Algebras of quasiary and of bi-quasiary relations

M.S. Nikitchenko, S.S. Shkilniak

Abstract


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


Keywords


algebra; logic; relation; isomorphism; quasiary predicate

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References


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Nikitchenko M. and Shkilniak S. (2014). Algebras of quasiary relations. In Theoretical and Applied Aspects of Program Systems Development (TAAPSD'2014): 11th international conference: proceeding. – Кyiv. P. 174–181 (in Ukrainian).


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