Re: more closed-world chatter
Date: Wed, 09 May 2007 11:21:56 +0200
Message-ID: <f1s3us$dvb$1_at_orkan.itea.ntnu.no>
Marshall wrote:
> On May 7, 4:15 am, Jon Heggland <jon.heggl..._at_idi.ntnu.no> wrote:
>> The crux of the matter in that prescription is the equivalence between >> R1 & R2 and R1 - (R1 - R2). How do you handle that?
>
> On further reflection, I don't think they're equivalent.
> We would say two expressions e1 and e2 on variables
> A and B were equivalent if
>
> forall A: forall B: e1(A) = e2(B)
>
> But that's clearly not the case here. All we have here is
>
> exists A: exists B: e1(A) = e2(B)
>
> And that's not a very strong claim. By those criteria,
> we could say that sqrt(x) and x/2 were equivalent,
> because, you know, 4. The fact that there is a *category*
> of A and B values for which the equation holds is
> a distraction, and not compelling.
I'm not sure I understand. Are you disputing the equivalence of the set intersection A INTERSECT B and the difference A MINUS (A MINUS B)?
Or are you pointing out that the equivalence only holds if the join R1 & R2 actually is an intersection? If so, sorry about not saying that explicitly, but I considered that obvious from the context of the IM prescription we're discussing; and anyway, I don't see what difference it makes. D&D's point is that intersection is a special case of join, as well as a special case of difference, so the rules for type inference ought to produce the same result in all three cases.
> We could try to rephrase the issue in terms of unary
> relations, intersection, and subtraction, but that wouldn't
> be very interesting, because we don't care much about
> operators that only work on unary relations.
You've lost me here, too. Why only unary relations?
-- JonReceived on Wed May 09 2007 - 11:21:56 CEST