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Lorenzen-Style Strategies as Proof-Search Strategies

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Multi-Agent Systems (EUMAS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14282))

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Abstract

Dialogical logic, originated in the work of Lorenzen and his student Lorenz, is an approach to logic in which the validity of a certain formula is defined as the existence of a winning strategy for a particular kind of turn-based two-players games. This paper studies the relationship between winning strategies for Lorenzen-style dialogical games and sequent calculus derivations. We define three different classes of dialogical logic games for the implicational fragment of intuitionistic logic, showing that winning strategies for such games naturally correspond to classes of derivations defined by uniformly restraining the rules of the sequent calculus.

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Notes

  1. 1.

    We use the adjective countable in the standard mathematical sense: a set is countable iff it is in a one-to-one correspondence with a (finite or infinite) subset of the set of natural numbers.

  2. 2.

    This definition of validity corresponds to the standard one i.e., valid in every Kripke model whose accessibility relation is a preorder and whose labeling is monotone. See e.g. [15, 32].

  3. 3.

    The height of a formula is the height of its construction tree.

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Acknowledgments

The first author is supported by Villum Fonden, grant no. 50079. The second author is supported by the PRIN project RIPER (No. 20203FFYLK).

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Authors and Affiliations

  1. University of Southern Denmark, Odense, Denmark

    Matteo Acclavio

  2. Università degli studi di Napoli, Federico II, Naples, Italy

    Davide Catta

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Correspondence to Matteo Acclavio .

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  1. Télécom Paris, Paris, France

    Vadim Malvone

  2. Universitá degli Studi di Napoli Federico II, Naples, Italy

    Aniello Murano

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Acclavio, M., Catta, D. (2023). Lorenzen-Style Strategies as Proof-Search Strategies. In: Malvone, V., Murano, A. (eds) Multi-Agent Systems. EUMAS 2023. Lecture Notes in Computer Science(), vol 14282. Springer, Cham. https://doi.org/10.1007/978-3-031-43264-4_10

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  • DOI: https://doi.org/10.1007/978-3-031-43264-4_10

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