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

From: Steve Kass <skass_at_drew.edu>
Date: Tue, 18 Feb 2003 20:17:46 -0500
Message-ID: <b2ulsp$10v$1_at_slb2.atl.mindspring.net>


Here are a few, including examples where <item, multiplicity> is a natural conceptual model and where <item, item, item> is. (also see my post previous to this, answering Bernard)

An inventory.
When I inquire at a bookstore as to the availability of a book, someone looks it up in a database and may report "we have three in stock". If I purchase one, the physical implementation changes
a "3" to a "2". It doesn't delete a fact from a table. Similarly, my local pharmacy probably maintains an inventory of medications on hand. I doubt that 1,237 tablets of alprazolam are represented by that many entries in a database.

Ticket sales.
"We sold 325 adult tickets and 104 child tickets today." The tickets are separate physical entities, and when a family purchase several, a machine issues several identical objects (they may well be numbered, unfortunately), so this example is one where there is some representation of the multiset as individual but identical items.

A receipt.
SQL Burger $3.29
Big Int $1.24
Table Service $.99
SQL Burger $3.29
SQL Burger $3.29

Groceries.

"Could I have two dozen jumbo shrimp, please?"
"and a dozen eggs?"
"and 5 pork and scallion buns?"

Perhaps I gave you the impression that I had something more subtle in mind, but these are the kinds of things for which I think multisets, sometimes conceived as sets of <item,multiplicity> pairs and sometimes as true bags, are useful.

SK

>>
>>
>
>Steve,
>
>Could you provide a practical example that might help me in wrapping my mind
>around the notion of utility for logical models of items with
>multiplicities?
>
>I'm afraid I'm having problems understanding how one can even have some
>sense of determinancy of what constitutes a multiset in contrast to a set
>without some implicit logical mapping to identity. In the mind's eye, the
>very basis for contrasting a multiset from a set, or vice versa, is
>dependent on our very notion of identity.
>
>For example, if I see {1,1,1,1,1}, I would have a tendency to describe it as
>a collection of integer 1 values with a cardinality of five. In the process
>of synthesizing my description, I find that I implicitly assign cardinality
>to each member even though set theory would reduce this to {1}. Thus, I can
>distinguish between the two collections.
>
>What am I missing?
>
>I guess the root of my confusion lies in the fact that I don't see how we
>relate to anything in the real world without trying to apply some notion of
>identity in a logical sense.
>
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>>>
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Received on Wed Feb 19 2003 - 02:17:46 CET

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