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Re: SEM: "natural" entailments

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Tue, 24 Sep 2002 15:33:24 +0100
Message-ID: <15760.30644.619208.637754@merlin.horrocks.net>
To: pat hayes <phayes@ai.uwf.edu>
Cc: www-webont-wg@w3.org

On September 17, pat hayes writes:

[snip]

> >Finally, I would like to point out (again) that DLs are nothing more
> >than decidable subsets of FOL with useful computational
> >properties.
> 
> You keep saying this, but that isn't the impression I get. For 
> example, the recent DQL document has to have a footnote pointing out 
> that DAML doesn't have any notion of 'conjunction', strictly 
> speaking.

It doesn't say that, it says that "DAML+OIL does not have a logical
connective for conjoining sentences or for conjoining knowledge
bases". It is simply the case that in DAML+OIL the use of the
conjunctive connective is not defined for sentences or KBs (it would
be easy to add such a definition). The lack of such a definition
doesn't stop the language from being (isomorphic with) a SUBSET of
FOL.

>  So the inference
> 
> A, B |= (A and B)
> 
> which is about the simplest inference imaginable, so simple that 
> Aristotle didn't bother to give it a name, apparently isn't supported 
> by DLs.

In a DL there are some syntactic restrictions on the form of A and B:
recall that it is a SUBSET of FOL and not full FOL. If A and B are
classes (i.e., formulae with one free variable), then there is no
problem:

A(x),B(x) |= (A and B)(x)

for all A, B and x.


>  And the 'strong' OWL semantics requires us to assert (or 
> assume) that the class (union A B) must *exist* in order to validate 
> the DL version of the inference
> 
> A |= (A or B).

again, it does:

A(x) |= (A or B)(x)


> That sure doesn't feel like a subset of FOL to me; it feels a lot 
> more like a subset of ZF set theory. Those inferences are valid in 
> propositional logic where there aren't any classes to exist in the 
> first place. Union and intersection are *analogous* to disjunction 
> and conjunction, but they are not the *same*.

This is getting silly. The correspondence between Description/modal
logics and *standard* FOL is very well know, e.g., see [1] for an
overview and relevant results dating back to the 1960s. I don't want
to get into a philosophical argument about what it means to be the
"same". For me it is enough to point out that DLs and their
corresponding fragment of FOL have models that are completely
isomorphic.

I must say that I just don't understand what your problem is with
this. 

Ian

[1] http://lat.inf.tu-dresden.de/research/papers/2001/LutzSattlerWolter-DL2001.ps.gz

> >So, in as much as FOL is an old technology, yes, DLs are
> >an old technology (and proud of it).
> 
> FOL isn't a technology, fortunately. I was referring to the 
> implementation requirements of DLs.
> 
> Pat
> -- 
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Received on Tuesday, 24 September 2002 09:36:19 GMT

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