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Re: ACTION-93 / ISSUE-63: Initiated work on OWL-1.1-Full semantics

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Mon, 31 Mar 2008 19:29:34 -0400 (EDT)
Message-Id: <20080331.192934.213677279.pfps@research.bell-labs.com>
To: schneid@fzi.de
Cc: public-owl-wg@w3.org

From: "Michael Schneider" <schneid@fzi.de>
Subject: RE: ACTION-93 / ISSUE-63: Initiated work on OWL-1.1-Full semantics
Date: Mon, 31 Mar 2008 12:49:02 +0200

> Hi Peter!
> Peter F. Patel-Schneider wrote on Wednesday, March 26, 2008:
> >> >2/ I do not believe that a comprehension principle is needed for
> >> >   owl11:disjointUnionOf (so long as there is a 
> >> >   comprehension principle
> >> >   for lists of descriptions) and the syntax requires that the
> >> >   disjointUnion be a named class.
> >> 
> >> I don't understand your last remark about the requirement of 
> >> a named class.
> >
> >If a named class is required (and it currently is)
> >
> >disjointUnion := 'DisjointUnion' '(' { annotation } 
> >owlClassURI description description { description } ')'
> >
> >then there is no need to ever require the existence of a node on the
> >"left hand side" of an owl:disjointUnionOf because the only nodes that
> >are needed there to make entailment work out are named classes.  
> I don't see a way to perform such a restriction to only /named/
> classes in OWL-Full.  
> This is, of course, possible in OWL-DL, which demands that an ontology
> has to be syntactically valid to its Abstract/Functional syntax. This
> syntax can then restrict the use of a node within a certain language
> construct to be only an URI. And the OWL-DL semantics are then only
> specified for such a syntactically valid expression.  
> But how can I specify such a constraint in OWL-Full, for which /every/
> RDF graph is a syntactically valid input and gets interpreted by
> OWL-Full semantics?  

You can't.  

But if all you are interested in is extending the OWL-DL semantics, then
you don't need to be able to infer 

	:_b owl:DisjointUnionOf .....

for arbitrary blank nodes.  

However, the question is moot!  Because there is a comprehension
principle for owl:unionOf for any sequence of descriptions there is
going to be a blank description node (_:u) related to that sequence via
an owl:unionOf link.  If the sequence is pairwise disjoint, then by the
semantics of owl:DisjointUnionOf _:u will be (or should be!) related to
the sequence by owl:DisjointUnionOf.

> [...]
> >> (A) How do you think about my approach to introduce the 
> >> "missing" axiomatic
> >> triples? Was is intended to not include them, and if so, for 
> >> what reason? Or
> >> has it just been forgotton?

> >It was intended not to include them.  It's not as if there are any real
> >problems if these are not included, and, again, putting them in just
> >increases the chance of some unintended consequence.
> In principle, I share this stance, because I have not yet seen a real
> >advantage for having axiomatic triples in RDF(S). But in this case, I
> >would have expected to see /no additional/ axiomatic triples at all
> >in OWL-Full. However, OWL-Full has lots of them! 

> * Everything listed in the section "OWL built-in syntactic classes and
> * properties" is in fact an axiomatic triple, even if it is not called
> * so explicitly. For example, saying "I(owl:FunctionalProperty) is in
> * C_I" (btw: it should be "S_I(owl:FunctionalProperty)", right?)
> * corresponds to the axiomatic triple 

>   owl:FunctionalProperty rdf:type rdfs:Class

Well, the semantic condition implies that that triple is in each
interpretation, yes.

> There are 33(!) axiomatic triples of this kind alone in this single
> section. And there are several more in the "parts of the OWL universe"
> table. For example, the third entry about E := owl:Restriction
> contains two of them: 

>   owl:Restriction rdf:type rdfs:Class        # "S_I(E) in C_I"
>   owl:Restriction rdfs:subClassOf owl:Class  # "IOR subset IOC"

> There are no premises of the form: "if a certain triple containing
> these entities exist in the graph, then...", and so these assertions
> are true for every graph, in particular they are entailed by the
> /empty/ graph. 


> My idea was to just add the /missing/ axiomatic triples. I did not see
> a clear criterion for why those which exist are in, and why those
> which do not exist are not in. The selection looks all a bit random to
> me. I wanted to have a somewhat more systematic approach, or at least
> follow existing precedence, and so I thought to follow the lead of
> RDFS. 

I put it to you that following the lead of RDFS is not a good idea.  In
any case, the RDFS axiomatic triples do not follow from the other RDFS
semantic conditions, which I believe is not the case for your triples.

> Btw: I believe that there are people in the RDF-semantics world who
> actually assume that the missing axiomatic triples are in
> OWL-Full. For example, I can see that the domain and range axiomatic
> triples for the owl:onProperty property is listed in the pD*
> paper. But since it is not given in the OWL-Full spec, this means that
> pD* is /not/ a semantical sublanguage of OWL-Full. I suspect that this
> will come to a surprise to the author of pD*.  

In OWL 1.0 Full it is not the case that the domain of owl:onProperty is
owl:Restriction nor is it the case that the range of owl:onProperty is
owl:Property.  Whether or not this is a bug (and I do not believe that
it is), it does mean, as you point out, that reasoning in pD* is not
sound with respect to OWL 1.0 Full.

> >> (B) Why are there only "ONLY-IF" semantic conditions for 
> >> restrictions? The
> >> introduction of sec. 5.2 in the AS&S says:
> >> 
> >>   "The only-if semantic conditions for the [restrictions] are needed 
> >>   to prevent semantic paradoxes and other problems with the 
> >>   semantics."
> >
> >> Can you please elaborate on this?


> Many thanks, I now understand the [principal] problem.
> >Which I suppose is not a complete collapse of the semantics, but is
> >certainly not what you want.
> Would it surprise you to hear that the collapse (i.e. the
> unsatisfiability of OWL-Full) would happen under IFF semantics for
> restrictions? :) 

No I would not.  A demonstration of this would be interesting.

> Cheers,
> Michael

Received on Monday, 31 March 2008 23:36:57 UTC

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