BerardideLiguoro:IC09 (Article)

Author(s)  Stefano Berardi and Ugo de' Liguoro 
Title  « Toward the interpretation of nonconstructive reasoning as nonmonotonic learning » 
Journal  Information and Computation 
Volume  207 
Number  1 
Page(s)  6381 
Year  2009 
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 LimitComputable 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 nonmonotonic learning sequences in terms of the extension relation between guesses. 
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@article{BerardideLiguoro: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 nonconstructive reasoning as
nonmonotonic 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
LimitComputable 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 nonmonotonic learning
sequences in terms of the extension relation between guesses.},
year = {2009},
pages = {6381},
journal = {Information and Computation},
}
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