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Optimal Tableau Method for Constructive Satisfiability Testing and Model Synthesis in the Alternating-Time Temporal Logic ATL⁺

Authors:

Serenella Cerrito,

Amélie David,

Valentin GorankoAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 17, Issue 1

Article No.: 4, Pages 1 - 34

https://doi.org/10.1145/2811261

Published: 28 October 2015 Publication History

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Abstract

We develop a sound, complete, and practically implementable tableau-based decision method for constructive satisfiability testing and model synthesis for the fragment ATL⁺ of the full alternating-time temporal logic ALT^*. The method extends in an essential way a previously developed tableau-based decision method for ATL and works in 2EXPTIME, which is the optimal worst-case complexity of the satisfiability problem for ATL⁺. We also discuss how suitable parameterizations and syntactic restrictions on the class of input ATL⁺ formulas can reduce the complexity of the satisfiability problem.

References

[1]

R. Alur, T. A. Henzinger, and O. Kupferman. 2002. Alternating-time temporal logic. Journal of the ACM 49, 5, 672--713.

Digital Library

Google Scholar

[2]

Mordechai Ben-Ari, Amir Pnueli, and Zohar Manna. 1983. The temporal logic of branching time. Acta Informatica 20, 207--226.

Digital Library

Google Scholar

[3]

Serenella Cerrito, Amélie David, and Valentin Goranko. 2014. Optimal tableaux-based decision procedure for testing satisfiability in the alternating-time temporal logic ATL⁺. In Proceedings of IJCAR 2014 (LNCS), Vol. 8562. Springer, 277--291.

Crossref

Google Scholar

[4]

Amélie David. 2013. TATL: Implementation of ATL tableau-based decision procedure. In Proceedings of TABLEAUX 2013 (LNCS), Vol. 8123. Springer, 97--103.

Crossref

Google Scholar

[5]

E. Emerson and J. Halpern. 1985. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computation and System Sciences 30, 1, 1--24.

Digital Library

Google Scholar

[6]

E. Allen Emerson. 1990. Temporal and modal logics. In Handbook of Theoretical Computer Science, J. van Leeuwen (Ed.). Vol. B. MIT Press, 995--1072.

Digital Library

Google Scholar

[7]

Valentin Goranko and Dmitry Shkatov. 2009. Tableau-based decision procedures for logics of strategic ability in multiagent systems. ACM Transactions in Computer Logic 11, 1, 1--49.

Digital Library

Google Scholar

[8]

V. Goranko and G. van Drimmelen. 2006. Complete axiomatization and decidablity of alternating-time temporal logic. Theoretic and Computational Science 353, 93--117.

Digital Library

Google Scholar

[9]

J. Johannsen and M. Lange. 2003. CTL+ is complete for double exponential time. In Proceedings of ICALP’03 (LNCS), Vol. 2719. Springer, 767--775.

Digital Library

Google Scholar

[10]

Vaughan R. Pratt. 1980. A near optimal method for reasoning about action. Journal of Computer System Science 20, 231--254.

Crossref

Google Scholar

[11]

Sven Schewe. 2008. ATL&ast; satisfiability is 2EXPTIME-complete. In Proceedings of ICALP (Part 2) (LNCS), Vol. 5126. Springer, 373--385.

Digital Library

Google Scholar

[12]

Govert van Drimmelen. 2003. Satisfiability in alternating-time temporal logic. In Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science (LICS’03). IEEE Computer Society Press, 208--217.

Digital Library

Google Scholar

[13]

Dirk Walther, Carsten Lutz, Frank Wolter, and Michael Wooldridge. 2006. ATL satisfiability is indeed ExpTime-complete. Journal of Logic and Computation 16, 6, 765--787.

Crossref

Google Scholar

[14]

Pierre Wolper. 1985. The tableau method for temporal logic: An overview. Logique et Analyse 28, 110--111, 119--136.

Google Scholar

Cited By

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Goranko V(2023)Logics for Strategic Reasoning of Socially Interacting Rational Agents: An Overview and PerspectivesLogics10.3390/logics10100031:1(4-35)Online publication date: 6-Feb-2023
https://doi.org/10.3390/logics1010003
Demri SRönnholm RMarquis PSon TKern-Isberner G(2023)How to manage a budget with ATL+Proceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning10.24963/kr.2023/19(188-197)Online publication date: 2-Sep-2023
https://dl.acm.org/doi/10.24963/kr.2023/19
Goranko VKuusisto ARönnholm R(2019)Alternating-time temporal logic ATL with finitely bounded semanticsTheoretical Computer Science10.1016/j.tcs.2019.05.029Online publication date: Jul-2019
https://doi.org/10.1016/j.tcs.2019.05.029

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Optimal Tableau Method for Constructive Satisfiability Testing and Model Synthesis in the Alternating-Time Temporal Logic ATL⁺

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 17, Issue 1

December 2015

258 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/2830313

Editor:
Orna Kupferman
School of Computer Science and Engineering, Hebrew University, Israel

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 October 2015

Accepted: 01 July 2015

Revised: 01 May 2015

Received: 01 July 2014

Published in TOCL Volume 17, Issue 1

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Cited By

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Goranko V(2023)Logics for Strategic Reasoning of Socially Interacting Rational Agents: An Overview and PerspectivesLogics10.3390/logics10100031:1(4-35)Online publication date: 6-Feb-2023
https://doi.org/10.3390/logics1010003
Demri SRönnholm RMarquis PSon TKern-Isberner G(2023)How to manage a budget with ATL+Proceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning10.24963/kr.2023/19(188-197)Online publication date: 2-Sep-2023
https://dl.acm.org/doi/10.24963/kr.2023/19
Goranko VKuusisto ARönnholm R(2019)Alternating-time temporal logic ATL with finitely bounded semanticsTheoretical Computer Science10.1016/j.tcs.2019.05.029Online publication date: Jul-2019
https://doi.org/10.1016/j.tcs.2019.05.029

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Constructive linear-time temporal logic: Proof systems and Kripke semantics

Alternating-time temporal logic ATL with finitely bounded semantics

A decision procedure for satisfiability in separation logic with inductive predicates