Re: Is a function a relation?
Date: Thu, 25 Jun 2009 21:54:31 -0700 (PDT)
Message-ID: <49f1d816-747a-46c7-84b7-14eb0b1fc04e_at_y10g2000prc.googlegroups.com>
On Jun 25, 5:32 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
>
> But a database relation is not the same thing as a mathematical relation.
> The difference may not be immediately obvious--and I'm not referring to the
> fact that components of tuples in a database relation are named whereas
> components of tuples in a mathematical relation are indexed. The difference
> is in how the relations are arrived at, and the extent to which they endure.
> In the case of a database relation, the predicate is extended and each
> atomic formula is judged to be either true or false at the instant of
> interpretation, but in the case of a mathematical relation, the predicate is
> extended and there is no need to judge whether each atomic formula is true
> or false because owing to the fact that whenever there is a particular
> abstract object, it is necessary that there is that particular abstract
> object, each atomic formula in the extension of a mathematical relation is
> true necessarily. So for mathematical relations, one can safely dispense
> with judging the truths of the atomic formulae represented by tuples. Also,
> the assignment of meaning to terms in the atomic formulae in the extension
> of mathematical relations can be deferred because abstract objects neither
> come into existence, change in appearance nor cease to exist. It is
> tempting, therefore, to treat database relations as mathematical relations,
> and one safely can for activities or specifications that involve just one
> instance at a time, such as queries or the specification of referential
> constraints, but the danger in expanding the scope of activities or
> specifications so that they involve more than one instance at a time, as is
> the case for updates, is that there would be more than one assignment of
> meaning and more than one judgement of truth for the same activity.
I don't know what that means, so I'll ask some questions to try to establish a common point of reference!
- Do you draw a distinction between a relation variable and a
relation value?
- Do you think it's possible to talk about the relation value recorded in a relation variable in a particular database at a particular time?
- Is a relation value necessarily associated with some external predicate?
- What is the definition of equivalent relation values?
- Do you think it's possible to say that distinct relation variables (possibly in distinct databases) happen to have recorded the same
relation value at particular times - even though the relation variables have distinct external predicates?