The axiom system of data dependence of database design in 2016.6.17

* * The axiom system of data dependence is the theoretical basis of the model decomposition algorithm, Armstrong axiom system.

* * Logic implication: To satisfy a set of function dependent F relationship pattern R<u,f>, and any one of its relationship r, if the function depends on X->y is established, then said F logic implies x->y.

(1) The relational schema r<u,f> has the following inference rules:

① reflexive law: if y belongs to x belongs to U, then x->y is implied by F;

② Augmentation Law: If X->y is contained in F, and z belongs to u, then Xz->yz is the implication of F;

③ Transfer law: If X->y is the y->z of F, then X->z is the implication of F;

(2) The following three useful inference rules can be obtained according to the inference rules:

① consolidation rules: by X->y,x->z, with x->yz;

② Pseudo-pass rule: by X->y,wy->z, with xw->z;

③ decomposition rules: by X->y, and Z belongs to Y, there are x->z;

(3) Closure of F:

* * The logic implication of F in the relational schema r<u,f> is dependent on the closure of the whole called F, which is recorded as f+.

* * Set F is a set of function dependencies on the attribute set U, x.y belongs to u,x+ (F) ={a| X->a can have an F based on the Armstrong axiom to derive},x+ (f) called the attribute set X closure on the function dependency set F.

* * Set F for a set of function dependencies on the attribute set U, x, y belongs to U,x->y can be derived from F according to Armstrong Axiom sufficient and necessary condition is Y belongs to x+ (f).

* * If g+=f+, it is said that the function dependency set F overrides G or f is equivalent to G.

The sufficient and necessary condition of **f+=g+ is that f+ belongs to g+ or G belongs to f+;

* * If the function dependency set F satisfies the following conditions, it is said that f is a minimum function dependency set, also known as a minimum dependency set or minimum overwrite:

The right part of any function dependency in ①f contains only one property;

There is no such function dependency x->a in ②f, which makes F and f-{x->a} equivalent;

There is no such function dependency in ③f X->a,x has a true subset Z makes F-{x->a} and {z->a} and F equivalent

* * Each function depends on the set F equal price to a minimum function dependency set F (m). This f (m) is called the minimum dependent set of F.

* * Two relationship mode r1<u,f>,r2<u,g> if F is equivalent to G, then the relationship of R1 must be R2; in turn, R2 relationship must be R1; so in r<u,f> It is permissible to replace F with the F equivalent dependency set G.

The axiom system of data dependence of database design in 2016.6.17