Maximum predicate descriptions of sets of mappings

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Abstract

The work is carried out in the framework of the algebraic approach and is devoted to the problem of describing sets of mappings by pairs of m-place predicates. Maximum descriptions are distinguished in the set of all predicate descriptions, and necessary and sufficient maximality conditions are obtained. Using a partial order and betweenness relations as examples, it is shown that, for a given predicate on the set of values, the necessary maximality conditions imply some properties of this predicate on its domain. Taking this fact into account, a set of axioms for the betweenness relation is proposed, and examples of such relations are considered.

Original languageEnglish
Pages (from-to)1570-1581
Number of pages12
JournalComputational Mathematics and Mathematical Physics
Volume47
Issue number9
DOIs
Publication statusPublished - Sep 1 2007

Keywords

  • Algebraic approach
  • Pattern recognition
  • Precedent learning
  • Predicate description

ASJC Scopus subject areas

  • Computational Mathematics

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