Re: RM formalism supporting partial information

On Nov 26, 11:53 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> "David BL" <davi..._at_iinet.net.au> wrote in message

> > AFAIK you say this because of something to do with the CWA but I can't
> > get past the feeling that the CWA is incompatible with partial
> > information and that's all there is to it! Perhaps you could give me
> > an example to back up that statement.
>
> The CWA is not incompatible with partial information. The Closed World
> Assumption is applied to each individual relation, not to the database as a
> whole. The content in a relation, EMPLOYEE_AGES, could be "known ages for
> employees." The absence of a tuple for a particular employee simply means
> that the age is not known (assuming of course that there is a tuple in
> EMPLOYEE that asserts the existence of said employee).

In a way I agree with you. What I meant was that for a given predicate the CWA applies if and only if the extension recorded in the DB is complete with respect to the predicate's intension. This seems a matter of definition. Weaken the intension and the CWA can miraculously appear!

Consider the following intensional definition of a predicate

    president1(P) <=> P has been a president of the USA

Presumably a respectable intensional definition has a uniquely defined finite extension, and the above definition meets that criteria.

[Side note: the intensional definition tells us what DB updates are needed over time. However, formally it would seem better to make the time dependence explicit so the mapping from intensional definition to extension is well defined]

Now consider that we weaken it as follows

    president2(P) => P has been a president of the USA

or

    president3(P) <=> It is known that P has been a president of the USA One could reasonably say that the first represents the OWA, by only providing the one way implication, whereas the second is actually a CWA with a weaker intensional definition. However the distinction seems rather shallow.

It is actually conceivable to say that president3 has a uniquely defined extension, assuming we are clear on who is the source of the information and at what point in time. In fact the purpose of a database may be to model what knowledge was available to a group of people (eg in a legal matter on the directors of a company accused of misleading shareholders).

I'm wondering whether the best approach is to require "if and only if" intentional definitions of predicates, so that as far as the formalism is concerned the CWA applies everywhere, and we end up with appropriately messy intensional definitions that support partial information if and where required.

This pushes the CWA question out of the formalism and into the natural language interpretations where I think it belongs.

The weakening of 1:1 relative cardinalities as discussed by Bob Badour seems related but nevertheless different in purpose to the weakening of intentional definitions, even though both seem necessary to support partial information. Received on Tue Nov 27 2007 - 06:27:22 CET