License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2012.77
URN: urn:nbn:de:0030-drops-36656
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3665/
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Berardi, Stefano ; de'Liguoro, Ugo

Knowledge Spaces and the Completeness of Learning Strategies

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Abstract

We propose a theory of learning aimed to formalize some ideas underlying Coquand's game semantics and Krivine's realizability of classical logic. We introduce a notion of knowledge state together with a new topology, capturing finite positive and negative information that guides a learning strategy. We use a leading example to illustrate how non-constructive proofs lead to continuous and effective learning strategies over knowledge spaces, and prove that our learning semantics is sound and complete w.r.t. classical truth, as it is the case for Coquand's and Krivine's approaches.

BibTeX - Entry

@InProceedings{berardi_et_al:LIPIcs:2012:3665,
  author =	{Stefano Berardi and Ugo de'Liguoro},
  title =	{{Knowledge Spaces and the Completeness of Learning Strategies}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{77--91},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{Patrick C{\'e}gielski and Arnaud Durand},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3665},
  URN =		{urn:nbn:de:0030-drops-36656},
  doi =		{10.4230/LIPIcs.CSL.2012.77},
  annote =	{Keywords: Classical Logic, Proof Mining, Game Semantics, Learning, Realizability}
}

Keywords: Classical Logic, Proof Mining, Game Semantics, Learning, Realizability
Collection: Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL
Issue Date: 2012
Date of publication: 03.09.2012

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