Re: Is a function a relation?

"David BL" <davidbl_at_iinet.net.au> wrote in message news:ffc01e89-5832-4930-b879-1a96e0a06f15_at_c18g2000prh.googlegroups.com...
> On Jun 27, 10:10 am, "Joe Thurbon" <use..._at_thurbon.com> wrote:
>> On Sat, 27 Jun 2009 09:35:36 +1000, David BL <davi..._at_iinet.net.au>
>> wrote:
>> > On Jun 25, 12:26 pm, David BL <davi..._at_iinet.net.au> wrote:
>>
>> >> I agree that the topic of interpretation is relevant to database
>> >> theory.
>>
>> > I'll take that back. I would rather narrow the term "database theory"
>> > to a pure mathematical discipline, and therefore instead say that
>> > interpretation is only relevant to the practical application of
>> > database theory.
>>
>> There may be some talking at cross purposes here.
>>
>> I had assumed that when database theoreticians talked about
>> interpretations they were talking about something similar to what
>> logicians call an interpretation (or interpretation function, depending
>> on
>> what you're reading). In logic, an interpretation is very much a
>> mathematical construct (c.f. model theory).
>>
>> (I've just received my mail-order of Date's Logic and Databases, so
>> hopefully soon I'll be able to confirm or deny the above assumption.)
>>
>> What are you talking about when you say interpretation?
>
> I completely agree that an interpretation in model theory is a
> mathematical construct. I don't believe Brian was using the word
> interpretation in that sense, because he spoke about a UoD that can
> exist in time and space. His words:
>
> "... if what is in the Universe of Discourse can
> exist in time and space, then database values can
> exist in time and space. A value is the result of
> applying for a given term the valuation function
> which maps terms expressed in a formal language to
> things in the Universe of Discourse under an
> interpretation."
>
> I assumed he was talking about the idea to interpret mathematical
> relations as predicates that apply to the real world. i.e. external
> predicates.
>
> As C.Date says:
>
> "... while internal predicates are a formal
> construct, external predicates are an informal
> construct merely. Internal predicates are (loosely)
> what the data means to the DBMS; external
> predicates, by contrast, are what the data means
> to the user."
>
> An external predicate, being informal, is typically stated in natural
> language.

I think your assumption is faulty. I merely claim that there can be things that can change--that is, that there can be objects that can exemplify different properties at different times. Obviously, if one seeks to discuss such objects, they must be included in the Universe of Discourse. Received on Sat Jun 27 2009 - 17:16:56 CEST