Re: set-valued values
Date: Fri, 08 Dec 2006 13:28:22 GMT
Message-ID: <WLdeh.448936$5R2.36978_at_pd7urf3no>
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 Received on Fri Dec 08 2006 - 14:28:22 CET