From: Peter F. Patel-Schneider (pfps@research.bell-labs.com)
Date: 01/16/01
There would be no (or not much of a) problem with using equivalentTo for the purposes of asserting equality, if we only look at equivalentTo in isolation. However, DAML+OIL makes sameClassAs and samePropertyAs subproperties of equivalentTo. Now, in my books at least, a subproperty has to have all the characteristics of its superproperties. Equality is (or should be) a very strong property, either requiring that the two ``terms'' being equated map to the same semantic object (if we are thinking of a denotational meaning for equality) or behave in exactly the same way (if we are thinking of an axiomatic meaning for equality). This means that two terms related by equivalentTo will be the same class if one of them is a class and also the same property if one of them is a property. If we make sameClassAs and/or samePropertyAs be subproperties of equivalentTo, then there is no possibility of having two terms (or, maybe, two semantic objects) that are the same, taken as classes, and different, taken as properties, or even different, taken as regular objects. One way out of this would be to have several equivalence relationships, starting with ones that assert extensional equivalence (i.e., that two terms refer to classes that have the same instances but may not have the same properties), then ones that assert intensional equivalence (i.e., that two terms refer to classes that have the same properties but may not be the same semantic object), and finally full equality or coreference (i.e., that two terms refer to the same semantic object, and futher, have all the same semantic properties). [There are equivalent notions to these denotational notions on the axiomatic side.] Note that this makes equivalentTo be a subproperty of sameClassAs (whether we interpret sameClassAs as same extension or same intension). Peter Patel-Schneider
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