Re: more closed-world chatter

From: paul c <toledobythesea_at_oohay.ac>
Date: Sat, 05 May 2007 14:21:01 GMT
Message-ID: <hp0%h.160217$DE1.27328@pd7urf2no>

Marshall wrote:
> On May 3, 6:39 am, paul c <toledobythe..._at_oohay.ac> wrote:
>

>>Thanks, I feel better now.  Still, I'd like to know I could paraphrase
>>that query a little more formally, say using D&D <AND>.  But the
>>stipulation "It is required that if <A,T1> is in Hr1 and <A,T2> is in
>>Hr2, then T1 = T2" stymies me, eg., if pricedomain={1,2} and
>>anotherdomain={3}, it seems that <AND> isn't defined.

>
>
> This exact question has been in the back of my head for
> a long time. I lately feel like the answer is "it depends."
> Specifically it depends on the type system. The heart
> of a join (if I may wax poetic momentarily) is a bunch of
> tests for equality. So what is the result of:
>
> 1:pricedomain = 3:anotherdomain
>
> (The colon here is a type specifier.) The question
> is interesting in the case of disjoint types.
>
> So, there are a variety of possible answers. Bob
> for example considers this within the context of
> a type theory that has subtyping, whereas Jon
> proposes a type mismatch. Both answers have
> their merits. Another question: what is the type
> of that attribute in the result relation? Possible
> answers include the top of the type lattice and
> the bottom; I am inclined to prefer the bottom.
> ...

Regarding possible answers, I took it that both Bob B and Jon H are amenable to an answer of "false", assuming the dbms doesn't take exception and refuse to answer. "False" could be a boolean value, but if we want closure, I guess the answer has no attribute type per se, rather the answer is a relation that has no attributes and in this case, no tuples.

In conventional RT like D&D's, I gather that we could then join that answer with a relation that does have attributes and the result would be a relation with the same attributes. I believe this is "correct" within such an RT but I wonder if this is any more useful than a result that has no attributes or if it is just the effect of formal definitions.

Sorry if I'm drifting the thread again. Will try to absorb the latest syntax!

p Received on Sat May 05 2007 - 09:21:01 CDT