By Prof. Dr. Bernhard Thalheim (auth.)
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Additional info for Dependencies in Relational Databases
5 Now we introduce some special algebraic dependencies for uni-relational databases. 3. , ••• ,An}. } of subsets of U and X s rJ x. ])[X] s R(X] 1oin dependency (PJD) . ])[X] is valid in any RS-database £ If 'V x. = U the PJD is called total pro1ected loin dependency, and izl otherwise embedded pro1ected loin dependency. If X a x. the projected join dependency is called X-1oin dependency. i-1 If X ~ U the X-join dependency is called embedded loin dependency and if X = U the X-join dependency is called loin dependency (JD).
3. Given a class K of foraulas from L(RS) with a finite number of nonequivalent foraulas. The implication problem is solvable if and only if there is a sound and complete formal system for K • Proof. 1. Suppose the implication is solvable and consider the formal system consisting of one inference rule d Obviously, this formal system is sound and complete for K • 2. Suppose, rx is sound and complete for K • Let C s K and d t K be given. To decide whether C I· d we list every possible sequence of d,, ••• ,dk t K and check whether it is a derivation of d from C by rx .
R1) # f'(r,, ••• ,r1) • These formal languages can be used also for describing the connections between conceptual and external level in the three level model o~ database representation. The conceptual level corresponds to a database or relation scheme. The external level corresponds to the view of the whole or a part of the conceptual scheme as would be seen by a group of users concerned with a particular application. The external level can be defined by relational expressions. Another more restrictive possibility for definition of the external level is described by the concept of scheme morphism in /REI 84/.
Dependencies in Relational Databases by Prof. Dr. Bernhard Thalheim (auth.)