Re: BCNF: superkey or candidate key ?
From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Mon, 25 Sep 2006 11:26:42 GMT
Message-ID: <S1PRg.38577$9u.330670_at_ursa-nb00s0.nbnet.nb.ca>
>
>
> Of course, those are the standard definitions, but you claimed that you
> had seen one that said:
>
> "Previously he (and others) defined it where A had to be a candidate
> key
> (which is irreducible)."
>
> So a definition like: A relation schema R is in BCNF if whenever a
> nontrivial functional
> dependency A -> X holds in R, then A is a candidate key of R.
>
> That would not be equivalent to the standard definitions, so I wondered
> where you had seen such a definition.
Date: Mon, 25 Sep 2006 11:26:42 GMT
Message-ID: <S1PRg.38577$9u.330670_at_ursa-nb00s0.nbnet.nb.ca>
Jan Hidders wrote:
> masong_at_sbcglobal.net wrote:
>
>>"Database In Depth", C.J. Date, May 2005, p.140: >>Relvar R is in BCNF if and only if, for every nontrivial FD A -> B satisfied >>by R, A is a superkey for R. >> >>"Database Modeling and Design", 4th Ed., Torey/Lightstone/Nadeau, Sep 2005, >>p.115: >>A table R is in Boyce-Codd normal form (BCNF) if for every nontrivial FD X >>-> A, X is a superkey. >> >>"Fundamentals of Database Systems", 5th Ed., Elmasri/Navathe, May 2006, >>p.368: >>A relation schema R is in BCNF if whenever a nontrivial functional >>dependency X -> A holds in R, then X is a superkey of R.
>
>
> Of course, those are the standard definitions, but you claimed that you
> had seen one that said:
>
> "Previously he (and others) defined it where A had to be a candidate
> key
> (which is irreducible)."
>
> So a definition like: A relation schema R is in BCNF if whenever a
> nontrivial functional
> dependency A -> X holds in R, then A is a candidate key of R.
>
> That would not be equivalent to the standard definitions, so I wondered
> where you had seen such a definition.
If A is a candidate key, then a functional dependency of the form B -> X would hold where B is any superkey of A. Would it not? Received on Mon Sep 25 2006 - 13:26:42 CEST