RM formalism supporting partial information

#1

Nearly two weeks ago I posted to the thread "atomic" regarding a join
operator I had defined back in January. A discussion with Paul C
inspired me to more carefully develop the mathematical formalism.

I have been surprised to discover some elegant mathematical ideas
making me feel like this is a very promising area of study. It could
easily turn out to be valuable for a formal approach to partial
information in the RM within the confines of a 2vl.

There are a number of definitions of relational operators in the
spirit of the RA, and many properties are stated, complete with formal
proofs. In a number of ways the operators are more flexible than in
the conventional RA. For example, union, intersection and difference
are defined on relations that are not necessarily union compatible,
and the association with partial information is simple and intuitive.

There is far too much detail to post. The following is a link to a MS
word document.

http://www.members.iinet.net.au/~dav...attributes.doc

This is still a work in progress.

I welcome any comments.

#2

paul c wrote:

Quote:

David BL wrote:
...

http://www.members.iinet.net.au/~dav...attributes.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.

Quote:

David, on the first page, what does "τ" stand for? (It looks likethe
lower-case Greek "tau" to me. Also my vision isn't very good, so I find
I need to enlarge the text and I end up with different page numbers than
your original. What about numbering the various steps?)

It was nonsense before it ever got to tau.

#3

On Nov 15, 1:20 am, Bob Badour <bbad... (AT) pei (DOT) sympatico.ca> wrote:

Quote:

paul c wrote:
David BL wrote:
...

http://www.members.iinet.net.au/~dav...attributes.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?

Quote:

David, on the first page, what does " " stand for? (It looks like the
lower-case Greek "tau" to me. Also my vision isn't very good, so I find
I need to enlarge the text and I end up with different page numbers than
your original. What about numbering the various steps?)

It was nonsense before it ever got to tau.

I can't understand Bob. Why does he say this?

#4

On Nov 14, 2:21 pm, David BL <davi... (AT) iinet (DOT) net.au> wrote:

Quote:

On Nov 15, 1:20 am, Bob Badour <bbad... (AT) pei (DOT) sympatico.ca> wrote:

paul c wrote:
David BL wrote:
...

http://www.members.iinet.net.au/~dav...attributes.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.

Marshall

#5

Marshall wrote:

Quote:

On Nov 14, 2:21 pm, David BL <davi... (AT) iinet (DOT) net.au> wrote:

On Nov 15, 1:20 am, Bob Badour <bbad... (AT) pei (DOT) sympatico.ca> wrote:

paul c wrote:

David BL wrote:
...

http://www.members.iinet.net.au/~dav...attributes.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.

He also said an attribute is a set of values.

#6

paul c wrote:

Quote:

Bob Badour wrote:
...

He also said an attribute is a set of values.

Not saying I'll ever get past the first page but I feel fairly
comfortable with the first couple of "paragraphs", even if an ellipsis
might be missing and even though I would have rather seen attribute
described as a pair the way D&D do - my reason for this is that it might
be easier to compare with whatever the later pages say, eg., avoiding
words like "consists". (Maybe this is only because my pet peeve in RM
talk and IT in general is that the common vocabulary is way too large; a
lesser peeve is that some words are way over-used but I think my lesser
peeve is the pet peeve of many other people, "object" is an example -
I'd say it's what Edward de Bono called a porridge word.)

Do the first few paragraphs really say an attribute is a set of values?
(I saw the bit about a domain being a set of values which doesn't seem
untoward to me.)

Did you catch the part where it said an attribute is a domain? And then
it went on to say a domain is a set of values.

#7

On Nov 15, 10:01 am, Marshall <marshall.spi... (AT) gmail (DOT) com> wrote:

Quote:

On Nov 14, 2:21 pm, David BL <davi... (AT) iinet (DOT) net.au> wrote:

On Nov 15, 1:20 am, Bob Badour <bbad... (AT) pei (DOT) sympatico.ca> wrote:

paul c wrote:
David BL wrote:
...

http://www.members.iinet.net.au/~dav...attributes.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.

#8

On Nov 15, 11:13 am, Bob Badour <bbad... (AT) pei (DOT) sympatico.ca> wrote:

Quote:

paul c wrote:
Bob Badour wrote:
...

He also said an attribute is a set of values.

Not saying I'll ever get past the first page but I feel fairly
comfortable with the first couple of "paragraphs", even if an ellipsis
might be missing and even though I would have rather seen attribute
described as a pair the way D&D do - my reason for this is that it might
be easier to compare with whatever the later pages say, eg., avoiding
words like "consists". (Maybe this is only because my pet peeve in RM
talk and IT in general is that the common vocabulary is way too large; a
lesser peeve is that some words are way over-used but I think my lesser
peeve is the pet peeve of many other people, "object" is an example -
I'd say it's what Edward de Bono called a porridge word.)

Do the first few paragraphs really say an attribute is a set of values?
(I saw the bit about a domain being a set of values which doesn't seem
untoward to me.)

Did you catch the part where it said an attribute is a domain? And then
it went on to say a domain is a set of values.

I said an attribute consists of a name and a domain.

Would Bob say the following is true?

car consists of engine, steering wheel, ...
=>
car is a engine

#9

On Nov 15, 2:20 pm, paul c <toledobythe... (AT) ooyah (DOT) ac> wrote:

Quote:

David BL wrote:
On Nov 15, 10:01 am, Marshall <marshall.spi... (AT) gmail (DOT) com> wrote:
On Nov 14, 2:21 pm, David BL <davi... (AT) iinet (DOT) net.au> wrote:

On Nov 15, 1:20 am, Bob Badour <bbad... (AT) pei (DOT) sympatico.ca> wrote:
paul c wrote:
David BL wrote:
...
http://www.members.iinet.net.au/~dav...attributes.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!
...

I think un-formal words like "consists" hold just as many dangers as
words like "has" and "is", those two being know to have caused all kinds
of controversy. I say keep it formal, less chance of vague imagination
taking hold. Imagination should be reserved to the thought behind the
words, if you ask me.

Agreed. The words were only meant as an explanatory comment to help
the reader. Didn't seem to work though!

There is nothing missing in the formal exposition. I side stepped
the need for a pair construct to define an attribute by using a
functional formalism (ie N() and D() functions) to define the
composite mathematical structure. You may notice that I included a
definition of equality of attributes. In a way this is more formal
than an explicit syntax for composite mathematical structures (which
makes the meaning of equality implicit).

The functional notation is convenient. I think the exposition would
be more verbose with special syntax for the composite mathematical
structures.

#10

On Nov 15, 11:26 am, paul c <toledobythe... (AT) ooyah (DOT) ac> wrote:

Quote:

Bob Badour wrote:

...

Did you catch the part where it said an attribute is a domain? And then
it went on to say a domain is a set of values.

Sorry if I'm too slow here, did you mean:

"An attribute a consists of a name N(a) and a domain D(a)"?

If so, I can see you read it less generously but more precisely than I
did. Being a fan of the D&D definitions because I think they are pretty
darned concise, I would have rather seem them here, that's why I fretted
about "consists". It would be easy from the above to say that if an
attribute consists (even in part) of a domain, that it then somehow
includes a domain. I was probably reading it the way I wanted it to
mean, but I can see it doesn't emphasize the independence of a "header"
and, doesn't underline that an attribute names a domain.

It seems to me that to formally state that an attribute names a
domain, rather than merely state it has a domain is rather typical
computer science baggage!

Quote:

Trying to match D&D prose must be pretty hard, so I hope this won't
discourage David BL. As I've tried to say before, I think exercises
like this are valuable in their own right.

Without your comments I would be discouraged. Thanks!