Re: Extending my question. Was: The relational model and relational algebra - why did SQL become the industry standard?

Excellent question. Before the present discussion, I would have said that the logical model of multisets is conceptually close to some real-world models, and certainly a good logical model for the "relaxed" relational model implemented by many "R"DBMS products, where the distinguishing attribute of rows is hidden.

That said, there's also room for confusion about whether one conceptualizes the logical model as representing bags that can contain indistinguishable duplicates (imagine the bag is constantly being shaken, so we can't even say "the John Smith at the bottom of the bag"), or as representing an inventory of distinct entities with the additional attribute of multiplicity.

These two conceptualizations of the logical model lead naturally to two distinct physical implementations. The more natural one (in my mind) of "bags" is the more problematic, because no computer I've ever used has a 30 Gig "hard bag"--there will necessarily be an additional attribute, hidden or not, that internally distinguishes every item. The less natural one, using multiplicities, is not as convenient for some operations, such as displaying the contents of a multiset (with no apologies for the fact that an order attribute is acceptable with regard to a result set, because the display and the bag are two different things), but using multiplicities does a better job of representing the logical model, given the reality of actual physical computers.

I really don't know if that answers your question, and I'll gladly admit that anything I conceptualize as a multiset can simply be represented logical and physically as a set, with the addition of the attribute of multiplicity. But just as a consistent theory of and notation for real numbers are useful in spite of there being a possible representation using only sets of (sets of ...} integers, I think an algebra of multisets, to use in logical models and to drive physical models, is useful, and it can be completely well-defined and consistent.

SK

Bob Badour wrote:

>If the facts are truly indistinguishable, they are a single fact and we have
>a model based on sets. If they only represent multiplicities, one really has
>a relational logical data model with an implicit count attribute.
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>What benefit does this implicit attribute provide?
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Received on Wed Feb 19 2003 - 00:30:03 CET