- From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
- Date: Fri, 21 Nov 2003 12:26:27 -0500 (EST)
- To: stefan@ISI.EDU
- Cc: www-rdf-rules@w3.org
From: Stefan Decker <stefan@ISI.EDU> Subject: Re: Rules WG -- draft charter -- NAF Date: Fri, 21 Nov 2003 16:51:05 +0000 > At 08:09 PM 11/20/2003, Peter F. Patel-Schneider wrote: > >From: Stefan Decker <stefan@ISI.EDU> > >Subject: Re: Rules WG -- draft charter -- NAF > >Date: Thu, 20 Nov 2003 19:19:56 +0000 > > > > > Peter, > > > > > > >Well, I am still confused as to how this would work. How would one > > > >interpret a rule on an RDF graph without reference to the RDF (or some > > > >other) semantics? > > > > > > > > > It should take the RDF semantics into account. > > > But compared to the OWL the semantics of RDF semantics is minimal. > > > But maybe I should first try to define what I mean by (extended) semantics > > > of an RDF graph. > > > The following definition could serve as a starter: > > > > > > Set T be the set of all triples. > > > An extended semantics esem is a mapping from pow(T) -> pow(T) such that > > > esem(R) \subseteq R, R \in pow(T) ^p Let X be any particular triple. Define esemX(R) to be R if the size of R is finite and even and RuX otherwise. I claim that esemXY satisfies the definition above (if you really meant subseteq, then just replace union with difference). esemXY is not monotonic. > > > So every extended semantics is itself monotonic :-) > > > E.g., RDF Schema semantics applied to an RDF graph delivers > > > only additional triples (e.g., additional subClassOf triples), > > > but would never remove anything. > > > >Well, not necessarily. Nonmonotonic here roughly means that if R1 is > >smaller than R2 then esem(R1) is smaller than esem(R2), > > Yes. > > >which you certainly > >don't get as a consequence of this definition. > > Actually, you do. > Every esem is a continuous function on a complete lattice. Where was that stated? > Every continuous function on a complete lattice is monotonic. Well, given that the definition of continuous functions between complete partial orders usually includes monotonic, sure. > >I any case, what does this have to do with the RDF semantics at all? > I try to explain what I means by a semantics - like RDF Schema and what it > could mean > to apply the CWA on a semantics of a datamodel. > In a way I would like to clearify the confusion around CWA applied to RDF, > RDF Schema, etc. > Let me know if this is of no interest to you. Well sure, I would like to see what you are trying to get at. > > > Then a way to define CWA to extended semantics is by simply > > > doing CWA(rdfschema(R)); > > > I think this works at least for some semantics - I don't think it works > > for > > > all, but it would be interesting > > > to investigate where it works. > > > >What is the CWA relationship here? It certainly isn't a relationship > >between triple sets! > > I had Ray Reiters definition in mind, modified to the RDF case > > CWA(A) = A \union {\neg t \mid t is a triple and is not contained in A)) > > //since RDF Interpretations add triples we need to take these additional > triples into account as well - > // so there is a sloppyness here, which is not a big problem. Well, there may be a problem or there may not. For example, it is possible that CWA(A) is RDF(S,D)-inconsistent for all (or many) A's. [...] > > > If yes, one could try to go one step higher on the semantics ladder and > > > investigate what an RDFS interpretation would add. > > > Taking the definition from above, one would try to compute the extended > > > semantics > > > and then apply CWA to it. Do you see obvious problems with that? > > > >Yes, certainly. First, how can you determine whether to do the RDF or the > >RDFS (or the OWL) CWA? Second, the RDF and RDFS CWA of any graph are going > >to be OWL-inconsistent. > > Good question. One way is simply to say: the user knows which semantics > to apply. another possibility is that RDF Graphs carry metadata which > indicates which semantics applies. > > > >What would the CWA make of the folowing graph? > > > > > > > >ex:Student rdfs:subClassOf _:x . > > > >_:x rdf:type owl:Restriction . > > > >_:x owl:onProperty ex:sid . > > > >_:x owl:allValuesFrom xsd:integer . > > > Interpreting _:x as a skolem constant > > > and the rest as simple triple data I don't see the problem? > > > >Well, first, how does the CWA work on _:x. Suppose, for example, there are > >two blank nodes that look the same. Is the CWA going to force them to > >denote different domain elements? (For that matter, what about two URI > >refs that have the same information attached to them?) > These two questions are not related - there can be an equality theory > applied before CWA (as another esem). But yes, blank nodes are > interesting. I think a Herbrand interpretation would be useful - that > would mean, yes CWA would generate different domain elements. Where could > something go wrong with this? You think otherwise? Yes. Everything goes wrong with this. The CWA then forces a very strong version of the unique names assumption - all nodes, even blank nodes, have to denote different domain elements. This has been an issue with various versions of the CWA for quite some time now. > > > >In particular, would it require that there be no domain element for _:y in > > > >the following. > > > > > > > >_:y rdf:type owl:Restriction . > > > >_:y owl:onProperty ex:sid . > > > >_:y owl:allValuesFrom rdfs:Literal . > > > Again, just using an RDF interpretation from the model theory I don't see > > > the problem. > > > Of course if I apply an OWL interpretation things look differently. > > > But maybe one should first start simple. > > > >Well, simple starting points that prevent future growth are certainly not > >preferred, and this is what I am seeing here. > Why? The naive application of the CWA to graphs requires interpreting these graphs in a particular formalism and breaks the upward compatability between RDF and RDFS and between RDFS and OWL. > > > Am I missing anything? > > > >Well, your proposal is certainly missing something. I don't see how it can > >work well, if at all. > Why? See above. Consider also issues having to do with forcing different nodes (even blank nodes) to denote different domain elements. > > > >I forsee many similar problems in applying a CWA without use of semantics. > > > > > > Could you explain them? > > > >Well, without a semantics I don't see that you have any connection to RDF > >at all. The (beginnings of a) semantics that you provide above still > >doesn't have much connection (if any) to RDF. How do you reconcile how > >your CWA works with how the RDF semantics works? I've given a couple of > >examples, but there are many more. It appears to me that you will have to > >mirror all the RDF (or RDFS or OWL) inferences to make your scheme work, > >and even then I don't see how you actually get a CWA out of your scheme at > >all. > See the definition of CWA above - together with the definition of an esem > it seems to me to provide a framework to discuss multiple semantics and > still are able to use the CWA. For RDF semantics itselfs this works by > just adding the axiomatic triples to the model For RDF Schema you add the > additional triples coming from the RDF Schema semantics. The CWA can be > applied the the graph be queried. I don't see this. I don't see a usable definition of an esem. I don't see a solution to the forcing-apart of node denotations. Even so, I would like to see a completely-worked-out document on this. There is much to be gained from some way of closing/circumscribing/... information in the Semantic Web and maybe this could serve as a starting point. peter
Received on Friday, 21 November 2003 12:26:38 UTC