Re: RM formalism supporting partial information

From: Jan Hidders <>
Date: Fri, 16 Nov 2007 07:30:04 -0800 (PST)
Message-ID: <>

On 16 nov, 02:51, David BL <> wrote:
> On Nov 16, 8:31 am, Jan Hidders <> wrote:
> > On 15 nov, 20:11, David BL <> wrote:
> > > I'm sure your time is precious and I don't want to be presumptuous,
> > > but have you digested much of the document? Do you have any
> > > particular comments on the operators, such as the information
> > > comparison operator which gives a partial ordering and a concept of
> > > information equivalence?
> > It's actually not a partial order, but a preorder because it is not
> > antisymmetric.
> I didn't know partial order had that more specific meaning. Nor did I
> know that the term preorder was available for what I wanted to say.
> Thanks for pointing that out.

The term pseudo order is also sometimes used.

> > It's also a bit strange in that it says that the
> > following relation bodies (for simplicity the tuples are unlabeled)
> > all have the same information:
> > - { }
> > - { ({}, {}) }
> > - { ({a}, {}) }
> > - { ({}, {b}) }
> I don't think that's correct.

Indeed, my apologies, you are right. A case of "reading what I think it should say", I'm afraid. :-)

> Intuitively the information content can be regarded as the set of all
> conventional propositions that can be "read out" of the mv-relation,
> for all possible projections.

Aha! Now *that* makes more sense, and as far as I can tell that is roughly the "value does not apply" interpretation of null values. But I'm not really convinced that the equivalence relationship over relations that you derive from that really follows from it. I'd strongly advice you to read the following paper, "Database Relations with Null values" by Carlo Zaniolo, which starts more or less from the same principle, but works it out in a subtly different way:

Let me give a brief summary of what he does to explain what my problem is. I'll give a formal but simplified version of what he does:

Do you see how this is similar but different from what you are doing? Let me try to make this link a bit more explicit.

I can now define an ordering based on this in two ways:

I'm running a bit out of time now, so I'm closing with the relevant questions:
- What is the relationship between the three equivalence
- Which corresponds to yours, and which to Zaniolo's? - Which is more intuitive?

To give a hint about my opinion on the final question. If you assume the closed world assumption, and we usually do in this context, then it is not true that a smaller relation necessarily contains less information. The absence of tuples then also carries information.

So far for now.

  • Jan Hidders
Received on Fri Nov 16 2007 - 16:30:04 CET

Original text of this message