From: Ian Horrocks (horrocks@cs.man.ac.uk)
Date: 03/01/01
On March 1, Mike Dean writes: > DAML+OIL currently supports TransitiveProperty and > inverseOf. Should we also be able to indicate a > SymmetricProperty > > P(a, b) implies P(b, a) > > such as sibling or spouse? > > I checked and see that OIL [1] supports this. We can already capture this in daml+oil. To quote from "differences-oil.html": "DAML+OIL currently does not support SymmetricProperty. However, the same effect can be achieved simply by asserting that the property is a subproperty of its inverse and vice versa (i.e., that the property and its inverse are equivalent)." Of course this leads to subProperty cycles. I think the decision was made not to add an explicit SymmetricProperty class of properties on the grounds that it wasn't a very widely used idiom (I don't know of any evidence for or against this suggestion). > How about ReflexiveProperty > > P(x, x) > > such as equivalentTo? Although some daml+oil properties are reflexive (by dint of their semantics), we cannot in general capture reflexive relations using the expressive power of the existing language - so adding ReflexiveProperty would be a real extension and not just syntactic sugar. > I'm told that TransitiveProperty and SymmetricProperty and > ReflexiveProperty would imply samePropertyAs (equivalence). I'm not sure I understand this. Transitive, symmetric and reflexive relations are known as equivalence relations (because they define equivalence classes), but that isn't the same thing as implying equivalence. For example, sameColourAs could be an equivalence relation, but objects having the same colour are not necessarily equivalent. > Comments? > > Mike > > [1] http://www.ontoknowledge.org/oil/rdf-schema/2000/11/10-oil-standard Ian
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