John M and Tara, (01)
JM
> I'm told RDF was meant to be a proper subset, to avoid the
> so-called complexity of FOL and its tools. (02)
That was the intent. But the actual complexity of the RDF semantics
is more complex than ordinary FOL. The intended interpretation of
a triple (S V O) was that V is a relation that is applied to S and O.
That means that any triple that consists of three constants can be
mapped to a very simple statement in FOL: (03)
V(S,O) (04)
However, RDF allows any or all of the three elements of a triple
to be *blank*. If S or O happens to be blank, you have to insert
an existential quantifier for it. In FOL, you get (05)
(Ex) V(x,O)
(Ex)(Ey) V(x,y) (06)
But if V happens to be blank, you get an existential quantifier
that ranges over relations. That goes beyond FOL: (07)
(Ex) x(S,O) (08)
TA
> I suggest you read the RDF semantics (http://www.w3.org/TR/rdf-mt/)
> to understand its relationship to FOL. (09)
Yes. That article, by the way, was written by Pat Hayes (with updates
and revisions over the years). Section 1.1 on the semantics of RDF,
which Tara cited, cites an article by Hayes and Menzel that goes the
issues above. In that article, Pat and Chris explain why the KIF
syntax and semantics had to be extended to support RDF. That was
the motivation for the more general semantics of Common Logic. (010)
TA
> the names that occur in the subject, predicate and object positions
> of a triple would all be individual constants that are arguments
> for an implicit predicate that is informally called "Triple" in
> http://www.w3.org/TR/rdf-mt/#sinterp.
>
> The RDF triple
> a b c.
>
> becomes the FOL
>
> Triple(a, b, c)
>
> NOT
>
> b(a, c)
>
> So by your [JM's] argument, all RDF predicates should be nouns. (011)
Yes. As Pat and Chris explain, the semantics of Triple(a,b,c) does
allow any of the three positions to contain an existentially quantified
variable. That allows the middle variable to quantify over relations
while still allowing an FOL-style of model theory and proofs. (012)
That option of quantifying over relations is why full OWL goes beyond
the semantics of description logics. OWL DL took the simple way out:
they do not support the option of reasoning about RDF triples that
contain blank nodes in the middle position. (013)
John (014)
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