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Re: Question about Extensional Entailment Rules

From: Jan Grant <Jan.Grant@bristol.ac.uk>
Date: Thu, 26 Aug 2004 10:10:51 +0100 (BST)
To: Nick Bassiliades <nbassili@csd.auth.gr>
cc: www-rdf-comments@w3.org
Message-ID: <Pine.GSO.4.61.0408261005550.17591@mail.ilrt.bris.ac.uk>

On Thu, 26 Aug 2004, Nick Bassiliades wrote:

> Jan Grant wrote:
> 
> > On Thu, 26 Aug 2004, Nick Bassiliades wrote:
> > 
> >  
> > > Hi all,
> > > 
> > > I would like to ask you whether I am missing something from the
> > > extensional
> > > entailment rules ext1&2
> > > in the RDF Semantics document (http://www.w3.org/TR/rdf-mt/).
> > > 
> > > Rule ext1 says that when:
> > >  uuu rdfs:domain vvv .
> > > and
> > >  vvv rdfs:subClassOf zzz .
> > > are true, then the triple:
> > >  uuu rdfs:domain zzz .
> > > should be added.
> > > 
> > > However, IMHO this looks rather bizarre! This rule states that when a
> > > property
> > > has a certain class as a
> > > domain, it must also have all its superclasses as a domain. I believe that
> > > it's the other way around:
> > > all the subclasses of a class can be domains for the property uuu.
> > > 
> > > For example,
> > >  uni:faculty rdfs:subClassOf uni:staff .   (/Faculty members are member of
> > > the staff/)
> > >  uni:teaches rdfs:domain uni:faculty .     (/Faculty members teach/)
> > > then we infer with rule ext1 that:
> > >  uni:teaches rdfs:domain uni:staff .       (/All members of the staff can
> > > teach!/)
> > > 
> > > I would expect it to work the other way around:
> > >  uni:lecturer rdfs:subClassOf uni:faculty .   (/Lecturers are //Faculty
> > > members/)
> > >  uni:teaches rdfs:domain uni:faculty .        (/Faculty members teach/)
> > > then we infer that:
> > >  uni:teaches rdfs:domain uni:lecturer .       (/Lecturers // can teach/)
> > > 
> > > Am I missing something here?
> > >    
> > 
> > The semantics are conjunctive. To say that "the domain of uni:teaches is
> > uni:faculty" means, if you have statements of the kind
> > 	X uni:teaches Y .
> > then X must be a member of uni:faculty: we can infer that about its type.
> > What we can't do is infer that X is a uni:lecturer; but we _can_ logically
> > infer that X must also be a member of uni:staff. The rules for domain and
> > range are universally quantified in this fashion, so whilst it looks odd
> > it's right.
> > 
> >  
> However, the above scenario is already covered by existing entailment rules:
> IF
>    1) X uni:teaches Y .   &
>    2) uni:teaches rdfs:domain uni:faculty . &
>    3) uni:faculty rdfs:subClassOf uni:staff .
> THEN
>    4) X rdf:type uni:faculty . (due to (1) & (2) and rule rdfs2)
> &
>    5) X rdf:type uni:staff .  (due to (4) & (3) and rule rdfs9)
> 
> I am not sure why rule ext1 is necessary, since it is subsumed by the two
> other rules.

The derivation you give is accurate. However, it does not in and of 
itself allow us to conclude that

	uni:teaches rdfs:domain uni:faculty .
entails
	uni:teaches rdfs:domain uni:staff .

_using_the_entailment_closure_rules_. It's simple to see that this 
should be true, but the extra closure rule is required to derive this 
mechanically.

jan

(I'm sure Pat or Jeremy will step in if I've misspoken here.)


-- 
jan grant, ILRT, University of Bristol. http://www.ilrt.bris.ac.uk/
Tel +44(0)117 9287088 Fax +44 (0)117 9287112 http://ioctl.org/jan/
Random act of violence against bread: whole pint.
  -- extract from the "Hawk the Slayer" drinking game
Received on Thursday, 26 August 2004 09:12:29 UTC

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