Re: Interpretation of Relations
From: Joe Thurbon <usenet_at_thurbon.com>
Date: Tue, 23 Jan 2007 21:46:07 GMT
Message-ID: <200701240745457987-usenet_at_thurboncom>
>
> I am not sure I follow your statement about functional dependency being
> a function from A onto B. I see functional dependency as an invariant,
> which is exactly a function that maps A and B onto {true,false}.
>
> In the relational model, one expresses a general integrity constraint
> as a wff. Foreign key references are just an important special case for
> which we use a short-hand notation. Similarly for candidate keys.
>
> I don't have the time or resources to reproduce the works of Codd and
> other relational investigators from the 1970's and onward. If you are
> interested, I suggest you hunt down those papers and perhaps find a
> decent book on relational databases. Date's _Introduction..._ is
> comprehensive.
>
> = ~(a ^ ~b)
> = ~(a minus b)
>
> hmmmm... I was thinking of that as A minus (A minus B) but it isn't. It
> is some universe minus (A minus B), isn't it?
>
> I don't know.
>
> You will find plenty of good material here:
> http://www.almaden.ibm.com/cs/people/fagin/papers.html
>
> Granted, Fagin is so prolific you will find plenty of good stuff
> unrelated to the relational model too.
>
> You may be able to get all of Codd's important papers on CD or DVD from
> the ACM:
> http://www.informatik.uni-trier.de/~ley/db/about/codd.html
>
> If I am not mistaken, the 1972 paper, /Relational Completeness of Data
> Base Sublanguages/, demonstrates the equivalence of set algebra and
> predicate calculus.
Date: Tue, 23 Jan 2007 21:46:07 GMT
Message-ID: <200701240745457987-usenet_at_thurboncom>
On 2007-01-24 00:11:53 +1000, Bob Badour <bbadour_at_pei.sympatico.ca> said:
>>
>> It's different, but it is _so_ different. Good question. It's different
>> because for attributes A and B a functional dependancy is a function
>> from A -> B. For propositions A and B, modus ponens is a function from
>> AxB -> {true, false}. (Please forgive the complete abuse of notation,
>> but a proper analogy depends (and I'm repeating myself) on how you
>> interprety relations into predicates)).
>
> I am not sure I follow your statement about functional dependency being
> a function from A onto B. I see functional dependency as an invariant,
> which is exactly a function that maps A and B onto {true,false}.
I see. Fair enough.
[...]
>>
>
> In the relational model, one expresses a general integrity constraint
> as a wff. Foreign key references are just an important special case for
> which we use a short-hand notation. Similarly for candidate keys.
>
> I don't have the time or resources to reproduce the works of Codd and
> other relational investigators from the 1970's and onward. If you are
> interested, I suggest you hunt down those papers and perhaps find a
> decent book on relational databases. Date's _Introduction..._ is
> comprehensive.
Sure. Thanks.
>
>
>>>> I have other questions, too, of course. What does it mean to close a >>>> set of relations under consequence? (Is is the repeated application of >>>> JOIN and PROJECT?) >>> >>> I think you might find your answer stuffed away under the subject of >>> predicate inheritence or inference especially wrt views. >> >> My vocabulary is expanding! >> >>> >>> >>> What is the analog of, say, material implication? >>> >>> Isn't that just intersection? Or am I misreading something? >> >> >> I would have thought that the analog of conjunction was intersection. I >> guess it depends what you are intersecting. Material implication >> >> a -> b >> >> is just >> >> ~a V b
>
> = ~(a ^ ~b)
> = ~(a minus b)
>
> hmmmm... I was thinking of that as A minus (A minus B) but it isn't. It
> is some universe minus (A minus B), isn't it?
> Then the question becomes: What is the universe?
Indeed.
>
>
>> Are we talking about the same thing?
>
> I don't know.
When I know more, I might be able to come back and answer this one.
>
>
>> I appreciate that you're taking time to respond to these posts. I am >> finding it difficult to get access to the seminal works, and as a >> result I'm trying to piece together a coherent picture. Between >> yourself and JOG, I've at least got an idea of what to read next. (I've >> moved away from the city, so I only get access to a reasonable library >> about every 3 months. I've got a reading list, though).
>
> You will find plenty of good material here:
> http://www.almaden.ibm.com/cs/people/fagin/papers.html
>
> Granted, Fagin is so prolific you will find plenty of good stuff
> unrelated to the relational model too.
>
> You may be able to get all of Codd's important papers on CD or DVD from
> the ACM:
> http://www.informatik.uni-trier.de/~ley/db/about/codd.html
>
> If I am not mistaken, the 1972 paper, /Relational Completeness of Data
> Base Sublanguages/, demonstrates the equivalence of set algebra and
> predicate calculus.
A thousand thanks!.
Cheers,
Joe
Received on Tue Jan 23 2007 - 22:46:07 CET