Skip to main content
SpringerLink
Log in

Branching Time Logics with Multiagent Temporal Accessibility Relations

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

Under study are the branching time temporal logics with temporal accessibility relations for the agents different in length and content. We find an algorithm for solving the problems of satisfiability and decidability of the logic through describing finite satisfiable models of computable size (through the size of the input formulas). We remove the constraints on the size of all temporal accessibility intervals for the agents (to be all inside a common temporal accessibility interval at any local time point); i.e., all constraints can be arbitrary. Also, we formulate some open problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Gabbay D. M., Hodkinson I. M., and Reynolds M. A., Temporal Logic, Clarendon, Oxford (1994) (Math. Found. Comput. Aspects; Vol. 1).

    Book  Google Scholar 

  2. Gabbay D. M. and Hodkinson I. M., “An axiomatization of the temporal logic with Until and Since over the real numbers,” J. Logic Comput., vol. 1, 229–260 (1990).

    Article  MathSciNet  Google Scholar 

  3. Gabbay D. M. and Hodkinson I. M., Temporal Logic in the Context of Databases, Oxford Univ., Oxford (1995) (Logic and Reality: Essays on the Legacy of Arthur Prior. Copeland J., Ed.).

    MATH  Google Scholar 

  4. Wooldridge M. and Lomuscio A., “Multi-agent VSK logic” in:, Proc. Seventh European Workshop on Logics in Artificial Intelligence (JELIAI–2000), Springer, London (2000), 300–312.

  5. Wooldridge M., “An automata-theoretic approach to multiagent planning” in:, Proc. First European Workshop on Multiagent Systems (EUMAS 2003), Oxford Univ., Oxford (2003), 1–15. http://www.cs.ox.ac.uk/people/michael.wooldridge/pubs/eumas2003.pdf

  6. Wooldridge M., Huget M. P., Fisher M., and Parsons S., “Model checking multi-agent systems: The MABLE language and its applications,” Intern. J. Artificial Intelligence Tools, vol. 15, no. 2, 195–225 (2006).

    Article  Google Scholar 

  7. Belardinelli F. and Lomuscio A., “Interactions between Knowledge and Time in a first-order logic for multi-agent systems: Completeness results,” J. Artificial Intelligence Res., vol. 45, 1–45 (2012).

    Article  MathSciNet  Google Scholar 

  8. Emerson E. A. and Halpern J. Y., “Decision procedures and expressiveness in the temporal logic of branching time,” J. Comput. Syst. Sci., vol. 30, no. 1, 1–24 (1985).

    Article  MathSciNet  Google Scholar 

  9. Clarke E. M., Emerson E. A., and Sistla A. P., “Automatic verification of finite-state concurrent systems using temporal logic specifications,” ACM Trans. Programming Languages and Systems, vol. 8, no. 2, 244–263 (1986).

    Article  Google Scholar 

  10. Carmo J. and Sernadas S., “Branching vs linear logics yet a gain,” Formal Aspects Comput., vol. 2, 24–59 (1990).

    Article  Google Scholar 

  11. Rybakov V., “Non-transitive linear temporal logic and logical knowledge operations,” J. Logic Comput., vol. 26, no. 3, 945–958 (2016).

    Article  MathSciNet  Google Scholar 

  12. Rybakov V., “Intransitive temporal multi-agent’s logic, knowledge and uncertainty, plausibility” in:, Logical Foundations of Computer Science: International Symposium (LFCS 2016), Springer, New York (2016), 364–375 (Lecture Notes Comput. Sci.; Vol. 9537).

  13. Rybakov V. V., “Nontransitive temporal multiagent logic, information and knowledge, deciding algorithms,” Sib. Math. J., vol. 58, no. 5, 875–886 (2017).

    Article  MathSciNet  Google Scholar 

  14. Rybakov V. V., “Multiagent temporal logics with multivaluations,” Sib. Math. J., vol. 59, no. 4, 710–720 (2018).

    Article  MathSciNet  Google Scholar 

  15. Rybakov V., “Linear temporal logic with non-transitive time, algorithms for decidability and verification of admissibility” in:, Outstanding Contributions to Logic, Springer, Dordrecht (2018), 219–243.

  16. Rybakov V., “Temporal multi-valued logic with lost worlds in the past,” Sib. Electr. Math. Reports, vol. 15, 436–449 (2018).

    MathSciNet  MATH  Google Scholar 

  17. Rybakov V., “Branching time agents’ logic, satisfiability problem by rules in reduced form,” Sib. Electr. Math. Reports, vol. 16, 1158–1170 (2019).

    MathSciNet  MATH  Google Scholar 

  18. Rybakov V., “Temporal logic with accessibility temporal relations generated by time states themselves,” Sib. Electr. Math. Reports, vol. 17, 923–932 (2020).

    MATH  Google Scholar 

  19. Babenyshev S. and Rybakov V., “Linear temporal logic LTL: Basis for admissible rules,” J. Logic Comput., vol. 21, no. 2, 157–177 (2011).

    Article  MathSciNet  Google Scholar 

  20. Rybakov V., “Logical consecutions in discrete linear temporal logic,” J. Symbolic Logic, vol. 70, no. 4, 1137–1149 (2005).

    Article  MathSciNet  Google Scholar 

Download references

Funding

The author was supported by the Research Program at HSE University (Higher School of Economics, University, Moscow, Russia). The author was also supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation (Grant 075–02–2020–1534/1).

Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Krasnoyarsk, Russia

    V. V. Rybakov

  2. Siberian Federal University, Krasnoyarsk, Russia

    V. V. Rybakov

  3. A.P. Ershov Institute of Informatics Systems, Novosibirsk, Russia

    V. V. Rybakov

Authors
  1. V. V. Rybakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Rybakov.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 3, pp. 623–632. https://doi.org/10.33048/smzh.2021.62.313

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rybakov, V.V. Branching Time Logics with Multiagent Temporal Accessibility Relations. Sib Math J 62, 503–510 (2021). https://doi.org/10.1134/S0037446621030137

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446621030137

Keywords

UDC

Search

Navigation