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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2013.540
URN: urn:nbn:de:0030-drops-42181
URL: http://drops.dagstuhl.de/opus/volltexte/2013/4218/
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Melliès, Paul-André

On dialogue games and coherent strategies

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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.

BibTeX - Entry

@InProceedings{mellis:LIPIcs:2013:4218,
  author =	{Paul-Andr{\'e} Melli{\`e}s},
  title =	{{On dialogue games and coherent strategies}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{540--562},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Simona Ronchi Della Rocca},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4218},
  URN =		{urn:nbn:de:0030-drops-42181},
  doi =		{10.4230/LIPIcs.CSL.2013.540},
  annote =	{Keywords: Game semantics, Stable order, Extensional order, Bistructures, Tensorial logic, Innocent strategies}
}

Keywords: Game semantics, Stable order, Extensional order, Bistructures, Tensorial logic, Innocent strategies
Seminar: Computer Science Logic 2013 (CSL 2013)
Issue Date: 2013
Date of publication: 27.08.2013


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