1
$\begingroup$

I'm currently reading about functional dependencies.
I've read Armstrong's axioms about:

Relexivity: $if$ $B\subseteq A$ $then$ $A\to B$
Augmentation: $if A\to B$ $then$ $AC\to BC$
Transitivity: $if A\to B$ $and$ $B\to C$ $then$ $A\to C$

and also about:

Union Rule: $if A\to B$ $and$ $A\to C$ $then$ $A\to BC$
Decomposition Rule: $if A\to BC$ $then$ $A\to B$ $and$ $A\to C$

I also know that for a relation R(A, B, C, D, E) that:
$if A\to B$ $then$ $ACDE\to B$.
In fact, the left side could be any superset of A.
Is there a name for this rule?
I've looked at various books but while they use it in examples, they never mention a name.

$\endgroup$
1
$\begingroup$

While I'm unaware that your suggested rule has a name and couldn't find it in any texts on my shelf, it's a consequence of reflexivity and transitivity, as you probably know already. Here's how: $$ \begin{align} ACDE &\rightarrow A &\text{(reflexivity)}\\ A &\rightarrow B &\text{(hypothesis)} \\ ACDE&\rightarrow B &\text{(transitivity)} \end{align}$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.