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Intuitionistic Games: Determinacy, Completeness, and Normalization

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Abstract

We investigate a simple game paradigm for intuitionistic logic, inspired by Wajsberg’s implicit inhabitation algorithm and Beth tableaux. The principal idea is that one player,  ∃ros, is trying to construct a proof in normal form (positions in the game represent his progress in proof construction) while his opponent, ∀phrodite,  attempts to build a counter-model (positions or plays can be seen as states in a Kripke model). The determinacy of the game (a proof-construction and a model-construction game in one) implies therefore both completeness and semantic cut-elimination.

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Paweł Urzyczyn

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  1. Paweł Urzyczyn
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Correspondence to Paweł Urzyczyn.

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This paper is a revised and expanded version of [17], presented at the conference Trends in Logic XIII.

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Urzyczyn, P. Intuitionistic Games: Determinacy, Completeness, and Normalization. Stud Logica 104, 957–1001 (2016). https://doi.org/10.1007/s11225-016-9661-4

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  • DOI: https://doi.org/10.1007/s11225-016-9661-4

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