Database Design Theory by Michel Léonard (auth.)

By Michel Léonard (auth.)

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N n * iR[~+] is an instance of R because R = * R[~+]. iR' = j=l j=l According to the base property iR~ iR'. iR' is a complete instance of R forD because it verifies the jd (R 1... ~). We describe as associated a decomposition D of R and a jd of R which are formed on the same relations. Corollary A valid system of inferences for the jds is also valid for associated decompositions. Proof Take a relation R which decomposes to Dl D2 ... Dp. Its closure verifies the associated join dependencies d 1 d 2 ...

IRk.. i~ are mutually compatible if n (* (iRk) )[Rt] = i~ (V j e (l,n)). k=l COMPLETENESS PROPERTY If the relations R1... Rk···~ form a decomposition D of relation R, then for every entity ri, there is a set of mutually compatible entities (r 1 r2 ... rk ... r0 ) that contains it, and for every clear instance iRk, there is a mutually compatible set of instances (iR 1 iR2 .. i~) that contains it. Proof Since Rk is a projection of R, there is for every instance iRk an instance iR of R such that iR[R~] =iRk.

A key to the relation MACHINE-AVAIL is a minimum set of its attributes such that if two entities of MACHINE-AVAIL take the same values for these attributes in the same instance, these two entities are identical. If NMH is a key then it will not be possible to consider the availability of a machine during the course of several hours in the same instance! This is of course unacceptable. If NH is a key to MACHINE-AVAIL then the availability of a single machine for a given hour could be stored in an instance!

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