Re: RM formalism supporting partial information

On 16 nov, 16:30, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 16 nov, 02:51, David BL <davi..._at_iinet.net.au> wrote:
>
>
>
> > On Nov 16, 8:31 am, Jan Hidders <hidd..._at_gmail.com> wrote:
>
> > > On 15 nov, 20:11, David BL <davi..._at_iinet.net.au> 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:
>
> http://citeseer.ist.psu.edu/534211.html
>
> 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:

PS. Note that I am oversimplifying because I left out the headers, which need to be taken into account to get a completely correct definition of "information content" in this setting. The relation with header {a,b} and body {(a=1, b=null)} does not necessarily have the same information content as the one with header {a} and body {(a=1)}. But considering that (1) it is not hard to see how to add that and (2) it would make the definitions more complex without really adding to the essential insight, I left them out anyway.

• Jan Hidders