Open AccessAlgebras of quasiary and of bi-quasiary relations
Author(s) -
Mykola S. Nikitchenko,
S.S. Shkilniak
Publication year - 2016
Publication title -
problemy programmirovaniâ
Language(s) - English
Resource type - Journals
ISSN - 1727-4907
DOI - 10.15407/pp2016.01.017
Subject(s) - mathematics , isomorphism (crystallography) , intersection (aeronautics) , relation algebra , generalization , relation (database) , algebra over a field , pure mathematics , order (exchange) , equivalence relation , complement (music) , algebra representation , cellular algebra , computer science , finance , complementation , economics , gene , phenotype , database , aerospace engineering , mathematical analysis , chemistry , crystal structure , engineering , biochemistry , crystallography
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.