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Re: possible semantic bugs concerning domain and range

From: Jim Hendler <hendler@cs.umd.edu>
Date: Tue, 24 Sep 2002 08:28:01 -0400
Message-Id: <p0511172bb9b60753c128@[]>
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.


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

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)
Received on Tuesday, 24 September 2002 08:28:10 UTC

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