From: pat hayes (phayes@ai.uwf.edu)
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 same...As's. 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? Pat --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola, FL 32501 (850)202 4440 fax phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes
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