Hi Ed,
Thanks for the concise description.
It might help to add one word as follows:
The most common form one sees is "third normal form": each row is a set of
singular facts about one individual.
So far about structure.
With respect to structuring I believe the following is to be added:
Although the structure is of interest, the protocol (structuring) based on normal forms is very hard to use in those practical situations where the input of the subject matter expert is essential for the modeler.
Regards
Sjir Nijssen
Chief Technical Officer
PNA Group
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-----Oorspronkelijk bericht-----
Van: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] Namens Ed Barkmeyer
Verzonden: donderdag 10 januari 2013 0:16
Aan: doug@xxxxxxxxxx; [ontolog-forum]
Onderwerp: Re: [ontolog-forum] What is Data? What is a Datum?
On 1/9/2013 4:42 PM, doug foxvog wrote:
> <snip>
> I note that databases traditionally encode high arity relations. Very
> often a single column does not relate the value in that column for a
> row to the thing represented by the key of the row. It takes multiple
> columns to do so.
Database theory refers to different degrees of "relatedness" in a relational table as "normal forms". The most common form one sees is "third normal form": each row is a set of facts about one individual.
Some set of columns identifies the individual and each of the properties is represented by one or more other columns. This form is the one commonly identified as "best practice".
A "fourth normal form" relation represents an atomic n-ary semantic relationship involving one or more individuals. That is, each row of a 4th normal form table represents exactly one atomic proposition. Each individual is represented
by a set of 1 or more columns whose values together identify a unique individual.
One of my favorite manufacturing examples is: Machine type M requires T time to perform operation P on material S.
One can consider that to be a quaternary relationship, representing a function that takes three arguments (Machine type, operation, material) and produces a Time value.
But one might also consider it to be a binary relationship representing the same function, seen as having one argument that is an "instantiated operation", where the instantiated operation object is identified by the machine type, the
operation, and the material. From the 4th normal form point of view, those are different descriptions of the same table and they don't really change the interpretation of a row.
The table, BTW, may have more than 4 columns, because a "machine type"
or a "material" might have a "composite key" that takes more than one value (column) to represent, e.g., manufacturer and manufacturer's product id. So the binary interpretation of the table is that the columns making up the identifiers
for machine type, operation, and material constitute one big "composite key" for the "instantiated operation".
By comparison, in 5th normal form, there is exactly one column for each participating individual in an instance of the represented relationship. The idea is to eliminate any ambiguity in the interpretation of combinations of key columns.
In that form, the binary interpretation will have exactly two columns, while the quaternary interpretation will have four. Further, many experts would agree that, because the binary interpretation is a function, the binary table is the proper 5th normal form.
The point of all this is that, although database theory speaks of relational algebras, keys, functions and relations, the "normal form"
ideas are about the relationship between tables and propositions.
As Doug says:
> Both the high-arity relation and the data base provide foundations for
> such propositions.
I completely agree with the following as well, but that isn't the point of this email.
> I find arguments for basing semantics on triples to be similar to
> arguments for basing arithmetic computations on Peano arithmetic, due
> to its providing a foundation for arithmetic. A system based on Peano
> arithmetic has no need for a system to encode addition, subtraction,
> or multiplication, or their associated tables. Sure, all that can be
> derived, but the efficiency leaves something to be desired, and the
> clarity of operations (reasoning) is hidden. I find that the same
> holds for restricting the encoding of semantics to triples.
>
> -- doug f
-Ed
--
Edward J. Barkmeyer Email:
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National Institute of Standards & Technology Systems Integration Division, Engineering Laboratory
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and have not been reviewed by any Government authority."
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