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Re: semantics of daml:equivalentTo [was: Comments on Annotated DAML 1.6]

From: Jeff Heflin <heflin@cs.umd.edu>
Date: Fri, 13 Oct 2000 15:32:03 -0400
Message-ID: <39E76333.B779852F@cs.umd.edu>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
CC: phayes@ai.uwf.edu, www-rdf-logic@w3.org
Maybe I'm a little thick-headed (I don't have the experience that Peter
and Pat have in semantics), but I don't really see the difference in
their opinions. First, let me try to restate what they think I said:

Pat: equivalentTo(X,Y) means that X and Y refer to same conceptual
thing, i.e., they have the same denotation

Peter: equivalentTo(X,Y) means that X and Y have the same definition

Could someone please explain how X and Y could denote the same thing,
but not have the same definition? Does the confusion lie in whether we
consider X and Y to be symbols vs. definitions? In any case, if there
really is as a difference between what Pat and Peter said, then I'm
inclined to agree with Pat. I tend to think of ontology as providing a
set of symbols and logical definitions for those symbols.

In an attempt to be clear, let me take a shot at formalizing my notion
of equivalentTo:

Let D=a domain of concepts
Let V=the set of DAML symbols
Assume an interpretation function I:V->D

Then if X,Y are elements of V, equivalentTo(X,Y) means I(X) = I(Y). Of
course, since we're playing on the Web, we have to modify this a little
bit: just b/c someone says equivalentTo(X,Y) doesn't make it true.
Rather, maybe the definition should be "if an agent accepts
equivalentTo(X,Y) then the agent must accept I(X)=I(Y)."

Note, section 2.2 of my paper "Dynamic Ontologies on the Web" (see the
Proceedings of AAAI-2000 or
http://www.cs.umd.edu/projects/plus/SHOE/pubs/aaai2000.pdf) provides a
simple formal model of SHOE. This may serve as one of the starting
points (in addition to OIL) for defining a DAML semantics.

Jeff

"Peter F. Patel-Schneider" wrote:
> 
> From: pat hayes <phayes@ai.uwf.edu>
> Subject: Re: semantics of daml:equivalentTo [was: Comments on Annotated    DAML   1.6]
> Date: Fri, 13 Oct 2000 12:00:45 -0500
> 
> > >From: Jeff Heflin <heflin@cs.umd.edu>
> > >Subject: Re: semantics of daml:equivalentTo [was: Comments on
> > >Annotated  DAML   1.6]
> > >Date: Thu, 12 Oct 2000 15:29:56 -0400
> > >
> > > > I'd just like to elaborate on Jim's message. I believe that equivalentTo
> > > > is the DAML version of the SHOE <DEF-RENAME> element. In SHOE,
> > > > DEF-RENAME allows an ontology to provide an alias for a term defined
> > > > elsewhere. Essentially, it means that both terms reference the same
> > > > concept, and thus any assertion that is made using one term is also true
> > > > if the other term was substituted in its place. This is really easy to
> > > > implement: you keep a hash table that matches aliases with the base
> > > > terms (used in the original definitions) that they renamed, and upon
> > > > parsing a document or issuing a query you can perform the necessary
> > > > substitutions to rephrase it in only base terms.
> > > > Jeff
> 
> > There is
> > a reasonably well-defined meaning for equality (=identity =
> > equivalence) which is pretty much what Jeff says above: it means that
> > the terms refer to the same thing. So to assert
> >   equivalentTo(X, Y)
> > is to claim that X and Y have the same denotation. Now, this in turn
> > is just as clear or as murky as the notion of denotation is for X and
> > Y.
> >
> > Pat Hayes
> 
> It is my belief that Jeff's belief is that equivalentTO should be much more
> like the other option I outlined, namely that X is given the definition
> that Y has and that X can have no other definition.
> 
> peter
Received on Friday, 13 October 2000 15:32:17 GMT

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