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Berardi-deLiguoro:CSL12 (In proceedings)
Author(s) Stefano Berardi and Ugo de' Liguoro
Title« Knowledge Spaces and the Completeness of Learning Strategies »
InComputer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL, CSL 2012, September 3-6, 2012, Fontainebleau, France
SeriesLIPIcs
Editor(s) Patrick Cégielski and Arnaud Durand
Volume16
Page(s)77-91
Year2012
PublisherSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik
ISBN number978-3-939897-42-2
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.

Download the complete article: KnowSpace.pdf

BibTeX code

@inproceedings{Berardi-deLiguoro:CSL12,
  volume = {16},
  author = {Stefano Berardi and Ugo de' Liguoro},
  series = {LIPIcs},
  booktitle = {{Computer Science Logic (CSL'12) - 26th International
               Workshop/21st Annual Conference of the EACSL, CSL 2012, September
               3-6, 2012, Fontainebleau, France}},
  editor = {Patrick C{\'e}gielski and Arnaud Durand},
  title = {{Knowledge Spaces and the Completeness of Learning Strategies}},
  localfile = {http://www.di.unito.it/~deligu/papers/KnowSpace.pdf},
  isbn = {978-3-939897-42-2},
  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.},
  tag = {CSL'12},
  publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik},
  year = {2012},
  pages = {77-91},
}


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