# Re: Question about Extensional Entailment Rules

From: Jan Grant <Jan.Grant@bristol.ac.uk>
Date: Thu, 26 Aug 2004 11:00:14 +0100 (BST)

Message-ID: <Pine.GSO.4.61.0408261053560.17591@mail.ilrt.bris.ac.uk>
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On Thu, 26 Aug 2004, Nick Bassiliades wrote:

[previous discussion cut for brevity, see thread archives]

NB:

> > > 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.
> > >

JG:

> > 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.

NB:

> That is the core point I was trying to make clear. Why is the above
> entailment necessary, since the reason of its existence (which is
> supposedly the inference that the type of a subject of a triple is the
> superclass of the domain of the property of the triple) is subsumed by
> other entailment rules. Why is it necessary to make the above
> entailment explicit? Are there any other reasons, beyond the scenario
> we have been discussing?

The rdfs-entailment of
uni:teaches rdfs:domain uni:staff .
from
uni:teaches rdfs:domain uni:faculty .
uni:faculty rdfs:subClassOf uni:staff .

is a direct consequence of the model-theoretic semantics: the model
theory already has this as a consequence.

However, the closure rules are a (non-normative) recouching of the same
entailment rules. We would like every rdfs-entailment (according to the
model theory) to come out of the rdfs closure rules. Now, whilst the
closure rules already let us conclude facts from statements that use
"uni:teaches" as a property, without this particular rule they don't
have another way of supplying the conclusion above.

--
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/
Scrabble gematria: "BIBLE" = "DOGMA"
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Received on Thursday, 26 August 2004 10:03:26 UTC

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