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On dialogue games and coherent strategies

Author Paul-André Melliès



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LIPIcs.CSL.2013.540.pdf
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Paul-André Melliès

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Paul-André Melliès. On dialogue games and coherent strategies. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 540-562, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.CSL.2013.540

Abstract

We explain how to see the set of positions of a dialogue game as a coherence space in the sense of Girard or as a bistructure in the sense of Curien, Plotkin and Winskel. The coherence structure on the set of positions results from a Kripke translation of tensorial logic into linear logic extended with a necessity modality. The translation is done in such a way that every innocent strategy defines a clique or a configuration in the resulting space of positions. This leads us to study the notion of configuration designed by Curien, Plotkin and Winskel for general bistructures in the particular case of a bistructure associated to a dialogue game. We show that every such configuration may be seen as an interactive strategy equipped with a backward as well as a forward dynamics based on the interplay between the stable order and the extensional order. In that way, the category of bistructures is shown to include a full subcategory of games and coherent strategies of an interesting nature.
Keywords
  • Game semantics
  • Stable order
  • Extensional order
  • Bistructures
  • Tensorial logic
  • Innocent strategies

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