Algebras of quasiary and of bi-quasiary relations
The notion of quasiary relation which can be considered generalization of the notion of traditional n-ary relation is proposed. A number of algebras of quasiary relations is built and investigated. Alongside with conventional operations of union, intersection, and complement, special nominative oper...
Збережено в:
| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Ukrainian |
| Опубліковано: |
Інститут програмних систем НАН України
2018
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| Теми: | |
| Онлайн доступ: | https://pp.isofts.kiev.ua/index.php/ojs1/article/view/165 |
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| Назва журналу: | Problems in programming |
Репозитарії
Problems in programming| Резюме: | The notion of quasiary relation which can be considered generalization of the notion of traditional n-ary relation is proposed. A number of algebras of quasiary relations is built and investigated. Alongside with conventional operations of union, intersection, and complement, special nominative operations of renomi-nation and quantification are defined for quasiary relations. The isomorphism between the algebra of quasiary relations and the first-order algebra of total single-valued quasiary predicates is proved. Al-gebras of bi-quasiary relations defined over sets of pairs of quasiary relations are built. The isomorphism between algebras of bi-quasiary relations and alge-bras of quasiary predicates is proved. The following subclasses of algebras of bi-quasiary relations are specified: alge-bras of partial single-valued (functional), total, total many-valued bi-quasiary relations. For all defined subclasses their counterparts of the classes of algebras of quasiary predicates are described. Also subalgebras of the algebra of bi-quasiary relations induced by upward closedness and downward closedness are investigated.Prombles in programming 2016; 1: 17-28 |
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