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Some questions about the exact meanings

From: Tanel Tammet <tammet@staff.ttu.ee>
Date: Wed, 01 Oct 2003 15:20:37 +0300
Message-ID: <3F7AC695.3020502@staff.ttu.ee>
To: www-rdf-logic@w3.org

Hi,

I have been teaching a group of students some RDF and OWL.

Concerning semantics, the approach has been transforming
everything to classical FOL, using "holds(predicate, subject, object)"
to encode triples.

As expected, mostly it is straightofrward, but in some places
I have not been able to understand what would be the
right translation (ie what would be the exact semantics)
of RDF and OWL constructions. Right now I have two
main questions.

First, suppose we want to say that "P" is a symmetric property.

We can axiomatize what "symmetric" means by:

forall X,Y,Z.  holds(symmetric,X,Y) <=>
                         (holds(X,Y,Z) => holds(X,Z,Y)).

The question is whether in OWL the equivalence <=>
in this definition should really be an implication =>
or it should be an equivalence <=>

What is the _right_ axiom schema for OWL: with implication
or with equivalence?

The second question stems from collections in RDF.

We have bag, seq and alt collections. The meanings
of these seem to be a bit vague in the sense that
I am not sure how to axiomatize them.

I'd start the axiomatisation by using function terms
(we can later convert the function terms to
predicates if we wish).

So, let us have a bag of three objects: (car, plane, train).

We can

a) construct a list in FOF, say like this:
 
    bagcons(car, bagcons(plane, bagcons(train,nil)))

    (where we could later replace "bagcons" terms
     by "applies(bagcons, ...." etc) if we want)

b) axiomatising "bagcons".

     For example, when a collection is a bag, it
     means that the order of elements is unimportant.
     Hence we should axiomatise:

     forall X,Y,Z. bagcons(X,bagcons(Y,Z))=bagcons(Y,bagcons(X,Z))

      in FOL.

The question now arises: which are the right axioms
for bag, seq and alt?

While "seq" seems fine, since it looks like being a
plain list (ie no axioms), bag and alt pose problems.

I am not sure that the "bagcons" axiom above is really
what is meant by RDF "bag". It is even more unclear
with "alt": how should we really axiomatise "alt"?
Most RDF documents leave this to be understood
"intuitively", which is not OK in RDF context.
And I could not understand the corresponding parts
of RDF semantics paper.

Regards,
               Tanel Tammet
Received on Wednesday, 1 October 2003 09:12:46 GMT

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