Advances in Data Base Theory: Volume 1 by Hervé Gallaire, Jack Minker, Jean Marie Nicolas

By Hervé Gallaire, Jack Minker, Jean Marie Nicolas

Through the 1970's a thought of knowledge ases started to evolve seasoned viding a origin for a few latest instruments and methods. the importance of this conception is commencing to have an effect particu larly with admire to the layout and implementation of the relational version of information bases. To additional the state-of-the-art within the concept of information bases, a workshop was once held in TOulouse, France on December 12-14, 1979. The workshop used to be a sequel to 1 held years formerly and entitled, "Logic and knowledge Base Workshop." As with the sooner paintings store, the conferences have been carried out on the centre d'Etudes et de Recherches de l'Ecole Nationale Superieure de l'Aeronautique et de l'Espace de Toulouse (C.E.R.T). we're happy to recognize the monetary aid bought from the course des Recherches, Etudes et suggestions d'Armement (D.R.E.T.), and from C.E.R.T. that made the workshop attainable.

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Without loss of generality, assume that f is the fd X + A, A ~ X. If C X + A, then by rule FD-JDl, C *[XA, xA] and by the previous corollary, C ~~ * [XA,xA] • NOw, this jd has {A} as one of its X-branches and X is the corresponding X-stem. Therefore, it suffices to show that C contains an fd S + A, A ~ S. For if C contains such an fd, then an application of rule FD-JD2 yields the desired fd X + A. That C contains such an fd will be proved in the next section. 0 F F corollary 9 (a) Let C F * [~] fOhd.

Q] = *[(BD, A), (BD, C), (BE, G), (DE, F), (D,I), (E,HJ)]. o A Rule with an Unbounded Number of Premises The next rule we present is different from all previous rules in that it may have an arbitrary number of premises. i such that, for all i, R. C ATTR(Sl)and1MANY(Sl) . Then k 1- - *[~], {*[~l]}i=1 ~ *[Q] k Q. = 'UI J 1= . = . - *[{Qj};:~(mi)], «R. ) • 1 The soundness of the rule is proved a~ follows. First we use EJDI to replace each R. E R by R. U MANY (Sl) . Then we use EJD2 and EJD3 to replace each 1R.

0 The Rule of Substitution The rules EJDl and EJD2 both allow us to infer from one given dependency another dependency that is less informative than the one that is given. EJDO is an axiom tha~ allows us to infer only trivial dependencies. We now present a rule that will allow us to combine two dependencies to yield a third dependency that is more informative than either one of the given dependencies. ] • - e ~, then The rule is sound. ) = R. , and let I be in SAT(*[R],*[S]). ~ TI (I) and TI (I) = .

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