### 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 |
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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 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Computational Mathematics and Mathematical Physics*, vol. 47, no. 9, pp. 1570-1581. https://doi.org/10.1134/S0965542507090175

}

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

AN - SCOPUS:34848911013

VL - 47

SP - 1570

EP - 1581

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 9

ER -