, , , , ( !) , , . , , , . : , . .
R (5), - (), , - R () R, :
- *{ , ,..., Z } R , , ,..., Z R.
- *{ , ,..., Z } R () R , , B,..., Z R.
- (DKNF)
, , .
, . ( ) , .
, , .
, , 5. .
(6NF)
. .
.
FD S FD S+, FD, FD S.
FD, ( ) FD. _. , , FD _→{_, _}. FD FD _→_ _→_.
_ FD _→_ _→_. FD _→_.
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, FD _→_ , _ _ "", _.
S+ FD S . FD ( , FD). . A, B C ( , ) r. A, B C . AB A UNION B. :
1. B A, A → B ();
2. A → B, AC → BC ();
3. A → B B → C, A → C ().
, B UNION A FD AB .
. , FD AC → BC . , t1 t2, , t1 {AC} = t2 {AC} (a), t1 {BC}!= t2 {BC} (b) ( t {A} t A). (a) , t1 {A} = t2 {A}. FD A → B, t1 {B} = t2 {B}. (b) , t1 {C}!= t2 {C}, FD AC → C. , FD AC → BC , .
. , FD A → C . , t1 t2, , t1 {A} = t2 {A}, t1 {C}!= t2 {C}. FD A → B , t1 {B} = t2 {B}, FD B → C , t1 {C} = t2 {C}. , FD A → C , .
, (sound and complete) , FD S FD, S, , FD. :
1. A → A () (1);
2. A → BC, A → B A → C () (1) , BC → B; (3) A → B; , BC → (3) => A → C;
3. A → B A → C, A → BC () (2) , A → AB AB → BC; (3) =>, A → BC
4. A → B C → D, AC → BD () (2) , A → B BC → BD; (3) =>, AC → BD
5. A → BC B → D, A → BCD () (2) , B → BCD; (3) =>, A → BCD.