SZTAKI Közlemények 34. (1986)

Vu Duc Thi: Remarks on dual dependencies

MTA SZTAKI Közlemények 34/1986 pp.113-122 Let REMARKS ON DUAL DEPENDENCIES Vu Duo Thi MTA SZTAKI §0, INTRODUCTION One of the main concepts in relational database theory is the full family of functional dependencies, that was first axiomatized by W.W.Armstrong СИ. The full family of dual dependencies have also been introduced and axiomatized C2,33. In this paper, we give some results, that are related to dual dependencies. Some properties of functional dependencies are investigated also. §1. DEFINITIONS In this section, we present some necessary definitions. Definition 1.1. Let 0 be a finite set of attributes, and R={h1,...,h } be a relation over Q, A,B^O. Then we sav that В I'm d dually depends A in R (denote A ^ B) if (Vh. ,h-6R) ( (3a€A) (h. (a) =h . (a))- (3b€B) (h. (b) =h^ (b) ) ) ? X 1 J X , f В functionally depends A in R (denote A — B) if R (Vhi,hj€R) ( (Va6A) (hi (a)=hj (a) )-(VbSB) (h± (b) =h j (b) ) ) . d f D = { (A,B) : A -* B] and F_={(A,B) : A - B] . K R K R

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