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Berardi-deLiguoro:IC09 (Article)
Author(s) Stefano Berardi and Ugo de' Liguoro
Title« Toward the interpretation of non-constructive reasoning as non-monotonic learning »
JournalInformation and Computation
Volume207
Number1
Page(s)63-81
Year2009
Abstract
We study an abstract representation of the learning process, which we call learning sequence, aiming at a constructive interpretation of classical logical proofs, that we see as learning strategies, coming from Coquand’s game theoretic interpretation of classical logic. Inspired by Gold’s notion of limiting recursion and by the Limit-Computable Mathematics by Hayashi, we investigate the idea of learning in the limit in the general case, where both guess retraction and resumption are allowed. The main contribution is the characterization of the limits of non-monotonic learning sequences in terms of the extension relation between guesses.

Download the complete article: j.ic.2008.10.003

BibTeX code

@article{Berardi-deLiguoro:IC09,
  number = {1},
  volume = {207},
  author = {Stefano Berardi and de' Liguoro, Ugo},
  tag = {{Information and Computation}},
  localfile = {http://dx.doi.org/10.1016/j.ic.2008.10.003},
  title = {Toward the interpretation of non-constructive reasoning as
           non-monotonic learning},
  abstract = {We study an abstract representation of the learning process, which
              we call learning sequence, aiming at a constructive interpretation
              of classical logical proofs, that we see as learning strategies,
              coming from Coquand’s game theoretic interpretation of classical
              logic. Inspired by Gold’s notion of limiting recursion and by the
              Limit-Computable Mathematics by Hayashi, we investigate the idea
              of learning in the limit in the general case, where both guess
              retraction and resumption are allowed. The main contribution is
              the characterization of the limits of non-monotonic learning
              sequences in terms of the extension relation between guesses.},
  year = {2009},
  pages = {63-81},
  journal = {Information and Computation},
}


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