From: Brian <>
Date: Sun, 5 Sep 2010 11:12:39 -0700 (PDT)
Message-ID: <>

On Sep 5, 10:22 am, Erwin <> wrote:
> On 5 sep, 14:44, Brian <> wrote:
> > Under the closed world
> > interpretation, on the other hand, it /is/ automatically assumed that
> > the corresponding proposition is false.
> So, you agree that under CWA, "tuple absent" implies "proposition
> false".

Not exactly. A supposition is not the same thing as a known fact. Under the CWA what isn't known to be true or false is supposed to be false. For example, in a poorly designed database that doesn't have a foreign key relationship from OrderDetails to Orders, it's possible for there to be a tuple in OrderDetails without a corresponding tuple in Orders. The existence of the OrderDetail denies the supposition that there is no corresponding Order, and since the OrderDetail is a known fact, that denial must take precedence over the supposition that is due to the CWA. One can safely conclude that there is supposed to be an Order, despite the CWA, even though it hasn't been supplied.

But in a perfect world, with a correctly designed schema: "tuple absent" iff "proposition false." Of course, in a perfect world, everything that is knowable is known.


> You claimed at one point that the meaning of a tuple is somehow "yet a
> bit more than just the corresponding proposition".  

A proposition that hasn't been interpreted is meaningless. It is only after it has been interpreted and judged to be true (or false) that it conveys meaning. A fact is nothing more than a proposition that has been interpreted and judged to be true. In logic, an atom has the form P(t), where P is a n-ary predicate and t is an ordered n-tuple of function applications (constants being nothing more than 0-ary function applications). Under an interpretation, the function applications are evaluated (Put simply, they are replaced with images of the objects in the universe of discourse that they map to at the instant of interpretation.), and then a judgement is made as to whether or not the values (images of the objects in the universe) exemplify the predicate at the instant of interpretation. If they do, then a positive truth value is assigned; if they don't, then a negative truth value is assigned.

> Making the
> decision process of whether or not a given tuple ought to appear in
> the database one that is more complex than it needs to be.

The process is what it is. The users that issue inserts, updates and deletes determine whether or not a given tuple 'ought' to appear in the database. No assumption or constraint has any bearing on whether or not a given tuple 'ought' to appear in the database, though they definitely bear on whether or not a given tuple 'can' appear in the database. Received on Sun Sep 05 2010 - 20:12:39 CEST

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