BerardideLiguoro:FICS13 (In proceedings)

Author(s)  Stefano Berardi and Ugo de' Liguoro 
Title  « Nonmonotonic prefix points and Learning » 
In  Proceedings of FICS 2013 
Series  EPTCS 
Editor(s)  David Baelde and Arnaud Carayol 
Volume  126 
Page(s)  110 
Year  2013 
Abstract 
We consider the problem of finding prefix points of interactive realizers over arbitrary knowledge spaces, obtaining a relative recursive procedure. Knowledge spaces and interactive realizers are an abstract setting to represent learning processes, that can interpret nonconstructive proofs. Atomic pieces of information of a knowledge space are stratified into levels, and evaluated into truth values depending on knowledge states. Realizers are then used to define operators that extend a given state by adding and possibly removing atoms: in a learning process states of knowledge change nonmonotonically. Existence of a prefix point of a realizer is equivalent to the termination of the learning process with some state of knowledge which is free of patent contradictions and such that there is nothing to add. In this paper we generalize our previous results in the case of level 2 knowledge spaces and deterministic operators to the case of $\omega $level knowledge spaces and of nondeterministic operators. 
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@inproceedings{BerardideLiguoro:FICS13,
volume = {126},
author = {Stefano Berardi and Ugo de' Liguoro},
series = {{EPTCS}},
booktitle = {{Proceedings of FICS 2013}},
editor = {David Baelde and Arnaud Carayol},
title = {{Nonmonotonic prefix points and Learning}},
abstract = {We consider the problem of finding prefix points of interactive
realizers over arbitrary knowledge spaces, obtaining a relative
recursive procedure. Knowledge spaces and interactive realizers
are an abstract setting to represent learning processes, that can
interpret nonconstructive proofs. Atomic pieces of information of
a knowledge space are stratified into levels, and evaluated into
truth values depending on knowledge states. Realizers are then
used to define operators that extend a given state by adding and
possibly removing atoms: in a learning process states of knowledge
change nonmonotonically. Existence of a prefix point of a
realizer is equivalent to the termination of the learning process
with some state of knowledge which is free of patent
contradictions and such that there is nothing to add. In this
paper we generalize our previous results in the case of level 2
knowledge spaces and deterministic operators to the case of
$\omega$level knowledge spaces and of nondeterministic
operators.},
tag = {FICS'13},
localfile = {http://dx.doi.org/10.4204/EPTCS.126.1},
year = {2013},
pages = {110},
}
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