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Re: Annotation entailment!

From: Pat Hayes <phayes@ihmc.us>
Date: Fri, 29 Jun 2007 13:56:07 -0500
Message-Id: <p06230907c2ab0226a114@[10.100.0.3]>
To: Alan Ruttenberg <alanruttenberg@gmail.com>
Cc: Denny Vrandecic <dvr@aifb.uni-karlsruhe.de>, OWL list <public-owl-dev@w3.org>

>On Jun 29, 2007, at 11:51 AM, Pat Hayes wrote:
>
>>OWL-DL refuses to countenance such a possibility [between 
>>extensional versus intensional]
>
>IIRC, I believe that Pat Hayes doesn't countenance such a possibility either?

Not at all. I rejoice in this possibility, at least for writing 
formal ontologies. All the formal semantics I have constructed (for 
RDF, RDFS, OWL-Full, CL and IKL) make the distinction. Moreover, you 
get better reasoners that way, it seems. For example, Herman ter 
Horst's version of OWL, which does not assume extensionality, is 
quite tractable, and a genuine semantic extension to RDFS.

What one usually wants to be able to do is to infer from C1=C2 and a 
is a member of C1 to a is a member of c2. One rarely wants or needs 
to be able to infer that if (for all a, a is a member of C1 iff it is 
a member of C2) that therefore C1=C2. Usually, you only come to a 
conclusion about class identity from knowing something about the 
classes involved, rather than about the class members. But in OWL-DL, 
you can't know anything about a class, since classes can't have 
properties or be in other classes.

The CL perspective, BTW, is that NOTHING is identical to its 
extension, and ANYTHING can be treated as a class or a property or an 
individual, if necessary all at the same time. And, believe it or 
not, this works just fine, and is quite a 'natural' way to write 
axioms. Basically, you just forget about making the distinctions. So 
you can write things like

(forall (r)(iff (TransitiveOn r c)
                  (forall ((x c)(y c)(z c))(if
                                                   (and (r x y)(r y z))
                                                   (r x z)
                                                  )
                  )
              )
)

without having to worry about whether or not r is a property or an 
individual (its both) or whether c is a class or an individual (its 
both). And then you can write things like

(transitiveOn motherOf Human)

which if nothing else saves on typing.

Pat


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Received on Friday, 29 June 2007 18:56:18 GMT

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