Knowledge Spaces and the Completeness of Learning Strategies

Berardi, Stefano; de'Liguoro, Ugo

doi:10.4230/LIPIcs.CSL.2012.77

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Knowledge Spaces and the Completeness of Learning Strategies

Authors Stefano Berardi, Ugo de'Liguoro

Part of: Volume: Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (CSL 2012)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Computer Science Logic (CSL)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2012-09-03

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Document Identifiers

DOI: 10.4230/LIPIcs.CSL.2012.77
URN: urn:nbn:de:0030-drops-36656

Subject Classification

Keywords

Classical Logic
Proof Mining
Game Semantics
Learning
Realizability

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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.

Cite As Get BibTex

Stefano Berardi and Ugo de'Liguoro. Knowledge Spaces and the Completeness of Learning Strategies. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 77-91, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012) https://doi.org/10.4230/LIPIcs.CSL.2012.77

Author Details

Stefano Berardi

Ugo de'Liguoro

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