Hi Ed, (01)
I have always considered the definition of an RDB-class correspondence to be
partially in the mind of the modeler, not in the RDB structure itself. I
know of no formal definition of what a RDB-class consists of, which would
provide a rigorous foundation for translating RDBs to classes with one
exception; there is at least one class per table. Modelers may often add
definitions of subclasses within a table, but that's usually some form of
correspondence between groups of columns from a table that fit within the
human "chunk" size of 7+/-2 concepts. So it seems every bit as subjective
as any other method of constructing classes from data. Data mining (and
text mining) consists of discovering those subclasses, along with classes
that relate one table to other(s). (02)
Do you have reference(s) (URLs especially) to other documented points of
view which might more rigorously define how the RDB translates into classes? (03)
-Rich (04)
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com (05)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Ed Barkmeyer
Sent: Friday, January 30, 2009 12:33 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Is there something I missed? (06)
Matthew West wrote:
> Dear Mitch
>
>> - Any (relational) database schema describes a set of relations/an
>> ontology and most are extremely multi-ary.
>
> [MW] Yes but these are mostly denormalisations to overcome the costs of
> table joins. (07)
The whole aspect of arity of tables is bound up with the theory of
"normal forms". Among other things, a table of 5 columns might still
only represent a binary relation, and in "4th normal form" that is what
it represents. The problem is how many columns it takes to provide the
key values that identify each of the two participating individuals. So
4th normal form requires a table of n columns to express a function F of
the form:
F(c\1, ..., c\k) = (c\k+1, ..., c\n) (08)
So the table representing the total price of each line item of a
purchase order may have four columns (order#, line#, amount, currency)
where the function "total price" is:
total_price (order#, line#) = (amount, currency) [4th NF]
or
(totalPrice lineItem monetaryAmount) [binary relation] (09)
It is only in "5th normal form" that all unary relations are one-column
tables and all binary relations are two-column tables. And this is
accomplished by creating artificial "identifiers" that correspond to
"co-variant vectors" -- the "compound keys" for the individuals. (010)
The highly prized "3rd normal form" has the property Matthew observes:
For each column c\i where i > k,
c\i = F\i(c\1, ..., c\k)
i.e., each data column is a function of _all_ the key columns, but there
is no requirement for the data columns to have any other relationship to
each other. All the functions are different. Thus the 3rd normal form
table is the "natural join" of a set of "4th normal form" tables. (011)
Relational algebra is just yet another mathematical theory that has some
relationships to knowledge engineering. (012)
-Ed (013)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (014)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (015)
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