From: Jim Hendler <hendler@cs.umd.edu>

Date: Tue, 24 Sep 2002 08:28:01 -0400

Message-Id: <p0511172bb9b60753c128@[10.0.0.17]>

To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, phayes@ai.uwf.edu

Cc: www-webont-wg@w3.org

Date: Tue, 24 Sep 2002 08:28:01 -0400

Message-Id: <p0511172bb9b60753c128@[10.0.0.17]>

To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, phayes@ai.uwf.edu

Cc: www-webont-wg@w3.org

Like most of us model-theoretically impaired, I've watched the range wars between Pat and Peter with a sort of awe -- however, it took me a while to realize it, but I think they're essentially both right to some extent. Look, I may not be a great logician, but my mathematics is good enough to recognize that domain and range are well-defined and fairly simple concepts: Assume we have two functions F:I->I (i.e. function F maps Integers to Integers) G:R->R (i.e. function G maps Reals to Reals) [and recall from mathematics that Integers are a proper subset of the Reals] In support of Pat: If you told me that F(x) = 2.5 I could assert that you are wrong (or that the original statement about F is wrong). The proof is trivial - F has Integer as its range, 2.5 is not an integer QED In support of Peter: I am mathematically well justified to believe G(F(x)) is defined for any integer X, because the range of F is integer, integers are reals, and the domain of G is the reals. QED This is pretty basic stuff in math, and as I understand at least the English description of domain and range in RDFS, they seem to capture this ok. I would certainly hope that OWL does NOT need a different treatment of Domain and Range than RDFS does, and if there are problems, this seems to me to be a case where we would ask RDFS to fix things rather than have competing solutions. -JH At 6:32 AM -0400 9/24/02, Peter F. Patel-Schneider wrote: >From: pat hayes <phayes@ai.uwf.edu> >Subject: Re: possible semantic bugs concerning domain and range >Date: Mon, 23 Sep 2002 22:18:39 -0500 > >> Rather than respond point by point, let me try to see if I can >> summarize what seem to be the main clashes of intuition here. >> >> My view of the range of a property is that it is a particular class >> which as far as possible defines the, well, range that the values of >> the property can take. Of course, there is no guarantee that any >> property will as it were 'fill up' its range, so it can make sense to >> apply conjunctive semantics to multiple range assertions; but the >> range is a definite thing associated with the property; it is part of >> the very specification of the property; knowing the range is knowing >> something particular about the property, a key piece of information. >> It allows one, for example, to detect inappropriate uses of the >> property under some circumstances. Ranges can be used to convey >> information relevant to a property, for example by having an >> associated datatype. > >OK, this is your view. > >> Your view, as I understand it, is that a range is simply any class >> which all the values are in. In particular, the idea of there being >> *a* range is silly, on this view: all properties will have multiple >> ranges. > >OK, this is my view. > >> What I am calling 'the' range, on this view, is something >> like the smallest range; > >Well, if this is your view, then you have to allow inference to determine >'the' range, because even RDFS allows multiple ranges. > >What is 'the' range of foo in > > foo rdfs:range bar . > foo rdfs:range baz . > >> but supersets of this can also be called >> ranges. I can see that with this view, the proposed semantics and >> Jeremy's entailment are both quite natural. But what worries me about >> this view is that it seems to discount the most useful aspects of the >> 'range' idea. >> >> The first view seems to go naturally with an intensional view of >> classes as real things that can have properties, while the second is >> more natural if one thinks of classes simply as sets in extension. >> Maybe the different directions our intuitions go in reflect a >> basically different world-view about the nature of classes. > >Well, I think that it is your view that has technical problems, as >evidenced by the property foo. > >> However, I would like to return to a more technical debate. You claim >> the several intuitive entailments go through on your semantics but > > not on mine. Seems to me that this isn't correct, so far: the correct >> form of Jeremy's entailment and the intersection example both work on >> both semantics. > >Your interpretation of Jeremy's natural-language paraphrase of his example, >that is. I prefer to go by the formal version of Jeremy's example. > >> So just on grounds of interoperability, it seems to >> me that the burden of proof is on you to show why OWL needs to change > >Well, precisely because of the above example. I believe that an >intersection of bar and baz is a range of foo. If you believe in 'the' >range, then what else can it be for foo? > >Perhaps you would like to annoint this most-restrictive range as the range. >However, this won't work, as there is no unique most-restrictive range in >OWL, nor, in general, in RDFS. > >So, from purely technical reasons, there is no single range possible for >either RDFS or OWL properties, and even determining a most-restrictive >range requires inference. > >> Pat > >peter -- Professor James Hendler hendler@cs.umd.edu Director, Semantic Web and Agent Technologies 301-405-2696 Maryland Information and Network Dynamics Lab. 301-405-6707 (Fax) Univ of Maryland, College Park, MD 20742 240-731-3822 (Cell) http://www.cs.umd.edu/users/hendlerReceived on Tuesday, 24 September 2002 08:28:10 GMT

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