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Temporal Logic in Multi-agent Environment

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Agents and Multi-Agent Systems: Technologies and Applications 2022

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 306))

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Abstract

This paper studies temporal multi-agent’s relational models with distinct time accessibility relations for agents. Distinct valuations of truth values for agents’ are also allowed, and a global valuation is the one which in a sense summarizes the opinion of agents. Some illustrating examples are provided (cf. displayed in paper below formulas (1.2), (1.3)). From mathematical point of view, we deal with satisfiability problem for formulas, and we construct a mathematical algorithm (cf. Theorem 1.3) verifying satisfiability. Also we prove that the problem of admissibility for inference rules in some such logics is decidable. Open problems from the area are proposed.

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Notes

  1. 1.

    This paper is supported by Krasnoyarsk Mathematical Center financed by Ministry of Education Russian Federation (grant 075-02-2022-876).

References

  1. Babenyshev, S., Rybakov, V.: Logic of plausibility for discovery in multi-agent environment deciding algorithms. In: KES (3) 2008: Lecture Notes in Computer Science, vol. 5179/2008, pp. 210–217 (2008)

    Google Scholar 

  2. Babenyshev, S., Rybakov, V.: Decidability of hybrid logic with local common knowledge based on linear temporal logic LTL. In: CiE 2008: Lecture Notes in Computer Science, vol. 5028/2008, pp. 32–41 (2008)

    Google Scholar 

  3. Babenyshev, S., Rybakov, V.: Logic of discovery and knowledge: decision algorithm. In: KES (2), Lecture Notes in Computer Science, vol. 5178/2008, pp. 711–718 (2008)

    Google Scholar 

  4. Babenyshev, S., Rybakov, V.: Describing evolutions of multi-agent systems. In: KES (1) 2009: Lecture Notes in Computer Science, vol. 5711/2009, pp. 38–45 (2009)

    Google Scholar 

  5. Babenyshev, S., Rybakov, V.: Linear temporal logic LTL: basis for admissible rules. J. Log. Comput. 21(2), 157–177 (2011)

    Google Scholar 

  6. Babenyshev, S., Rybakov, V.: Unification in linear temporal logic LTL. Ann. Pure Appl. Log. 162(12), 991–1000 (2011)

    Google Scholar 

  7. Baader, F., Sattler, U.: Expressive Number Restrictions in Description Logics. J. Log. Comput. 9(3), 319–350 (1999)

    Google Scholar 

  8. Baader, F., Küsters, R.: Unification in a description logic with transitive closure of roles. In: Nieuwenhuis, R., Voronkov, A. (eds.) Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2001, LNCS, vol. 2250, pp. 217–232. Springer, Berlin (2001)

    Google Scholar 

  9. Baader, F., Morawska, B.: Unification in the description logic EL. Log. Methods Comput. Sci. 6(3), 1–31 (2010)

    Google Scholar 

  10. Belardinelli, F., Lomuscio, A.: interactions between knowledge and time in a first-order logic for multi-agent systems: completeness results. J. Artif. Intell. Res. 45, 1–45 (2012)

    Google Scholar 

  11. Gabbay, D.M., Hodkinson, I.M., Reynolds, M.A.: Temporal Logic: - Mathematical Foundations and Computational Aspects, vol. 1. Clarendon Press, Oxford (1994)

    Google Scholar 

  12. Gabbay D.M., Hodkinson I.M.: An axiomatization of the temporal logic with Until and Since over the real numbers. J. Log. Comput. 1, 229–260 (1990)

    Google Scholar 

  13. Gabbay, D., Hodkinson, I.: Temporal logic in context of databases. In: Copeland, J. (ed.) Logic and Reality. Oxford University Press, Essays on the legacy of Arthur Prior (1995)

    Google Scholar 

  14. Horrocks, I., Sattler, U.: A description logic with transitive and inverse roles and role hierarchies. Descr. Log. (1998)

    Google Scholar 

  15. Horrocks, I., Giese, M., Kharlamov, E., Waaler, A.: Using semantic technology to tame the data variety challenge. IEEE Internet Comput. 20(6), 62–66 (2016)

    Google Scholar 

  16. Sattler, U.: Description Logics for the Representation of Aggregated Objects. ECAI, pp. 239–243 (2000)

    Google Scholar 

  17. Rybakov, V.V.: Linear temporal logic with until and before on integer numbers, deciding algorithms. In: Computer Science—Theory and Applications, Lecture Notes in Computer Science, vol. 3967, pp. 322–334. Springer, Berlin (2006)

    Google Scholar 

  18. Rybakov, V.V.: Linear temporal logic with until and next, logical consecutions. Ann. Pure Appl. Log.155(1), 32–45 (2008)

    Google Scholar 

  19. Rybakov, V.V.: Multi-modal and temporal logics with universal formula—reduction of admissibility to validity and unification. J. Log. Comput. 18(4), 509–519 (2008)

    Google Scholar 

  20. Rybakov, V.V.: LTKK extended by multi-agent logic Kn with interacting agents. J. Log. Comput. 19(6), 989–1017 (2009). Oxford Press

    Google Scholar 

  21. Rybakov, V.: Non-transitive linear temporal logic and logical knowledge operations. J. Log. Comput. 26(3), 945–958 (2016). Oxford Press

    Google Scholar 

  22. Rybakov, V.: Intransitive temporal multi-agents logic, knowledge and uncertainty, plausibility. In: International Symposium on Logical Foundations of Computer Science, Volume 9537 of the series Lecture Notes in Computer Science, pp. 364–375 (2016)

    Google Scholar 

  23. Rybakov, V.: Temporal logic with overlap temporal relations generated by time states themselves. Siberian Math. Rep. 17, 923–932 (2020)

    Google Scholar 

  24. Rybakov, V.: Multi-agent temporal nontransitive linear logics and the admissibility problem . Algebra Log. 59, 87–100 (2020)

    Google Scholar 

  25. Rybakov, V.: Branching time logics with multiagent temporal accessibility relations . Siberian Math. J. 62(3), 503–510 (2021)

    Google Scholar 

  26. Vardi, M.: An automata-theoretic approach to linear temporal logic. In: Banff Higher Order Workshop, pp. 238–266 (1955). Available at http://citeseer.ist.psu.edu/vardi96automatatheoretic.html

  27. Vardi, M.Y.: Reasoning about the past with two-way automata. In: Larsen K.G., Skyum S., Winskel G., (eds.) ICALP, LNCS, vol. 1443, pp. 628–641. Springer, Berlin (1998)

    Google Scholar 

  28. Wooldridge, M., Lomuscio, A.: Multi-agent VSK logic. In: Proceedings of the Seventh European Workshop on Logics in Artificial Intelligence (JELIAI-2000). Springer, Berlin (2000)

    Google Scholar 

  29. Wooldridge, M.: An Automata-theoretic approach to multi-agent planning. In: Proceedings of the First European Workshop on Multi-agent Systems (EUMAS 2003). Oxford University (2003)

    Google Scholar 

  30. Wooldridge, M., Huget, M.-P., Fisher, M., Parsons, S.: Model checking multi-agent systems: the MABLE language and its applications. Int. J. Artif. Intell. Tools 15(2), 195–225 (2006)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Fundamental Informatics, Siberian Federal University, Krasnoyarsk, Russian Federation

    Vladimir V. Rybakov

  2. Institute of Informatics Systems, Siberian Branch of RAS, Novosibirsk, Russia

    Vladimir V. Rybakov

  3. National Research University - High School of Economics, Moscow, Russia

    Vladimir V. Rybakov

Authors
  1. Vladimir V. Rybakov
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Corresponding author

Correspondence to Vladimir V. Rybakov .

Editor information

Editors and Affiliations

  1. University of Zagreb, Zagreb, Croatia

    Gordan Jezic

  2. The Heriot-Watt University, Scotland, UK

    Yun-Heh Jessica Chen-Burger

  3. University of Zagreb, Zagreb, Croatia

    Mario Kusek

  4. Silesian University in Opava, Opava, Czech Republic

    Roman Šperka

  5. KES International Research, Shoreham-by-sea, UK

    Robert J. Howlett

  6. KES International, Selby, UK

    Lakhmi C. Jain

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© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Rybakov, V.V. (2022). Temporal Logic in Multi-agent Environment. In: Jezic, G., Chen-Burger, YH.J., Kusek, M., Šperka, R., Howlett, R.J., Jain, L.C. (eds) Agents and Multi-Agent Systems: Technologies and Applications 2022. Smart Innovation, Systems and Technologies, vol 306. Springer, Singapore. https://doi.org/10.1007/978-981-19-3359-2_1

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