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 language | English |
---|---|
Pages (from-to) | 1570-1581 |
Number of pages | 12 |
Journal | Computational Mathematics and Mathematical Physics |
Volume | 47 |
Issue number | 9 |
DOIs | |
Publication status | Published - Sep 1 2007 |
Keywords
- Algebraic approach
- Pattern recognition
- Precedent learning
- Predicate description
ASJC Scopus subject areas
- Computational Mathematics