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Berardi-deLiguoro-CSL-full-2013 (Article)
Author(s) Stefano Berardi and Ugo de' Liguoro
Title« Knowledge Spaces and the Completeness of Learning Strategies (full version) »
JournalLMCS
Volume10
Page(s)1-21
Year2014
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: 1401.0885

BibTeX code

@article{Berardi-deLiguoro-CSL-full-2013,
  volume = {10},
  author = {Stefano Berardi and Ugo de' Liguoro},
  editor = {Patrick C{\'e}gielski and Arnaud Durand},
  tag = {{Logical Methods in Computer Science}},
  localfile = {http://arxiv.org/abs/1401.0885},
  title = {{Knowledge Spaces and the Completeness of Learning Strategies (full
           version)}},
  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.},
  year = {2014},
  pages = {1-21},
  journal = {{LMCS}},
}


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Formal Methods in Computing
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