Re: Properties no longer required to be resources?

At 10:10 31/07/03 +0100, Brian McBride wrote:
>On Wed, 2003-07-30 at 21:47, Graham Klyne wrote:
>
>[...]
>
> >
> > Then I( ppp rdf:type rdf:Property ) is true, which is the desired 
> entailment.
>
>False.  I(ppp rdf:type rdf:Resource) was the test case.

Rats!  I knew that, really!

Given the truth (from before) of:

(1)  I( ppp rdf:type rdf:Property )

and the axiomatic triple:

(2)  rdf:type rdfs:domain rdfs:Resource .

-- http://www.w3.org/2001/sw/RDFCore/TR/WD-rdf-mt-20030117/#rdfs_interp

and:

(3) if E is a triple s p o . then I(E) = true if

     s, p and o are in V, I(p) is in IP and <I(s),I(o)> is in IEXT(I(p))

     otherwise I(E)= false.

-- http://www.w3.org/2001/sw/RDFCore/TR/WD-rdf-mt-20030117/#gddenot

then:

(4) <I(rdf:type),I(rdfs:Resource)> in IEXT(I(rdfs:domain))   from (2),(3)

also:

(5) If <x,y> is in IEXT(I(rdfs:domain)) and <u,v> is in IEXT(x) then u is 
in ICEXT(y)

-- http://www.w3.org/2001/sw/RDFCore/TR/WD-rdf-mt-20030117/#rdfs_interp

then:

(6) <I(ppp),I(rdf:Property)> in IEXT(I(rdf:type))   from (1),(3)

and:

(7) I(ppp) in ICEXT(rdfs:Resource)   from (4),(6) in (5)

     [x=I(rdf:type), y=I(rdfs:Resource), u=I(ppp), v=I(rdf:Property)]

and given:

(8) x is in ICEXT(y) if and only if <x,y> is in IEXT(I(rdf:type))

-- http://www.w3.org/2001/sw/RDFCore/TR/WD-rdf-mt-20030117/#rdfs_interp

(9) <I(ppp),I(rdfs:Resource)> in IEXT(I(rdf:type))   from (7) in (8)

so finally:

     I( ppp rdf:type rdfs:Resource ) is true  from (8) in (3)

QED (this time?)

...

Or, more informally, I think that although IP and IR may be disjoint in 
RDF-interpretations, where there is no available vocabulary for this to be 
visible or otherwise in an RDF expression, the semantic conditions on RDFS 
interpretation require that IP be a subset of IR.

#g


---------------------------------
Graham Klyne  <GK@NineByNine.net>
Nine by Nine
http://www.ninebynine.net/