BdL17FI (Article)

Author(s)  Stefano Berardi and Ugo de' Liguoro 
Title  « Nonmonotonic prefix points and Learning » 
Journal  Fundamenta Informaticae 
Number  150 
Page(s)  259280 
Year  2017 
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 answers and possibly forcing us to remove some: in the 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 omegalevel knowledge spaces and of nondeterministic operators. 
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@article{BdL17FI,
number = {150},
author = {Stefano Berardi and Ugo de' Liguoro},
tag = {{Fundamenta Informaticae}},
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
answers and possibly forcing us to remove some: in the 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
omegalevel knowledge spaces and of nondeterministic operators.},
localfile = {http://www.di.unito.it/~deligu/papers/FINonmonotonicfixedpoint.pdf},
journal = {{Fundamenta Informaticae}},
pages = {259280},
year = {2017},
}
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