Re: axioms and (not) changing a language

From: Peter F. Patel-Schneider (
Date: 02/21/01

From: Dan Connolly <>
Subject: Re: axioms and (not) changing a language
Date: Tue, 20 Feb 2001 19:44:36 -0600

> "Peter F. Patel-Schneider" wrote:
> > 
> > There was a comment during today's teleconference to the effect that an
> > extension to DAML+OIL would be trivial as long as there was a (KIF)
> > axiomatization for it.
> Well, perhaps not trivial, but well-specified, yes.

But what does well-specified get us?  If this were the only requirement,
then why not use some higher-order intensional logic directly?

> > This is decidedly not the case.  Extending DAML+OIL by adding axioms to the
> > axiomatization is a very dangerous endeavour.  Some extra axioms can be
> > accommodated, and will not change the characteristics of DAML+OIL.
> Which characteristics are you talking about?
> Decidability? something else?

I, for one, would like to be able to reason with the information that is
written in DAML+OIL+DT (DAML+OIL + datatypes).  This means that there are
some computational properties that I don't want to give up, one of which is

Further, there are other properties that I think should be retained in
DAML+OIL+DT.  In particular, I want to retain the object-centered basis of

> Are these characteristics that we should guard closely
> documented in our spec? Please point me to them.

Unfortunately, these characteristics are not documented, just as the
characteristics of RDF and RDFS are not documented in their specifications.

> >  Others,
> > although seemingly innocuous, would drastically change DAML+OIL.
> > Determining just what changes will be made by a particular set of extra
> > axioms is extremely difficult.
> > 
> > To illustrate this point, consider RDF(S).  RDF(S) has a KIF
> > axiomatization.
> It does? I can sort of imagine one, but I've never seen one.

The DAML+OIL KIF axiomatization contains an axtiomatization for RDF(S), so
one does exist.  This is not a normative axiomatization, but I don't see
anything wrong with it.

> You have rasied a number of questions (about bags containing
> themselves etc.) that I don't know how to answer; I wouldn't
> expect a KIF axiomitzation would leave such unanswered questions.

The KIF axiomatization finesses this issue by having an uninterpreted
predicate for membership, which answers all these questions, but at a

> >  One could argue, as above, that extending RDF(S) by a
> > collection of extra axioms is trivial.
> > 
> > However, suppose that we extend RDF(S) by the DAML+OIL axioms.  We now end
> > up with a very different kind of representation language, with very
> > different characteristics.
> How so?

Do you actually mean that you consider RDF(S) and DAML+OIL to have the same
characteristics?  I consider them to be extremely different in many
respects.  For example

- DAML+OIL allows necessary and sufficient definition of classes, RDF(S) doesn't
- DAML+OIL has local restrictions on properties, RDF(S) doesn't
- DAML+OIL allows disjunctive information, RDF(S) doesn't
- inference in DAML+OIL is NP-hard, inference in RDF(S) is polynomial (I think)

All of the above are significant differences.


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