Re: Interpretation of Relations

From: Joe Thurbon <usenet_at_thurbon.com>
Date: Tue, 23 Jan 2007 10:23:53 GMT
Message-ID: <2007012320233138165-usenet_at_thurboncom>

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?

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)).

> 
> 
>>>> 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?

Actually, I take that Not Really back. I was unaware that there was a Relational Calculus. The wikipedia pages on the Relational Algebra do mention is, but I missed it. So, at least I'm getting more of the picture.

>>
>> 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?

I don't know, yet. I meant it when I said I'm new at it. At the risk of asking you for a tutorial, would you mind giving a small example?

> 
> 

>> 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

Are we talking about the same thing?

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).

Cheers,
Joe Received on Tue Jan 23 2007 - 11:23:53 CET