Re: equivalentTo

From: pat hayes (
Date: 03/23/01

OK, Im getting a feel here for an issue that has come up in the KIF group also.

There are two slightly different senses of 'equivalent' being used 
here, I think. The snag is that the difference cannot be stated in 
DAML+OIL-semantic terms, but it is still intuitively persuasive.

The only sense of equivalentTo that can be expressed semantically is 
the purely extensional sense, where (A equivalentTo B) is true when A 
and B denote the same thing. But there is an intuitively stronger 
sense, which is that the names *mean* the same thing; they are to be 
treated as *the same name*. One way to say this is that one name is 
just an abbreviation for, or a renaming of, the other name, a usage 
that the SHOE term 'DEF-RENAME' makes very clear; another way to 
express it is that the identity (A=B) is not just true, but 
*necessarily* true (a modal usage which is very popular in some 
ontology circles, eg by Nicola Guarino, Chris Welty and Tim Finin, 
among many others). However, DAML+OIL doesnt have any means to 
distinguish truth from necessary truth (and I am not meaning to 
suggest that it should have! ), so it has no way to represent this 
stronger meaning which would distinguish it from the purely 
extensional meaning. And as Peter has pointed out, with the purely 
extensional meaning, equivalentTo is redundant.

I suspect that those who feel so strongly that equivalentTo should be 
retained in the language are in fact closet modal thinkers, and have 
in mind some way of interpreting 'equivalent' which actually exceeds 
the expressive abilities of current DAML+OIL. If so, we have two 
alternative ways to react. One is a kind of Calvinist position, where 
we adopt semantic sternness and insist that such usage is in fact a 
misreading of scripture, and should therefore be outlawed. The other, 
more catholic, position, would allow equivalentTo into the language, 
state clearly what its semantics is, state that it is redundant, and 
yet still allow people to use it if it makes them feel better, for 
reasons that it would be best not to inquire into too closely.

I would vote for catholicism, myself. Peter had an objection to it:
1A/ Make same...As subproperties of equivalentTo, with no extra
        semantics (except for domain and range restrictions, maybe).  [This
        is probably what many people think the current situation is.]  This
        has the problem that sameClassAs also makes things be the same
        property and the same individual, and similarly for the other two

which I dont really follow. Couldn't we give sameClassAs the 
interpretation of = but restricted to classes, so that sameClassAs A 
B means: Class A and Class B and equivalentTo A B ? That would 
satisfy the 'rename' interpretation and would seem to be intuitively 
reasonable, and would block the above problem (?).

However, what if someone asserts equivalentTo between a(n abstract) 
class and a datatype?

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