From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>

Date: Wed, 01 Oct 2003 09:36:32 -0400 (EDT)

Message-Id: <20031001.093632.04558381.pfps@research.bell-labs.com>

To: tammet@staff.ttu.ee

Cc: www-rdf-logic@w3.org

Date: Wed, 01 Oct 2003 09:36:32 -0400 (EDT)

Message-Id: <20031001.093632.04558381.pfps@research.bell-labs.com>

To: tammet@staff.ttu.ee

Cc: www-rdf-logic@w3.org

From: Tanel Tammet <tammet@staff.ttu.ee> Subject: Some questions about the exact meanings Date: Wed, 01 Oct 2003 15:20:37 +0300 > 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 straight[fo]rward, 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)). I think that you meant to say forall X,Y,Z. holds(symmetric,X) <=> (holds(X,Y,Z) => holds(X,Z,Y)). or maybe even forall X,Y,Z. holds(rdf:type,X,owl:SymmetricProperty) <=> (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 answers to these questions can be found in ``OWL Web Ontology Language: Semantics and Abstract Synax'' (http://www.w3.org/TR/owl-semantics). However, actually determining the answer is generally not trivial because this document gives a model theory for OWL, and one has to investigate the consequences of this model theory. I invite you to do the investigation. However, if you want to peek, the answer is <=>. OWL generally takes an extensional stance on such questions. If the conditions for some characteristic hold, then the characteristic holds. (RDF generally takes a different stance here.) Note that it is possible to non-trivially infer that a property is symmetric in OWL, as the inverse of a symmetric property is also symmetric. > The second question stems from collections in RDF. ^^^containers > We have bag, seq and alt collections. The meanings ^^^containers > 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 ^^^container > 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. I don't think that this is getting you at all close to RDF containers. > The question now arises: which are the right axioms > for bag, seq and alt? The answer is, honestly, that there are none. RDF collections have no (or very, very little) semantics. > While "seq" seems fine, since it looks like being a > plain list (ie no axioms), bag and alt pose problems. Even seq poses severe problems. For example, how many elements are there in a sequence? > 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"? Alt is the worst of the three. > Most RDF documents leave this to be understood > "intuitively", which is not OK in RDF context. Agreed. That is why RDF Semantics has clarified the issue. > And I could not understand the corresponding parts > of RDF semantics paper. Section 3.2.2 of RDF Semantics is actually quite clear. It specifically states that ``[t]here are no special semantic conditions on the container vocabulary''. Collections are a slightly different matter. > Regards, > Tanel Tammet Peter F. Patel-SchneiderReceived on Wednesday, 1 October 2003 09:38:04 UTC

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