**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) »* |

Journal | LMCS |

Volume | 10 |

Page(s) | 1-21 |

Year | 2014 |

**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:

```
@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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