21:19:48Z","timestamp":1767993588030,"version":"3.49.0"},"reference-count":83,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T00:00:00Z","timestamp":1680825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2023,7,31]]},"abstract":"<jats:p>\n            <jats:italic>Temporal logics<\/jats:italic>\n            are extensively used for the specification of on-going behaviors of computer systems. Two\u00a0significant developments in this area are the extension of traditional temporal logics with modalities that enable the specification of on-going\n            <jats:italic>strategic<\/jats:italic>\n            behaviors in multi-agent systems, and the transition of temporal logics to a\n            <jats:italic>quantitative<\/jats:italic>\n            setting, where different satisfaction values enable the specifier to formalize concepts such as certainty or quality. In the first class, SL\u00a0(\n            <jats:italic>Strategy Logic<\/jats:italic>\n            ) is one of the most natural and expressive logics describing strategic behaviors. In the second class, a notable logic is LTL[\u2131]\u00a0, which extends LTL\u00a0with\n            <jats:italic>quality operators<\/jats:italic>\n            .\n          <\/jats:p>\n          <jats:p>\n            In this work, we introduce and study\n            <jats:italic>SL[\u2131]\u00a0<\/jats:italic>\n            , which enables the specification of quantitative strategic behaviors. The\u00a0satisfaction value of an SL[\u2131] formula is a real value in\u00a0[0,1], reflecting \u201chow much\u201d or \u201chow well\u201d the strategic on-going objectives of the underlying agents are satisfied. We demonstrate the applications of SL[\u2131]\u00a0in 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\u00a0also provide a model-checking algorithm for SL[\u2131]\u00a0, based on a quantitative extension of Quantified CTL\n            <jats:sup>\u22c6<\/jats:sup>\n            \u00a0. Our\u00a0algorithm provides the first decidability result for a quantitative extension of Strategy Logic. In\u00a0addition, it\u00a0can be used for synthesizing strategies that maximize the quality of the systems\u2019 behavior.\n          <\/jats:p>\n          <jats:p\/>","DOI":"10.1145\/3582498","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T13:45:29Z","timestamp":1675950329000},"page":"1-38","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Reasoning about Quality and Fuzziness of Strategic Behaviors"],"prefix":"10.1145","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2823-0911","authenticated-orcid":false,"given":"Patricia","family":"Bouyer","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS, ENS Paris-Saclay, LMF, Gif-sur-Yvette, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4699-6117","authenticated-orcid":false,"given":"Orna","family":"Kupferman","sequence":"additional","affiliation":[{"name":"Hebrew University, Jerusalem, Israel"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1977-7525","authenticated-orcid":false,"given":"Nicolas","family":"Markey","sequence":"additional","affiliation":[{"name":"Irisa, CNRS and Inria and Universit\u00e9 de Rennes, Rennes, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9081-2920","authenticated-orcid":false,"given":"Bastien","family":"Maubert","sequence":"additional","affiliation":[{"name":"Universit\u00e0 degli Studi di Napoli \u201cFederico II\u201d, Naples, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4876-3448","authenticated-orcid":false,"given":"Aniello","family":"Murano","sequence":"additional","affiliation":[{"name":"Universit\u00e0 degli Studi di Napoli \u201cFederico II\u201d, Naples, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8687-6323","authenticated-orcid":false,"given":"Giuseppe","family":"Perelli","sequence":"additional","affiliation":[{"name":"Sapienza University of Rome, Rome, Italy"}]}],"member":"320","published-online":{"date-parts":[[2023,4,7]]},"reference":[{"key":"e_1_3_3_2_2","first-page":"481","volume-title":"Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems.","author":"Alechina Natasha","year":"2010","unstructured":"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 Lesp\u00e9rance, Michael Luck, and Sandeep Sen (Eds.), International Foundation for Autonomous Agents and Multiagent Systems, 481\u2013488."},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-54862-8_37"},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/2875421"},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.4230\/LIPIcs.CSL.2016.28"},{"key":"e_1_3_3_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10626-017-0242-0"},{"key":"e_1_3_3_7_2","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2018\/5"},{"key":"e_1_3_3_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-63390-9_19"},{"key":"e_1_3_3_9_2","doi-asserted-by":"publisher","DOI":"10.1145\/585265.585270"},{"key":"e_1_3_3_10_2","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2019\/5"},{"key":"e_1_3_3_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2018.02.021"},{"key":"e_1_3_3_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1474-6670(17)42032-5"},{"key":"e_1_3_3_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00236-012-0156-0"},{"key":"e_1_3_3_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.2017.8005136"},{"key":"e_1_3_3_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-70918-3_17"},{"key":"e_1_3_3_16_2","doi-asserted-by":"publisher","DOI":"10.1145\/2629686"},{"key":"e_1_3_3_17_2","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2012.43"},{"key":"e_1_3_3_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-85778-5_4"},{"key":"e_1_3_3_19_2","doi-asserted-by":"publisher","DOI":"10.4230\/LIPIcs.FSTTCS.2015.69"},{"key":"e_1_3_3_20_2","doi-asserted-by":"publisher","DOI":"10.24963\/ijcai.2019\/220"},{"key":"e_1_3_3_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-44584-6_19"},{"key":"e_1_3_3_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-49630-5_13"},{"key":"e_1_3_3_23_2","doi-asserted-by":"publisher","DOI":"10.4230\/LIPIcs.FSTTCS.2016.42"},{"key":"e_1_3_3_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00236-016-0273-2"},{"key":"e_1_3_3_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-013-9495-7"},{"key":"e_1_3_3_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-74407-8_30"},{"key":"e_1_3_3_27_2","doi-asserted-by":"publisher","DOI":"10.1145\/2603088.2603109"},{"key":"e_1_3_3_28_2","doi-asserted-by":"publisher","DOI":"10.4204\/EPTCS.112.8"},{"key":"e_1_3_3_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-45212-6_9"},{"key":"e_1_3_3_30_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-54013-4_5"},{"key":"e_1_3_3_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2006.07.032"},{"key":"e_1_3_3_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2009.07.004"},{"key":"e_1_3_3_33_2","doi-asserted-by":"publisher","DOI":"10.1109\/FSKD.2007.458"},{"key":"e_1_3_3_34_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10703-006-0001-6"},{"key":"e_1_3_3_35_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0025774"},{"key":"e_1_3_3_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2005.09.010"},{"key":"e_1_3_3_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2005.07.033"},{"key":"e_1_3_3_38_2","doi-asserted-by":"publisher","DOI":"10.1590\/0101-7438.2016.036.01.0081"},{"key":"e_1_3_3_39_2","first-page":"1441","volume-title":"Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems.","author":"Monica Dario Della","year":"2018","unstructured":"Dario Della Monica and Aniello Murano. 2018. Parity-energy atl for qualitative and quantitative reasoning in MAS. In Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems.Elisabeth Andr\u00e9, Sven Koenig, Mehdi Dastani, and Gita Sukthankar (Eds.), International Foundation for Autonomous Agents and Multiagent Systems, 1441\u20131449."},{"issue":"13","key":"e_1_3_3_40_2","first-page":"305","article-title":"Multi-valued MSO logics over words and trees","volume":"84","author":"Droste Manfred","year":"2008","unstructured":"Manfred Droste, Werner Kuich, and George Rahonis. 2008. Multi-valued MSO logics over words and trees. Fundamenta Informaticae 84, 13-4 (2008), 305\u2013327.","journal-title":"Fundamenta Informaticae"},{"key":"e_1_3_3_41_2","doi-asserted-by":"publisher","DOI":"10.4204\/EPTCS.256.8"},{"key":"e_1_3_3_42_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01768705"},{"key":"e_1_3_3_43_2","doi-asserted-by":"publisher","DOI":"10.1145\/4904.4999"},{"key":"e_1_3_3_44_2","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1991.185392"},{"key":"e_1_3_3_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6423(87)90036-0"},{"key":"e_1_3_3_46_2","doi-asserted-by":"publisher","DOI":"10.4230\/LIPIcs.CSL.2018.23"},{"key":"e_1_3_3_47_2","volume-title":"Competitive Markov Decision Processes","author":"Filar Jerzy","year":"1997","unstructured":"Jerzy Filar and Koos Vrieze. 1997. Competitive Markov Decision Processes. Springer-Verlag."},{"key":"e_1_3_3_48_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-12002-2_16"},{"key":"e_1_3_3_49_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45656-2_15"},{"key":"e_1_3_3_50_2","doi-asserted-by":"publisher","DOI":"10.1145\/2629606"},{"key":"e_1_3_3_51_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-82453-1_17"},{"key":"e_1_3_3_52_2","doi-asserted-by":"publisher","DOI":"10.1145\/1374376.1374390"},{"key":"e_1_3_3_53_2","doi-asserted-by":"publisher","DOI":"10.1007\/11867340_1"},{"key":"e_1_3_3_54_2","first-page":"1180","volume-title":"Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems.","author":"Jamroga Wojciech","year":"2016","unstructured":"Wojciech Jamroga, Beata Konikowska, and Wojciech Penczek. 2016. Multi-valued verification of strategic ability. In Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems.Catholijn M. Jonker, Stacy Marsella, John Thangarajah, and Karl Tuyls (Eds.), International Foundation for Autonomous Agents and Multiagent Systems, 1180\u20131189."},{"key":"e_1_3_3_55_2","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/9.2.135"},{"key":"e_1_3_3_56_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-44618-4_9"},{"key":"e_1_3_3_57_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10472-016-9508-8"},{"key":"e_1_3_3_58_2","doi-asserted-by":"publisher","DOI":"10.1145\/333979.333987"},{"key":"e_1_3_3_59_2","doi-asserted-by":"publisher","DOI":"10.1145\/333979.333987"},{"key":"e_1_3_3_60_2","first-page":"116","volume-title":"Proceedings of the IASTED International Conference on Robotics and Applications","author":"Lamine Khaled Ben","year":"2000","unstructured":"Khaled Ben Lamine and Froduald Kabanza. 2000. Using fuzzy temporal logic for monitoring behavior-based mobile robots. In Proceedings of the IASTED International Conference on Robotics and Applications. 116\u2013121."},{"key":"e_1_3_3_61_2","doi-asserted-by":"publisher","DOI":"10.2168\/LMCS-10(4:17)2014"},{"key":"e_1_3_3_62_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2014.12.020"},{"key":"e_1_3_3_63_2","doi-asserted-by":"publisher","DOI":"10.1007\/11867340_18"},{"key":"e_1_3_3_64_2","article-title":"O logice Tr\u00f3jwarto\u015bciowej","author":"\u0141ukasiewicz Jan","year":"1920","unstructured":"Jan \u0141ukasiewicz. 1920. O logice Tr\u00f3jwarto\u015bciowej. Studia Filozoficzne 270, 5 (1920).","journal-title":"Studia Filozoficzne"},{"key":"e_1_3_3_65_2","doi-asserted-by":"publisher","DOI":"10.1145\/1967701.1967732"},{"key":"e_1_3_3_66_2","first-page":"689","volume-title":"Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems","author":"Malvone Vadim","year":"2016","unstructured":"Vadim Malvone, Aniello Murano, and Loredana Sorrentino. 2016. Concurrent multi-player parity games. In Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems. ACM, 689\u2013697."},{"key":"e_1_3_3_67_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-32940-1_15"},{"key":"e_1_3_3_68_2","doi-asserted-by":"publisher","DOI":"10.1145\/2631917"},{"key":"e_1_3_3_69_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)00214-4"},{"key":"e_1_3_3_70_2","doi-asserted-by":"publisher","DOI":"10.1145\/301250.301287"},{"key":"e_1_3_3_71_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511800481"},{"key":"e_1_3_3_72_2","doi-asserted-by":"publisher","DOI":"10.2168\/LMCS-3(3:5)2007"},{"key":"e_1_3_3_73_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(81)90110-9"},{"key":"e_1_3_3_74_2","doi-asserted-by":"publisher","DOI":"10.1145\/75277.75293"},{"key":"e_1_3_3_75_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1969-0246760-1"},{"key":"e_1_3_3_76_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01492-5_12"},{"key":"e_1_3_3_77_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.39.10.1095"},{"key":"e_1_3_3_78_2","unstructured":"A. Prasad Sistla. 1983. Theoretical Issues in the Design and Certification of Distributed Systems. Ph.D. Dissertation. Harvard University Cambridge MA."},{"key":"e_1_3_3_79_2","doi-asserted-by":"publisher","DOI":"10.1145\/2185632.2185648"},{"key":"e_1_3_3_80_2","doi-asserted-by":"crossref","unstructured":"Michael Ummels. 2010. Stochastic Multiplayer Games: Theory and Algorithms . Master\u2019s thesis. RWTH Aachen Germany.","DOI":"10.5117\/9789085550402"},{"key":"e_1_3_3_81_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(86)90026-7"},{"key":"e_1_3_3_82_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-24953-7_27"},{"key":"e_1_3_3_83_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-2356-0"},{"key":"e_1_3_3_84_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(95)00188-3"}],"container-title":["ACM Transactions on Computational Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3582498","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3582498","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T18:08:50Z","timestamp":1750183730000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3582498"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,7]]},"references-count":83,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,7,31]]}},"alternative-id":["10.1145\/3582498"],"URL":"https:\/\/doi.org\/10.1145\/3582498","relation":{},"ISSN":["1529-3785","1557-945X"],"issn-type":[{"value":"1529-3785","type":"print"},{"value":"1557-945X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,7]]},"assertion":[{"value":"2021-09-28","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-12-11","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-04-07","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}