{"type":"ScholarlyArticle","title":"Probabilistic Strategy Logic","authors":[{"name":"Benjamin Aminof","slug":"benjamin-aminof","given":"Benjamin","family":"Aminof","affiliation":"JKU Linz , Austria; TU Wien , Austria"},{"name":"Marta Kwiatkowska","slug":"marta-kwiatkowska","given":"Marta","family":"Kwiatkowska","affiliation":"University of Oxford , UK"},{"name":"Bastien Maubert","slug":"bastien-maubert","given":"Bastien","family":"Maubert","affiliation":"Università degli Studi di Napoli Federico II , Italy"},{"name":"Aniello Murano","slug":"aniello-murano","given":"Aniello","family":"Murano","affiliation":"Università degli Studi di Napoli Federico II , Italy"},{"name":"Sasha Rubin","slug":"sasha-rubin","given":"Sasha","family":"Rubin","affiliation":"Università degli Studi di Napoli Federico II , Italy"}],"abstract":"We introduce Probabilistic Strategy Logic, an extension of Strategy Logic for\r\nstochastic systems. The logic has probabilistic terms that allow it to express\r\nmany standard solution concepts, such as Nash equilibria in randomised\r\nstrategies, as well as constraints on probabilities, such as independence. We\r\nstudy the model-checking problem for agents with perfect- and imperfect-recall.\r\nThe former is undecidable, while the latter is decidable in space exponential\r\nin the system and triple-exponential in the formula.  We identify a natural\r\nfragment of the logic, in which every temporal operator is immediately preceded\r\nby a probabilistic operator, and show that it is decidable in space exponential\r\nin the system and the formula, and double-exponential in the nesting depth of\r\nthe probabilistic terms. Taking a fixed nesting depth, this gives a fragment\r\nthat still captures many standard solution concepts, and is decidable in\r\nexponential space.","doi":"10.24963/ijcai.2019/5","url":"https://ijcai.org/proceedings/2019/5","pdf":"https://ijcai.org/proceedings/2019/0005.pdf","markdown":"https://ijcai.org/proceedings/2019/5.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/5","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":5,"pages":{"first":32,"last":38},"keywords":["Agent-based and Multi-agent Systems: Formal Verification, Validation and Synthesis"],"videos":[],"references":[{"position":1,"raw":"[Alur et al., 2002] R. Alur, T.A. Henzinger, and O. Kupfer- man. Alternating-time temporal logic. J.ACM,49(5):672- 713, 2002.","title":"Alternating-time temporal logic","authors":"R Alur, T A Henzinger, O Kupferman","year":"2002","venue":"J.ACM","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Aminof et al., 2018] B. Aminof, V. Malvone, A. Murano, and S. Rubin. Graded modalities in strategy logic. Inf. Comput., 261:634-649, 2018.","title":"Graded modalities in strategy logic","authors":"B Aminof, V Malvone, A Murano, S Rubin","year":"2018","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Baier et al., 2012] C. Baier, T. Brázdil, M. Größer, and A. Kucera. Stochastic game logic. Acta Inf., 49(4):203- 224, 2012.","title":"Stochastic game logic","authors":"C Baier, T Brázdil, M Größer, A Kucera","year":"2012","venue":"Acta Inf","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Belardinelli et al., 2017] F. Belardinelli, A. Lomuscio, A. Murano, and S. Rubin. Verification of broadcasting multi-agent systems against an epistemic strategy logic. In IJCAI, 2017.","title":"Verification of broadcasting multi-agent systems against an epistemic strategy logic","authors":"F Belardinelli, A Lomuscio, A Murano, S Rubin","year":"2017","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2017/14"},{"position":5,"raw":"[Ben-Or et al., 1986] M. Ben-Or, D. Kozen, and J. H. Reif. The complexity of elementary algebra and geometry. JCSS, 32(2):251-264, 1986.","title":"The complexity of elementary algebra and geometry","authors":"M Ben-Or, D Kozen, J H Reif","year":"1986","venue":"JCSS","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Berman, 1980] L. Berman. The complexity of logical theo- ries. Theor. Comput. Sci., 11(1):71 -77, 1980.","title":"The complexity of logical theories","authors":"L Berman","year":"1980","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Berthon et al., 2017] R. Berthon, B. Maubert, A. Murano, S. Rubin, and M.Y. Vardi. Strategy logic with imperfect information. In LICS, 2017.","title":"Strategy logic with imperfect information","authors":"R Berthon, B Maubert, A Murano, S Rubin, M Y Vardi","year":"2017","venue":"LICS","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Bouyer et al., 2016] P. Bouyer, P. Gardy, and N. Markey. On the semantics of strategy logic. IPL, 116(2):75-79, 2016.","title":"On the semantics of strategy logic","authors":"P Bouyer, P Gardy, N Markey","year":"2016","venue":"IPL","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Brázdil et al., 2006] T. Brázdil, V. Brozek, V. Forejt, and A. Kucera. Stochastic games with branching-time winning objectives. In LICS, 2006.","title":"Stochastic games with branching-time winning objectives","authors":"T Brázdil, V Brozek, V Forejt, A Kucera","year":"2006","venue":"LICS","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Bulling and Jamroga, 2009] N. Bulling and W. Jamroga. What agents can probably enforce. Fundam. Inform., 93(1-3):81-96, 2009.","title":"What agents can probably enforce","authors":"N Bulling, W Jamroga","year":"2009","venue":"Fundam. Inform","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Cermák et al., 2018] P. Cermák, A. Lomuscio, F. Mo- gavero, and A. Murano. Practical verification of multi- agent systems against SLK specifications. Inf. Comput., 261:588-614, 2018.","title":"Practical verification of multiagent systems against SLK specifications","authors":"P Cermák, A Lomuscio, F Mogavero, A Murano","year":"2018","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Chatterjee and Henzinger, 2012] K. Chatterjee and T.A. Henzinger. A survey of stochastic ω-regular games. JCSS, 78(2):394-413, 2012.","title":"A survey of stochastic ω-regular games","authors":"K Chatterjee, T A Henzinger","year":"2012","venue":"JCSS","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Chatterjee et al., 2010] K. Chatterjee, T.A. Henzinger, and N. Piterman. Strategy Logic. Inf. Comput., 208(6):677- 693, 2010.","title":"Strategy Logic","authors":"K Chatterjee, T A Henzinger, N Piterman","year":"2010","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Chen and Lu, 2007] T. Chen and J. Lu. Probabilistic alternating-time temporal logic and model checking algo- rithm. In FSKD, 2007.","title":"Probabilistic alternating-time temporal logic and model checking algorithm","authors":"T Chen, J Lu","year":"2007","venue":"FSKD","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Chen et al., 2013a] T. Chen, V. Forejt, M. Kwiatkowska, D. Parker, and A. Simaitis. Automatic verification of com- petitive stochastic systems. FMSD, 43(1):61-92, 2013.","title":"Automatic verification of competitive stochastic systems","authors":"Chen","year":"2013","venue":"FMSD","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Chen et al., 2013b] T. Chen, V. Forejt, M. Kwiatkowska, D. Parker, and A. Simaitis. PRISM-games: A model che- cker for stochastic multi-player games. In TACAS, 2013.","title":"PRISM-games: A model checker for stochastic multi-player games","authors":"Chen","year":"2013","venue":"TACAS","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Courcoubetis and Yannakakis, 1995] C. Courcoubetis and M. Yannakakis. The complexity of probabilistic verifica- tion. J. ACM, 42(4):857-907, 1995.","title":"The complexity of probabilistic verification","authors":"C Courcoubetis, M Yannakakis","year":"1995","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Fagin et al., 1995] R. Fagin, J. Y. Halpern, Y. Moses, and M.Y. Vardi. Reasoning about Knowledge. MIT, 1995.","title":"Reasoning about Knowledge","authors":"R Fagin, J Y Halpern, Y Moses, M Y Vardi","year":"1995","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Fisman et al., 2010] D. Fisman, O. Kupferman, and Y. Lustig. Rational synthesis. In TACAS, 2010.","title":"Rational synthesis","authors":"D Fisman, O Kupferman, Y Lustig","year":"2010","venue":"TACAS","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Halpern, 2008] J. Y. Halpern. Beyond nash equilibrium: So- lution concepts for the 21st century. In KR, 2008.","title":"Beyond nash equilibrium: Solution concepts for the 21st century","authors":"J Y Halpern","year":"2008","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Huang and Luo, 2013] Xiaowei Huang and Cheng Luo. A logic of probabilistic knowledge and strategy. In AAMAS, pages 845-852, 2013.","title":"A logic of probabilistic knowledge and strategy","authors":"Xiaowei Huang, Cheng Luo","year":"2013","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Kemeny and Snell, 1976] J. G. Kemeny and J. L. Snell. Fi- nite markov chains. Springer, 1976.","title":"Finite markov chains","authors":"J G Kemeny, J L Snell","year":"1976","venue":null,"doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Kupferman et al., 2000] O. Kupferman, M.Y. Vardi, and P. Wolper. An automata-theoretic approach to branching- time model checking. J. ACM, 47(2):312-360, 2000.","title":"An automata-theoretic approach to branchingtime model checking","authors":"O Kupferman, M Y Vardi, P Wolper","year":"2000","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Kupferman et al., 2016] O. Kupferman, G. Perelli, and M.Y. Vardi. Synthesis with rational environments. Ann. Math. Artif. Intell., 78(1):3-20, 2016.","title":"Synthesis with rational environments","authors":"O Kupferman, G Perelli, M Y Vardi","year":"2016","venue":"Ann. Math. Artif. Intell","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Kwiatkowska et al., 2012] M. Kwiatkowska, G. Norman, and D. Parker. The PRISM benchmark suite. In QEST, 2012.","title":"The PRISM benchmark suite","authors":"M Kwiatkowska, G Norman, D Parker","year":"2012","venue":"QEST","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Kwiatkowska et al., 2018] M. Kwiatkowska, G. Norman, D. Parker, and G. Santos. Automated verification of con- current stochastic games. In QEST, 2018.","title":"Automated verification of concurrent stochastic games","authors":"M Kwiatkowska, G Norman, D Parker, G Santos","year":"2018","venue":"QEST","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Kwiatkowska et al., 2019] M. Kwiatkowska, G. Norman, D. Parker, and G. Santos. Equilibria-based probabilistic model checking for concurrent stochastic games. CoRR, abs/1811.07145, 2019.","title":"Equilibria-based probabilistic model checking for concurrent stochastic games","authors":"M Kwiatkowska, G Norman, D Parker, G Santos","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Laroussinie and Markey, 2015] F. Laroussinie and N. Markey. Augmenting ATL with strategy contexts. Inf. Comput., 245:98-123, 2015.","title":"Augmenting ATL with strategy contexts","authors":"F Laroussinie, N Markey","year":"2015","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Malvone et al., 2018] V. Malvone, F. Mogavero, A. Mu- rano, and L. Sorrentino. Reasoning about graded strategy quantifiers. Inf. Comput., 259(3):390-411, 2018.","title":"Reasoning about graded strategy quantifiers","authors":"V Malvone, F Mogavero, A Murano, L Sorrentino","year":"2018","venue":"Inf. Comput","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Mogavero et al., 2014] F. Mogavero, A. Murano, G. Perelli, and M.Y. Vardi. Reasoning about strategies: On the model-checking problem. ACM Trans. Comput. Log., 15(4):34:1-34:47, 2014.","title":"Reasoning about strategies: On the model-checking problem","authors":"F Mogavero, A Murano, G Perelli, M Y Vardi","year":"2014","venue":"ACM Trans. Comput. Log","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Pnueli, 1977] A. Pnueli. The temporal logic of programs. In FOCS, pages 46-57, 1977.","title":"The temporal logic of programs","authors":"A Pnueli","year":"1977","venue":"FOCS","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Russell and Norvig, 1995] S.J. Russell and P. Norvig. Arti- ficial Intelligence. A Modern Approach. Prentice, 1995.","title":"Artificial Intelligence. A Modern Approach","authors":"S J Russell, P Norvig","year":"1995","venue":null,"doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Schnoor, 2013] H. Schnoor. Epistemic and probabilis- tic ATL with quantification and explicit strategies. In ICAART, volume 449, pages 131-148, 2013.","title":"Epistemic and probabilistic ATL with quantification and explicit strategies","authors":"H Schnoor","year":"2013","venue":"ICAART","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Svorenová and Kwiatkowska, 2016] M. Svorenová and M. Kwiatkowska. Quantitative verification and strategy synthesis for stochastic games. EJC, 30:15-30, 2016.","title":"Quantitative verification and strategy synthesis for stochastic games","authors":"M Svorenová, M Kwiatkowska","year":"2016","venue":"EJC","doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Ummels and Wojtczak, 2011] M. Ummels and D. Wo- jtczak. The complexity of nash equilibria in stochastic multiplayer games. LMCS, 7(3), 2011.","title":"The complexity of nash equilibria in stochastic multiplayer games","authors":"M Ummels, D Wojtczak","year":"2011","venue":"LMCS","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Vardi, 1985] M.Y. Vardi. Automatic verification of proba- bilistic concurrent finite-state programs. In FOCS, 1985.","title":"Automatic verification of probabilistic concurrent finite-state programs","authors":"M Y Vardi","year":"1985","venue":"FOCS","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}