Download e-book for kindle: Dependencies in Relational Databases by Prof. Dr. Bernhard Thalheim (auth.)

By Prof. Dr. Bernhard Thalheim (auth.)

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DBAB85/. It is shown that no finite sound and complete formal system can exist for first-order hierarchical dependencies /PARE 80/. 5. : ••. :Y. and { (XY, ... , ... ,XY,) : liiim} . 59 From the practical viewpoint this means that the closure by successive application of inference rules can not be constructed. Although this is a limitation for the use of algorithms, it is still possible to obtain new dependencies which are of great aid to the user during the conceiving and development phases of a database for the system.

3. lt This chapter deals with the relationship between logic and relational database theory. The aim of the chapter is to show, by many results published in the literature, how logic can provide a formal support to study classic database problems, and in some cases, how logic can go further, helping first in their comprehension, and then their solution. Logic is just a formal systea; many other formal systems have been proposed and applied to databases. In the axiomatic approach, a formal system relies upon an object language, semantics or interpretation of formulas in that language and a proof theory.

De~en­ In /KANE 80/ the lossless join problem is considered for numerical dependencies and functional dependencies. The lossless join problem can be formulated as follows: Given a set of dependencies I and a join dependency d • Is there a database r satisfying I and not d ? There /KANE 80/ is proven that the lossless join problem is NP-complete if I consists of functional dependencies and just one 3-ary numerical dependency. For other classes of general functional dependencies there exist an axiomatization.

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