License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2013.24
URN: urn:nbn:de:0030-drops-46245
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4624/
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Aschieri, Federico ; Zorzi, Margherita

A "Game Semantical" Intuitionistic Realizability Validating Markov's Principle

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Abstract

We propose a very simple modification of Kreisel's modified realizability in order to computationally realize Markov's Principle in the context of Heyting Arithmetic. Intuitively, realizers correspond to arbitrary strategies in Hintikka-Tarski games, while in Kreisel's realizability they can only represent winning strategies. Our definition, however, does not employ directly game semantical concepts and remains in the style of functional interpretations. As term calculus, we employ a purely functional language, which is Goedel's System T enriched with some syntactic sugar.

BibTeX - Entry

@InProceedings{aschieri_et_al:LIPIcs:2014:4624,
  author =	{Federico Aschieri and Margherita Zorzi},
  title =	{{A "Game Semantical" Intuitionistic Realizability Validating Markov's Principle}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{24--44},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Ralph Matthes and Aleksy Schubert},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4624},
  URN =		{urn:nbn:de:0030-drops-46245},
  doi =		{10.4230/LIPIcs.TYPES.2013.24},
  annote =	{Keywords: Markov's Principle, Intuitionistic Realizability, Heyting Arithmetic, Game Semantics}
}

Keywords: Markov's Principle, Intuitionistic Realizability, Heyting Arithmetic, Game Semantics
Collection: 19th International Conference on Types for Proofs and Programs (TYPES 2013)
Issue Date: 2014
Date of publication: 25.07.2014

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