Re: RM formalism supporting partial information

On Nov 15, 10:13 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
> Marshall wrote:
> > On Nov 14, 9:12 pm, David BL <davi..._at_iinet.net.au> wrote:
>
> >>On Nov 15, 10:01 am, Marshall <marshall.spi..._at_gmail.com> wrote:
>
> >>>On Nov 14, 2:21 pm, David BL <davi..._at_iinet.net.au> wrote:
>
> >>>>On Nov 15, 1:20 am, Bob Badour <bbad..._at_pei.sympatico.ca> wrote:
>
> >>>>>paul c wrote:
>
> >>>>>>David BL wrote:
> >>>>>>...
>
> >>>>>>>http://www.members.iinet.net.au/~davidbl/MVattributes.doc
>
> >>>>>>>This is still a work in progress.
>
> >>>>>>>I welcome any comments.
>
> >>>>>By the second paragraph, the document entered into the realm of
> >>>>>nonsense, and I stopped reading.
>
> >>>>An attribute has a name and a domain. How is that nonsense?
>
> >>>You didn't say an attribute *has* a name and a domain. You said
> >>>an attribute *is* a name and a domain. So you can have two
> >>>different attributes with the same name.
>
> >>I said an attribute *consists* of a name and a domain. That is
> >>compatible with saying an attribute has (and only has) a name and a
> >>domain. I assume you're not making some philosophical point about
> >>the sum being greater than the parts; IMO distinguishing between
> >>"has" and "is" is splitting hairs. In natural language at that!
>
> >>Seeing as you're likely to try to interpret mathematical structures in
> >>terms of words like "has" and "is", I must point out that
> >>mathematical structures do not exclusively own their "parts". For
> >>example the point (10,15) in R^2 doesn't exclusively own the integers
> >>10,15 (ie they can be used for other things!). Similarly an attribute
> >>doesn't exclusively own it name or its domain. In keeping with the
> >>spirit of mathematical formalism I didn't say that an attribute has a
> >>domain-name - instead it has a domain. Formally that only means
> >>there exists a mapping D from attribute x to domain D(x).
>
> >>You cannot state that all attributes have different names. That would
> >>be nonsensical because universal quantification is only meaningful
> >>with respect to some defined set over which it quantifies. At the
> >>point of definition of "attribute" there is no such set to quantify
> >>over. I find it curious that you appear to allow a mathematical
> >>realism philosophy to invade mathematical definitions.
>
> >>In the document I (correctly) said nothing about unique names until
> >>defining a relation.
>
> > You attribute a bunch of positions here to me, but none of them
> > are things that I actually think or things that I actually said.
>
> While I have used the term many times in the past, and I am sure I will
> use it many times in the future, seeing this discussion has impressed
> upon me how unimportant "attribute" is as a concept.
>
> The important concepts are tuples, propositions, predicates etc.

For myself, I have found less and less use for the concept of tuple over time. I try as much as possible to do everything with just relations. Relations as sets-of-propositions, relations as predicates, cardinality-1 relations instead of tuples, etc. In fact I am going so far as to attempt the idea of a theory with relations as the only primitive. (And possibly also including scalars.)

Not 100% clear if the idea can be carried out all the way, but it's promising so far.

Marshall Received on Fri Nov 16 2007 - 18:40:06 CET