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Dynamic Epistemic Logic for Budget-Constrained Agents

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Dynamic Logic. New Trends and Applications (DaLí 2022)

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Abstract

We present a static (\(\textsf{EL}_{\textsf{bc}}\)) and dynamic (\(\textsf{DEL}_{\textsf{bc}}\)) epistemic logic for budget-constrained agents, in which an agent can obtain some information in exchange for budget resources. \(\textsf{EL}_{\textsf{bc}}\) extends a standard multi-agent epistemic logic with expressions concerning agent’s budgets and formulas’ costs. \(\textsf{DEL}_{\textsf{bc}}\) extends \(\textsf{EL}_{\textsf{bc}}\) with dynamic modality “\([?_i A]\varphi \)” which reads as “\(\varphi \) holds after i’s question whether a propositional formula A is true”. In this paper we provide a sound and complete axiomatization for \(\textsf{EL}_{\textsf{bc}}\) and \(\textsf{DEL}_{\textsf{bc}}\) and show that both logics are decidable.

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Acknowledgements

This work is an output of a research project implemented as part of the Basic Research Program at the National Research University Higher School of Economics (HSE University). Also we would like to thank Evgeny Zolin, Elia Zardini and three anonymous reviewers for comments and suggestions on earlier versions of this paper.

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Authors and Affiliations

  1. HSE University, Myasnitskaya 20, 101000, Moscow, Russian Federation

    Vitaliy Dolgorukov

  2. Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands

    Maksim Gladyshev

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  1. Vitaliy Dolgorukov
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  2. Maksim Gladyshev
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Correspondence to Maksim Gladyshev .

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Editors and Affiliations

  1. Universidad Nacional de Córdoba, Córdoba, Argentina

    Carlos Areces

  2. Universidade de Lisboa, Lisbon, Portugal

    Diana Costa

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Dolgorukov, V., Gladyshev, M. (2023). Dynamic Epistemic Logic for Budget-Constrained Agents. In: Areces, C., Costa, D. (eds) Dynamic Logic. New Trends and Applications. DaLí 2022. Lecture Notes in Computer Science, vol 13780. Springer, Cham. https://doi.org/10.1007/978-3-031-26622-5_4

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  • DOI: https://doi.org/10.1007/978-3-031-26622-5_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-26621-8

  • Online ISBN: 978-3-031-26622-5

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