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

From: Drew McDermott <drew.mcdermott@yale.edu>
Date: Fri, 13 Oct 2000 16:44:29 -0400 (EDT)
Message-Id: <200010132044.QAA00840@pantheon-po01.its.yale.edu>
To: heflin@cs.umd.edu
CC: pfps@research.bell-labs.com, 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? 

Most terms don't have definitions, so this question usually doesn't
come up.  E.g., "Albert Einstein" and "the inventor of general
relativity" denote the same thing, but the first doesn't have a
definition (I'm not sure about the second).

By "definition" you may mean "denotation," in which case then if X
and Y denote the same thing they have the same denotation.

   ...
   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). 

This does appear to indicate that you're using "definition" to refer
to I.  

   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)."

I agree that the Web changes the environment in interesting and
challenging ways, but I'm constantly mystified by the examples people
come up with.  Yes, if someone says P P is not necessarily true, but
why does that make it necessary to change the definition of P?  If
someone says "The world was created all at once in 5000 B.C.," it's
not necessarily true, but it means the same thing whether it's true or
not. 

If the formula above is meant to define "equivalentTo," then it's odd
to talk about agents accepting it.  Isn't it meant to be in a
metalanguage that's used by system implementors?  The agents
themselves will accept sentences like equivalentTo(Morning_Star,
Evening_Star), not sentences in the metalanguage.  They may even
believe sentence schemas such as "If equivalentTo(X,Y) and P(X) then
P(Y)" for all formulas P() with a free variable, although I can't see
much mileage being gotten from explicit mention of such beliefs.

This may seem like nitpicking to some, and I'm sure it has little
bearing on expressing interesting content, which is what we're aiming
for, but why say it wrong when it's fairly easy to say it right?

                                             -- Drew
Received on Friday, 13 October 2000 16:44:39 GMT

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