15.00 - Inference Axioms for Multivalued Dependencies - Teradata Database

Teradata Database Design

prodname
Teradata Database
vrm_release
15.00
category
User Guide
featnum
B035-1094-015K

Inference Axioms for Multivalued Dependencies

The following table lists the complete set of multivalued dependencies derived by Beeri, Fagin, and Howard:

 

Axiom

Formal Expression

Reflexive rule

X  X

Augmentation rule

IF

X ⇒  Y

THEN

XZ ⇒  Y

 

 

Union rule

IF

X ⇒  Y

AND

X  Z

THEN

X ⇒  YZ

 

 

Decomposition rule

IF

X ⇒  Y

AND

X  Z

THEN

X ⇒  Y Z

AND

X ⇒  (Z - Y)

Transitivity rule

IF

X ⇒  Y

AND

Y ⇒  Z

THEN

X ⇒  (Z - Y)

 

 

Pseudotransitivity rule

IF

X ⇒  Y

AND

YW ⇒  Z

THEN

XW ⇒  (Z - YW)

Complement rule

IF

X  Y

AND

Z R-XY

THEN

X ⇒  Z

 

 

Mixed inference rules

IF

X  Y

THEN

X  Y

 

 

 

 

IF

X  Y

AND

Z ⇒  W

WHERE W is contained in Y AND Y Z is not empty

THEN

X  W