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BdL17-FI (Article)
Author(s) Stefano Berardi and Ugo de' Liguoro
Title« Non-monotonic pre-fix points and Learning »
JournalFundamenta Informaticae
Number150
Page(s)259--280
Year2017
Abstract
We consider the problem of finding pre-fix 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 non-constructive 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 non-monotonically. Existence of a pre-fix 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 non-deterministic operators.

Download the complete article: FI-Nonmonotonicfixedpoint.pdf

BibTeX code

@article{BdL17-FI,
  number = {150},
  author = {Stefano Berardi and Ugo de' Liguoro},
  tag = {{Fundamenta Informaticae}},
  title = {Non-monotonic pre-fix points and Learning},
  abstract = {We consider the problem of finding pre-fix 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 non-constructive 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 non-monotonically. Existence of
              a pre-fix 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 non-deterministic operators.},
  localfile = {http://www.di.unito.it/~deligu/papers/FI-Nonmonotonicfixedpoint.pdf},
  journal = {{Fundamenta Informaticae}},
  pages = {259--280},
  year = {2017},
}


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