Re: RM formalism supporting partial information

Marshall wrote:

On Nov 15, 10:13 am, Bob Badour <bbad...@xxxxxxxxxxxxxxxx> wrote:

Marshall wrote:

On Nov 14, 9:12 pm, David BL <davi...@xxxxxxxxxxxx> wrote:

On Nov 15, 10:01 am, Marshall <marshall.spi...@xxxxxxxxx> wrote:

On Nov 14, 2:21 pm, David BL <davi...@xxxxxxxxxxxx> wrote:

On Nov 15, 1:20 am, Bob Badour <bbad...@xxxxxxxxxxxxxxxx> 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.

I agree with your sentiment; however, I have a nit to pick. Just as a relation is a set of propositions, it is also a set of tuples. There is a sort of duality involved where a tuple is to the algebra as a proposition is to the calculus.
.

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