Stefano Berardi ; Ugo de'Liguoro - Knowledge Spaces and the Completeness of Learning Strategies

lmcs:729 - Logical Methods in Computer Science, February 12, 2014, Volume 10, Issue 1 -
Knowledge Spaces and the Completeness of Learning Strategies

Authors: Stefano Berardi ; Ugo de'Liguoro

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.

Volume: Volume 10, Issue 1
Published on: February 12, 2014
Accepted on: June 25, 2015
Submitted on: January 18, 2013
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic


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