Sixth normal form

#61

"Brian Selzer" <brian (AT) selzer-software (DOT) com> wrote

Quote:

"David Cressey" <cressey73 (AT) verizon (DOT) net> wrote in message
news:4JFyi.3591$wr3.2580 (AT) trndny04 (DOT) ..

"Brian Selzer" <brian (AT) selzer-software (DOT) com> wrote in message
news:9NDyi.28722$RX.5655 (AT) newssvr11 (DOT) news.prodigy.net...
begin with. I never really came up with a clear definition of what it
means
for a schema to have /at least as much/ information, nor did I provide
any
proof that if a relation is in 5NF, then the relationships between the
dependent attributes are due to the fact that the relation is in 5NF, or
that the presence of a pathological relationship between the dependent
attributes indicates that the relation isn't in 5NF.

Part of the problem may be that the phrase "at least as much information"
suggests some sort of measure of information, but not the information
itself. For example, if you have "at least as much money in the bank as
I
have", it doesn't mean that you have the same money as I do in the bank.

I think what you may have meant might be better conveyed by a phrase like
"at least all the same information as". But I'm not sure what you did
mean,
so this is just a guess.

What I was trying to convey by the phrase /at least as much/ information
is that the only additional information that should ever appear in an
instance of the more normalized database schema is exactly that
information that should be allowed but can't be due to the structure of
the less normalized database schema. For example, if the FDs A --> B and
B --> C hold in a relation schema {A, B, C}, then it is not possible to
insert values for B and C without also inserting a value for A. If it
should be possible, then there is a structural problem which is due to the
fact that the MVD B ->-> A | C that holds in {A, B, C} is pathological.
The problem is that while the decomposition into {A, B} and {B, C} makes
it possible to insert values for B and C without also requiring a value
for A, it also permits values to be inserted for A and B without also
requiring a value for C. The inability to insert a value for A without
also inserting a value for C is due to the fact that the FD A --> C holds
in {A, B, C}. Even though it is true that the
FD A --> C implies the MVD B ->-> A | C, it is only due to the fact that B
appears in the relation schema that the MVD holds.

Correction: A --> C does not imply B ->->A | C; B --> C does. But the
MVD B ->-> A | C and the FD A --> C cannot both hold unless at least one
of the FDs B --> A or B --> C also holds.

Quote:

Therefore, in order to maintain the functional relationship from A to C,
it is necessary to add the IND {A,B}[b] in {B,C}[b].

Thread Tools
Show Printable Version Email this Page
Display Modes
Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

Sixth normal form

comp.databases.theory comp.databases.theory

Re: Sixth normal form - 08-27-2007 , 11:30 AM