DBMS
if A → B and C is a list of attributes, then AC → BC
Augmentation
if A → BC, then A → B and A → C
Decomposition
lossless decomposition
If the union of decomposed relations R1 and R2 gives the original relation R ie R1 ∪ R2 = R - the intersection of the subrelations is not null e.g. there is a common element - the intersection of both the subrelations must be a super key of one or both of the subrelations
Transitivity
P → Q and Q → T, therefore P → T
Pseudotransitivity
P → Q and QR → S, therefore PR → S
if A → B and BC → D, then AC → D
Pseudo-transitivity
Union
QR → S and QR → U, therefore QR → SU
Union then Pseudotransitivity
QR → S and QR → U, therefore QR → SU P → Q and QR → SU, therefore PR → SU
if B is a subset of A, then A → B
Reflexivity
if A → B and B → C, then A → C
Transitivity
if A → B and A → C, then A → BC
Union
dependency preserving
a decomposition is dependency preserving if the functional dependencies of the relation schema still hold
lossy decomposition
a decomposition where the join of R1 and R2 does not yield the same relation as in R
candidate key
minimal superkey with no redundant values (no extraneous values)
superkey
set of one or more attributes that uniquely identify a tuple