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KNOWLEDGE ACQUISITION IN MULTI-AGENT SYSTEMS: A FORMALIZATION OF THE ELEUSIS CARD GAME

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Abstract

We deal with logical approaches to knowledge acquisition in multi-agent systems. We enhance previous work by considering the inductive card game Eleusis where dynamic knowledge about the behavior of other agents or environment, rather than traditional static knowledge about system states is acquired. Our main contributions are as follows: (1) we formalize the knowledge acquisition process in the infinite version of the Eleusis game with perfect recall (i.e., the agents never forget the acquired information), using the propositional logic of knowledge and branching time Act-CTL-K\(_n\), and (2) we formally prove that the Eleusis system with perfect recall is well structured, which in practice enables applying the recently implemented model checking methods for infinite well-structured systems. In addition to the theoretical interest, our work is also motivated by potential application fields, including cryptography.

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Notes

  1. In the definition, for every set S, let \(S^*\) be the set of all finite sequences over S and the operation \(^\wedge\) stand for the concatenation of finite words.

  2. Because we model behavior depending on information history, but not on the single local state.

  3. Our formal description of Eleusis can easily be extended to a larger number of players: we just need to add the corresponding player names to the model and define their actions and protocols in the manner described below, down to the player names.

  4. We do not need in future F because Eleusis rule determines all cards in sequences at every position step by step.

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Acknowledgements

We thank the referees for their careful reading and editing of the paper. We also thank the editing service of the journal for the good improvements and the organization of the paper.

Funding

Natalia Garanina was supported by the scholarship of DAAD (German Academic Exchange Service). Sergei Gorlatch is supported by the DFG project Nr. 470527619 (PPP-DL) at the University of Munster.

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Authors and Affiliations

  1. University of Muenster, Münster, Germany

    Natalia Garanina & Sergei Gorlatch

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

    Natalia Garanina

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  1. Natalia Garanina
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  2. Sergei Gorlatch
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Correspondence to Natalia Garanina.

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Garanina, N., Gorlatch, S. KNOWLEDGE ACQUISITION IN MULTI-AGENT SYSTEMS: A FORMALIZATION OF THE ELEUSIS CARD GAME. J Math Sci (2024). https://doi.org/10.1007/s10958-024-07107-y

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