- From: pat hayes <phayes@ai.uwf.edu>
- Date: Fri, 11 Oct 2002 18:07:58 -0500
- To: Ian Horrocks <horrocks@cs.man.ac.uk>
- Cc: www-webont-wg@w3.org

> > >> Range(P, A) -> (forall x,y P(x,y) -> A(y) ) >> >> You want >> >> Range(P,A) <-> (forall x,y P(x,y) -> A(y) ) >> >> They are about equally clear and intuitive; but the latter rules out >> some possibilities which the former permits. I believe that all the >> 'intuitive' entailments that people want in fact hold in both these >> cases; and that the former is therefore to be preferred. > >I am agnostic about which of these is to be preferred - as a humble >engineer, all I need to know is which one it is so that I have a clear >spec to which I can build my systems. > >One point that is worth making though is that there are a number of >similar statements that can be made about OWL properties, and that it >may make sense to give them a uniform semantics, i.e., all treated as >implication or all treated as bi-implication. E.g., we also have: > >Domain(P,C) implies/iff (forall x,y P(x,y) -> C(x)) >TransitiveProperty(P) implies/iff (forall x,y,z (P(x,y) ^ P(y,z)) -> P(x,z)) >SymmetricProperty(P) implies/iff (forall x,y P(x,y) -> P(y,x)) >FunctionalProperty(P) implies/iff (forall x,y,z (P(x,y) ^ P(x,z)) -> y=z) >InverseFunctionalProperty(P) implies/iff (forall x,y,z (P(y,x) ^ >P(z,x)) -> y=z) >inverseOf(P,Q) implies/iff (forall x,y P(x,y) -> Q(y,x)) How about all the unary properties of properties having an IFF semantics? That would make sense, but it would leave domain, range and inverse up for discussion. >We already had the discussion w.r.t. transitive (or was it >functional). I argued for implies semantics, but the general view >seemed to be that iff semantics should hold (and by extension that it >should hold for all the above statements). This is now post-F2F and we had this discussion briefly, but let me expand on my reasons for the particular choices I prefer. First, I don't buy the argument (rather, I don't hear any actual argument) for the idea that we should treat all these cases uniformly. Seems to me that we should in each case make the language conform as far as possible to what might be called a reasonable pre-theoretic intuition about what the terms mean. Given that, it seems to me that the notions of properties being transitive, symmetric, functional and inverse functional really do only have what might be called mathematical pre-theoretic meanings. The only possible meanings one can attach to these terms are the purely extensional ones. That is what it *means* to be transitive, right? And similarly for the others. Also, note that these are all simple predicates on properties, so giving them an IFF semantics doesn't impose any identity conditions on properties (that is, it doesn't force users to agree that properties are identical when they don't think they should be). InverseOf is more debatable: I can see someone wanting to say that the inverse of the property 'isFatherOf' really is the unique property 'hasAsFather', even if some other property has the same extension. So I agree, there could be a case made there for an intensional reading; but I havn't heard anyone particularly requesting it. In contrast, domain and (especially) range not only could have intensional readings, they seem to often actually be given intensional readings in practice. Many people get a sharp intuitive sense that there is something wrong when they are told that the class, say, union(people, loaves of bread) is a range of Ancestor, or that the universe is a range of every function; and many people see nothing logically incoherent in the idea of restricting range classes to, say, XML datatypes. I see no reason, therefore, to impose a condition which rules out such intuitive usage, particularly when it has no obvious utility in any case. Pat -- --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32501 (850)291 0667 cell phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes

Received on Friday, 11 October 2002 19:07:59 UTC