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.
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.
- 3.
The height of a formula is the height of its construction tree.
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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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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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