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Temporal Multi-Agent’s Logic, Knowledge, Uncertainty, and Plausibility

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Agents and Multi-Agent Systems: Technologies and Applications 2021

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 241))

Abstract

The paper studies temporal logic implementing multi-agent’s approach and formalizing knowledge and uncertainty. We consider non-transitive linear time and multi-valued models—the ones using separate valuations \(V_j\) for the agent’s knowledge of facts and summarized (agreed) valuation together with rules for computation truth values for compound formulas. The basic mathematical problems we study here are decidability and decidability w.r.t. admissible rules. First, we study the general case—the logic with non-uniform intransitivity—and solve its decidability problem. Also, we consider a modification of this logic—temporal logic with uniform non-transitivity—and solve the problem of recognizing admissibility in this logic. The conclusion contains a discussion and a list of open problems.

This research is supported by High School of Economics (HSE), Moscow, the Krasnoyarsk Mathematical Center, and financed by the Ministry of Science and Higher Education of the Russian Federation (Grant No. 075-02-2020-1534/1).

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny Pr., 660041, Krasnoyarsk, Russia

    Vladimir Rybakov

  2. (part time) A.P. Ershov Institute of Informatics Systems SB RAS Academy, Lavrentjev pr., 6, Novosibirsk, 630090, Russia

    Vladimir Rybakov

Authors
  1. Vladimir Rybakov
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Corresponding author

Correspondence to Vladimir Rybakov .

Editor information

Editors and Affiliations

  1. Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia

    G. Jezic

  2. School of Mathematical and Computer Sciences, The Heriot-Watt University, Edinburgh, UK

    J. Chen-Burger

  3. Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia, Croatia

    M. Kusek

  4. Department of Business Economics and Management, Silesian University in Opava, Opava, Czech Republic

    R. Sperka

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

    R. J. Howlett

  6. University of Technology Sydney, Broadway, NSW, Australia

    Lakhmi C. Jain

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Rybakov, V. (2021). Temporal Multi-Agent’s Logic, Knowledge, Uncertainty, and Plausibility. In: Jezic, G., Chen-Burger, J., Kusek, M., Sperka, R., Howlett, R.J., Jain, L.C. (eds) Agents and Multi-Agent Systems: Technologies and Applications 2021. Smart Innovation, Systems and Technologies, vol 241. Springer, Singapore. https://doi.org/10.1007/978-981-16-2994-5_17

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