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...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут програмних систем НАН України
2018
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| Subjects: | |
| Online Access: | https://pp.isofts.kiev.ua/index.php/ojs1/article/view/165 |
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| Journal Title: | Problems in programming |
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Problems in programming| Summary: | 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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