- From: Sandro Hawke <sandro@w3.org>
- Date: Fri, 24 Apr 2009 07:12:05 -0400
- To: Jos de Bruijn <debruijn@inf.unibz.it>
- cc: kifer@cs.sunysb.edu, public-rif-wg@w3.org
...
> > ... and since it's not the same in every interpretation, it's not
> > entailed. I think I'm getting that. So...
> >
> > positive-entailment
> > PREMISE: (empty)
> > CONCLUSION: member(eg:foo, list(eg:foo eg:bar))
> >
> > negative-entailment
> > PREMISE: (empty)
> > CONCLUSION: member(eg:baz, list(eg:foo eg:bar))
> >
> > positive-entailment
> > PREMISE: eg:baz = eg:bar
> > CONCLUSION: member(eg:baz, list(eg:foo eg:bar))
> >
> > Agreed?
>
> agreed.
...
> >
> > positive-entailment
> > PREMISE: eg:bar = 1
> > eg:foo = 2
> > CONCLUSION: index-of(list(eg:foo eg:bar), eg:foo) = list(1)
>
> yes
>
> >
> > positive-entailment
> > PREMISE: eg:bar = eg:foo
> > CONCLUSION: index-of(list(eg:foo eg:bar), eg:foo) = list(1 1)
>
> Did you mean List(1 2)?
Yes, sorry. (And I suspect we really want 0-indexed lists, but I'll
stick with 1-indexed lists for this conversation, since I accidentally
started that way.)
> > But what if the premise is empty? I'm thinking that none of these
> > entailments would hold... (so these would be valid tests)....
> >
> > negative-entailment
> > PREMISE:
> > CONCLUSION: index-of(list(eg:foo eg:bar), eg:foo) = list(1 1)
>
> Yes
>
> >
> > negative-entailment
> > PREMISE:
> > CONCLUSION: index-of(list(eg:foo eg:bar), eg:foo) = list(1)
>
> No. eg:foo is mapped to the same object in every interpretation. Let's
> call this object a. And let's say eg:foo is mapped to b. Then
> list(eg:foo eg:bar) represents the sequence (a,b). And certainly the
> object a appears in the first position of this sequence.
>
> So, this should be a positive entailment test.
Well, I'd agree that in all interpretations, there's a match in the
first position. But in some interpretations there's also a match in the
second postion (namely interpretations where eg:foo=eg:bar). So, in
some interpretations, the left side of the equals is interpretated as
list(1) and in others it's list(1 2). So, I think that means the
equality doesn't hold in all interpretations, and the proposed
conclusion is not entailed...
Right?
-- Sandro
Received on Friday, 24 April 2009 11:12:18 UTC