Re: Interpretation of Relations

Joe Thurbon wrote:

> On 2007-01-23 08:00:22 +1000, Bob Badour <bbadour_at_pei.sympatico.ca> said:
>

>> Joe Thurbon wrote:
>>
>>> On 2007-01-22 23:39:14 +1000, Bob Badour <bbadour_at_pei.sympatico.ca> 
>>> said:
>>>
>>>> Joe Thurbon wrote:
>>>>
>>>> The RM includes the operations on relations by which one does the 
>>>> inferencing. Does it not?
>>>
>>> Depending on how you interpret relations into predicates, I would say 
>>> that JOIN and PROJECT are kinds of inferencing rules. But they seem 
>>> quite different to modus ponens.
>>
>> But is functional dependency so different from modus ponens?

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}.

>>>>> Anyway, I've rambled on quite a bit. The ideas are pretty new to 
>>>>> me, still in development, and really, I'm getting ahead of myself 
>>>>> because I still don't fully understand the RM.
>>>>
>>>> Would the observation that the relational calculus is basically 1st 
>>>> order predicate logic help you understand it better?

Relational Calculus is pretty-much predicate calculus. Relational Algebra is pretty-much set algebra.

>>> Not really. Well, I guess its validation that I'm not completely 
>>> crazy. I was actually starting from the assumption that the 
>>> relational calculus could be embedded in 1st order logic.
>>>
>>> I will feel like I understand the RM when I can answer the question: 
>>> for a relational theory (by theory I think I mean a set of relvars - 
>>> a set of 'instantiated' relations), what is the corresponding logical 
>>> theory (set of grounded wffs).
>>
>> Do you include the constraints as expressed by wffs in the set of 
>> relvars?

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.

>>> 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.

>>
>>
>>   What is the analog of, say, material implication?
>>
>> Isn't that just intersection? Or am I misreading something?

• ~(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?

> Are we talking about the same thing?

I don't know.

> 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. Received on Tue Jan 23 2007 - 15:11:53 CET