From: Peter F. Patel-Schneider (pfps@research.bell-labs.com)
Date: 02/21/01
From: Dan Connolly <connolly@w3.org> 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 decidability. 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 DAML+OIL. > 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 price. > > 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. peter
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