Re: Possible semantic bugs concerning domain and range

On Fri, 2002-10-11 at 18:07, pat hayes wrote:
> 
> >  >
> >>  Range(P, A) -> (forall x,y P(x,y) -> A(y) )
> >>
> >>  You want
> >>
> >>  Range(P,A) <-> (forall x,y P(x,y) -> A(y) )
> >>
> >>  They are about equally clear and intuitive; but the latter rules out
> >>  some possibilities which the former permits. I believe that all the
> >>  'intuitive' entailments that people want in fact hold in both these
> >>  cases; and that the former is therefore to be preferred.
> >
> >I am agnostic about which of these is to be preferred - as a humble
> >engineer, all I need to know is which one it is so that I have a clear
> >spec to which I can build my systems.

I'm kinda agnostic too... I was leaning toward the IF, rather
than the IFF...

But, for what it's worth, I happened to bring it up in conversation
with TimBL, and he expects the IFF meaning. "Anybody who
says P rdfs:range rdfs:Resource is wasting their breath"; i.e.
that's axiomatically true, to his mind.

> >One point that is worth making though is that there are a number of
> >similar statements that can be made about OWL properties, and that it
> >may make sense to give them a uniform semantics, i.e., all treated as
> >implication or all treated as bi-implication. E.g., we also have:
> >
> >Domain(P,C) implies/iff (forall x,y P(x,y) -> C(x))
> >TransitiveProperty(P) implies/iff (forall x,y,z (P(x,y) ^ P(y,z)) -> P(x,z))
> >SymmetricProperty(P) implies/iff (forall x,y P(x,y) -> P(y,x))
> >FunctionalProperty(P) implies/iff (forall x,y,z (P(x,y) ^ P(x,z)) -> y=z)
> >InverseFunctionalProperty(P) implies/iff (forall x,y,z (P(y,x) ^ 
> >P(z,x)) -> y=z)
> >inverseOf(P,Q) implies/iff (forall x,y P(x,y) -> Q(y,x))
> 
> How about all the unary properties of properties having an IFF 
> semantics?

OK by me.

> That would make sense, but it would leave domain, range 
> and inverse up for discussion.

I prefer IFF for those too.
But not too strongly.


-- 
Dan Connolly, W3C http://www.w3.org/People/Connolly/

Received on Tuesday, 15 October 2002 14:30:37 UTC