Re: more closed-world chatter

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

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