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Next: Where is the cdt glossary?
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External
Since: Apr 22, 2005
Posts: 845
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(Msg. 1) Posted: Fri Dec 08, 2006 12:22 am
Post subject: set-valued values
Archived from groups: comp>databases>theory (more info?)
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Another maybe crazy question - if instead of 'atomic values' (whatever
that means) a relational engine (note for David, I've avoided using the
term 'DBMS' !) expressed only values made up of sets, would the presence
of the empty set in both true and false extensions create any problems?
(I'm thinking that the relational requirement of attribute names means
there is no problem, eg., the presence of empty sets is just an artifact
of the mechanism that can usually be safely ignored.)
As for representation, sometimes such values can't be represented
without access to other 'attributes', eg., values that are internal to
an engine. My attitude (no reasoning involved I'm afraid to say) is
that it's okay to give the builtin result 'true' in such cases. That
way, the engine can proceed to manipulate the expression if further
requests of made of it, concerning that result.
p |
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External
Since: Mar 20, 2005
Posts: 543
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(Msg. 2) Posted: Fri Dec 08, 2006 12:22 am
Post subject: Re: set-valued values [Login to view extended thread Info.]
Archived from groups: per prev. post (more info?)
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paul c wrote:
> paul c wrote:
> > Another maybe crazy question - if instead of 'atomic values' (whatever
> > that means) a relational engine (note for David, I've avoided using the
> > term 'DBMS' !) expressed only values made up of sets, would the presence
> > of the empty set in both true and false extensions create any problems?
> > (I'm thinking that the relational requirement of attribute names means
> > there is no problem, eg., the presence of empty sets is just an artifact
> > of the mechanism that can usually be safely ignored.)
> >
> > As for representation, sometimes such values can't be represented
> > without access to other 'attributes', eg., values that are internal to
> > an engine. My attitude (no reasoning involved I'm afraid to say) is
> > that it's okay to give the builtin result 'true' in such cases. That
> > way, the engine can proceed to manipulate the expression if further
> > requests of made of it, concerning that result.
> >
> >
> > p
>
> One reason I asked this question is because Codd started with sets, then
> veered away from them in a way, I'm guessing because of such possible
> problems, whereas the singleton value has a logical complement that is
> easily recognized if one knows its domain. It's always puzzled me why
> he avoided sets when it came to the down and dirty of implementations.
I heard a story about this from someone who heard it from someone whom
he considered to be close enough to the situation to know. This is
distant enough and without any second source that I consider it
apocryphal (but definitely curious if anyone has heard a similar tale).
The story is that because the efforts underway within IBM to work on a
DBMS based on the relational model were starting with simple domains
(which makes some sense from a practical standpoint), folks at IBM
wanted Codd to zero in on that and leave "nonsimple domains" out of the
picture. So the theory morphed a bit to align with practical
considerations, thereby sending the IT profession into a few decades
of... (ah, some of you already know my opinion so I'll skip it here).
Since there is no good mathematical reason to leave out set-valued
attributes, such a story would explain why they were discounted up
front. Again, I certainly do not know this to be true, but the story
was passed along to me a few years back. Has anyone else heard any
story along these lines?
--dawn |
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External
Since: Apr 22, 2005
Posts: 845
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(Msg. 3) Posted: Fri Dec 08, 2006 12:27 am
Post subject: Re: set-valued values [Login to view extended thread Info.]
Archived from groups: per prev. post (more info?)
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paul c wrote:
> Another maybe crazy question - if instead of 'atomic values' (whatever
> that means) a relational engine (note for David, I've avoided using the
> term 'DBMS' !) expressed only values made up of sets, would the presence
> of the empty set in both true and false extensions create any problems?
> (I'm thinking that the relational requirement of attribute names means
> there is no problem, eg., the presence of empty sets is just an artifact
> of the mechanism that can usually be safely ignored.)
>
> As for representation, sometimes such values can't be represented
> without access to other 'attributes', eg., values that are internal to
> an engine. My attitude (no reasoning involved I'm afraid to say) is
> that it's okay to give the builtin result 'true' in such cases. That
> way, the engine can proceed to manipulate the expression if further
> requests of made of it, concerning that result.
>
>
> p
One reason I asked this question is because Codd started with sets, then
veered away from them in a way, I'm guessing because of such possible
problems, whereas the singleton value has a logical complement that is
easily recognized if one knows its domain. It's always puzzled me why
he avoided sets when it came to the down and dirty of implementations.
p >> Stay informed about: set-valued values |
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External
Since: Feb 14, 2006
Posts: 1550
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(Msg. 4) Posted: Fri Dec 08, 2006 1:01 am
Post subject: Re: set-valued values [Login to view extended thread Info.]
Archived from groups: per prev. post (more info?)
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paul c wrote:
> Another maybe crazy question - if instead of 'atomic values' (whatever
> that means) a relational engine (note for David, I've avoided using the
> term 'DBMS' !) expressed only values made up of sets, would the presence
> of the empty set in both true and false extensions create any problems?
> (I'm thinking that the relational requirement of attribute names means
> there is no problem, eg., the presence of empty sets is just an artifact
> of the mechanism that can usually be safely ignored.)
>
> As for representation, sometimes such values can't be represented
> without access to other 'attributes', eg., values that are internal to
> an engine. My attitude (no reasoning involved I'm afraid to say) is
> that it's okay to give the builtin result 'true' in such cases. That
> way, the engine can proceed to manipulate the expression if further
> requests of made of it, concerning that result.
>
> p
I don't see why the value would appear in both sets. An empty set is
different from a set containing the empty set as it's only element.
{} != {{}} >> Stay informed about: set-valued values |
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External
Since: Apr 22, 2005
Posts: 845
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(Msg. 5) Posted: Fri Dec 08, 2006 1:10 am
Post subject: Re: set-valued values [Login to view extended thread Info.]
Archived from groups: per prev. post (more info?)
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Bob Badour wrote:
> paul c wrote:
>
>> Another maybe crazy question - if instead of 'atomic values' (whatever
>> that means) a relational engine (note for David, I've avoided using
>> the term 'DBMS' !) expressed only values made up of sets, would the
>> presence of the empty set in both true and false extensions create any
>> problems? (I'm thinking that the relational requirement of attribute
>> names means there is no problem, eg., the presence of empty sets is
>> just an artifact of the mechanism that can usually be safely ignored.)
>>
>> As for representation, sometimes such values can't be represented
>> without access to other 'attributes', eg., values that are internal to
>> an engine. My attitude (no reasoning involved I'm afraid to say) is
>> that it's okay to give the builtin result 'true' in such cases. That
>> way, the engine can proceed to manipulate the expression if further
>> requests of made of it, concerning that result.
>>
>> p
>
>
> I don't see why the value would appear in both sets. An empty set is
> different from a set containing the empty set as it's only element.
>
> {} != {{}}
It's a conundrum for me. On one hand, if the empty set is contained in
one extension, de Morgan tells us it is not in the other. On the other
hand, its lack of an attribute seems to make it a member of both sets.
p >> Stay informed about: set-valued values |
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External
Since: Feb 14, 2006
Posts: 1550
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(Msg. 6) Posted: Fri Dec 08, 2006 1:12 am
Post subject: Re: set-valued values [Login to view extended thread Info.]
Archived from groups: per prev. post (more info?)
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paul c wrote:
> Bob Badour wrote:
>
>> paul c wrote:
>>
>>> Another maybe crazy question - if instead of 'atomic values'
>>> (whatever that means) a relational engine (note for David, I've
>>> avoided using the term 'DBMS' !) expressed only values made up of
>>> sets, would the presence of the empty set in both true and false
>>> extensions create any problems? (I'm thinking that the relational
>>> requirement of attribute names means there is no problem, eg., the
>>> presence of empty sets is just an artifact of the mechanism that can
>>> usually be safely ignored.)
>>>
>>> As for representation, sometimes such values can't be represented
>>> without access to other 'attributes', eg., values that are internal
>>> to an engine. My attitude (no reasoning involved I'm afraid to say)
>>> is that it's okay to give the builtin result 'true' in such cases.
>>> That way, the engine can proceed to manipulate the expression if
>>> further requests of made of it, concerning that result.
>>>
>>> p
>>
>>
>>
>> I don't see why the value would appear in both sets. An empty set is
>> different from a set containing the empty set as it's only element.
>>
>> {} != {{}}
>
>
> It's a conundrum for me. On one hand, if the empty set is contained in
> one extension, de Morgan tells us it is not in the other. On the other
> hand, its lack of an attribute seems to make it a member of both sets.
>
> p
Huh? No, the set that it is not in is just empty.
{} != {{}}
^--not in that set
{} != {{}}
^--in this one >> Stay informed about: set-valued values |
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External
Since: Apr 22, 2005
Posts: 845
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(Msg. 7) Posted: Fri Dec 08, 2006 1:28 pm
Post subject: Re: set-valued values [Login to view extended thread Info.]
Archived from groups: per prev. post (more info?)
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Bob Badour wrote:
> paul c wrote:
>
>> Bob Badour wrote:
>>
>>> paul c wrote:
>>>
>>>> Another maybe crazy question - if instead of 'atomic values'
>>>> (whatever that means) a relational engine (note for David, I've
>>>> avoided using the term 'DBMS' !) expressed only values made up of
>>>> sets, would the presence of the empty set in both true and false
>>>> extensions create any problems? (I'm thinking that the relational
>>>> requirement of attribute names means there is no problem, eg., the
>>>> presence of empty sets is just an artifact of the mechanism that can
>>>> usually be safely ignored.)
>>>>
>>>> As for representation, sometimes such values can't be represented
>>>> without access to other 'attributes', eg., values that are internal
>>>> to an engine. My attitude (no reasoning involved I'm afraid to say)
>>>> is that it's okay to give the builtin result 'true' in such cases.
>>>> That way, the engine can proceed to manipulate the expression if
>>>> further requests of made of it, concerning that result.
>>>>
>>>> p
>>>
>>>
>>>
>>>
>>> I don't see why the value would appear in both sets. An empty set is
>>> different from a set containing the empty set as it's only element.
>>>
>>> {} != {{}}
>>
>>
>>
>> It's a conundrum for me. On one hand, if the empty set is contained
>> in one extension, de Morgan tells us it is not in the other. On the
>> other hand, its lack of an attribute seems to make it a member of both
>> sets.
>>
>> p
>
>
> Huh? No, the set that it is not in is just empty.
>
> {} != {{}}
> ^--not in that set
>
> {} != {{}}
> ^--in this one
Thanks, I see now that my question was a wrong-headed one, confusing
subsets with values that users are aware of, maybe also confusing
headings with bodies. Ie., if a user hasn't 'inserted' an empty set
(let me ignore for now just how they might do that), then it seems
accurate to say that it is just not there.
It was really the representation problem with certain RVA's that I was
grappling with - I have the impression that Codd washed his hands of it
by insisting on his Information Principle, at least in his first two
papers. (No criticism of Codd, maybe he was right - this started for me
in part when I was wondering how much of TTM Appendix A would remain
standing, such as the <AND> operator, if the "v" in the ordered triple
<A,T,v> always meant a set of symbols of type T or would TTM's "genesis"
topple if that were done. Anyway, I'll have to think about this a
little further.)
p >> Stay informed about: set-valued values |
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External
Since: Nov 23, 2006
Posts: 73
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(Msg. 8) Posted: Fri Dec 08, 2006 2:26 pm
Post subject: Re: set-valued values [Login to view extended thread Info.]
Archived from groups: per prev. post (more info?)
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paul c <toledobythesea RemoveThis @oohay.ac> wrote in news:TX2eh.439310$1T2.321088
@pd7urf2no:
> It's a conundrum for me. On one hand, if the empty set is contained in
> one extension, de Morgan tells us it is not in the other. On the other
> hand, its lack of an attribute seems to make it a member of both sets.
The relational theory is build on void -- the empty set.
Proof: one postulates the empty set existance. Then one gets the natural
numbers in von Neumann numerals:
0 def. {}
1 def. {{}} = {0}
2 def. {{}, {{}}} = {0, 1}
et cetera
The rest is easy :] -- the rational numbers, real and the rest of
mathematique follows. Of course, the relational theory is one part of
mathematique. QED.
--
Tegi
>
> p
> >> Stay informed about: set-valued values |
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