From: Jan Grant <Jan.Grant@bristol.ac.uk>

Date: Sat, 11 Aug 2001 16:54:02 +0100 (BST)

To: RDFCore Working Group <w3c-rdfcore-wg@w3.org>

Message-ID: <Pine.GSO.4.31.0108062225460.15130-100000@mail.ilrt.bris.ac.uk>

Date: Sat, 11 Aug 2001 16:54:02 +0100 (BST)

To: RDFCore Working Group <w3c-rdfcore-wg@w3.org>

Message-ID: <Pine.GSO.4.31.0108062225460.15130-100000@mail.ilrt.bris.ac.uk>

Is a subproperty of rdfs:subPropertyOf necessarily transitive? No. The action point asks something slightly different, viz: Propose an explanation of why a subproperty of a transitive property need not be transititive. I don't have much of an explanation, except to say: transitivity and subpropertyness aren't particularly closely related. In particular, if A is a subproperty of B, then just because B is transitive doesn't mean that A has to be (and vice versa). I'll give examples below, at which point I suggest this issue be properly closed. Oh, and rdfs:subpropertyOf is no exception; while it is transitive itself, it has nontransitive subproperties. 1. A subproperty of a transitive property is not necessarily transitive. ancestorOf is a transitive relationship parentOf is not; it is, however, a subPropertyOf ancestorOf There are lots of examples like these. Conceptually, many of the obvious ones arise from having the subproperty be a "single step" (eg, one place up a family tree) and the superproperty be something akin to the Kleene closure (ie, zero or more) of that step. 2. A nontransitive property can have transitive subproperties. The example here is: "is less than" is a transitive subproperty of "is not equal to". In fact, _every_ nontransitive property has at least one (trivial) transitive subproperty. 3. Subproperties of rdfs:subPropertyOf need not be transitive. Below, P, Q and R stand for properties. a, b, c etc. are things related by those properties. I use a handwaving ntriples-alike that includes those variables* We note that P rdfs:subPropertyOf Q . means that forall x, y x P y . -> x Q y . (that is the definition of what it means for one property to be a subproperty of another). Now we define a new property, SP/2, as follows: forall x, y x SP/2 y . iff x, y are properties (relationships) and if <(a_1, b_1), (a_2, b_2), ...> is the sequence of pairs of a, b such that a y b . arranged alphabetically then a x b. iff (a,b) occurs in the sequence at an odd-numbered position. informally, a x b . holds true in half the cases that a y b . holds true. We're now done; it's pretty straightforward to show that 1. SP/2 rdfs:subPropertyOf rdfs:subPropertyOf . 2. SP/2 is not transitive. jan * which I propose we leave out of the MT for the moment :-) -- jan grant, ILRT, University of Bristol. http://www.ilrt.bris.ac.uk/ Tel +44(0)117 9287163 Fax +44 (0)117 9287112 RFC822 jan.grant@bris.ac.uk I am now available for general use under a modified BSD licence.Received on Saturday, 11 August 2001 11:59:05 EDT

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