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 2007 |
| Externally published | Yes |
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Keywords
- Algebraic approach
- Pattern recognition
- Precedent learning
- Predicate description
ASJC Scopus subject areas
- Computational Mathematics
Cite this
Maximum predicate descriptions of sets of mappings. / Takhanov, R. S.
In: Computational Mathematics and Mathematical Physics, Vol. 47, No. 9, 09.2007, p. 1570-1581.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Maximum predicate descriptions of sets of mappings
AU - Takhanov, R. S.
PY - 2007/9
Y1 - 2007/9
N2 - 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.
AB - 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.
KW - Algebraic approach
KW - Pattern recognition
KW - Precedent learning
KW - Predicate description
UR - http://www.scopus.com/inward/record.url?scp=34848911013&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34848911013&partnerID=8YFLogxK
U2 - 10.1134/S0965542507090175
DO - 10.1134/S0965542507090175
M3 - Article
VL - 47
SP - 1570
EP - 1581
JO - Computational Mathematics and Mathematical Physics
JF - Computational Mathematics and Mathematical Physics
SN - 0965-5425
IS - 9
ER -