Re: Is a function a relation?

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. Received on Sat Jun 27 2009 - 04:55:16 CEST