From: pat hayes <phayes@ai.uwf.edu>

Date: Fri, 20 Sep 2002 08:58:57 -0500

Message-Id: <p05111b19b9b0d9fb4cb8@[65.217.30.172]>

To: "Jos De_Roo" <jos.deroo.jd@belgium.agfa.com>

Cc: w3c-rdfcore-wg@w3.org

Date: Fri, 20 Sep 2002 08:58:57 -0500

Message-Id: <p05111b19b9b0d9fb4cb8@[65.217.30.172]>

To: "Jos De_Roo" <jos.deroo.jd@belgium.agfa.com>

Cc: w3c-rdfcore-wg@w3.org

>Pat, I think I'm fine with that > >how can we express that >when given > _:l1 rdf:first :a . > _:l1 rdf:rest :b . > > _:l2 rdf:first :a . > _:l2 rdf:rest :b . > >then _:l1 and _:l2 are tidy Er...you can't. That is, there could be two lists with the same members. Pat >(we have that "for some" is actually >"for one" in this case and I've missed >a notation for that important fact) > >-- , >Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/ > > > > > pat >hayes > <phayes@ai.uwf.edu To: >w3c-rdfcore-wg@w3.org > > >cc: > Sent by: Subject: RDF >lists > >w3c-rdfcore-wg-req > >uest@w3.org > > > > > 2002-09-20 >12:39 > >AM > > > > > > > > > >Since RDF now has DAML_style lists (right?), I thought it would be >good to get feedback on the proposed MT for them. So here it is: toss >back any comments, please. >----------- >Given a set S, we define a set of lists over S to be a set L >containing the empty sequence <> and all structures of the form <s, >l> where s is in S and l is in L. > >As with any recursive 'definition', this in fact is an equation with >many possible solutions. The usual way to interpret this kind of >definition is in terms of a minimal solution of the equation. That >means that one would understand the set of lists to be the smallest >collection of things that would satisfy the recursion, which would be >all finitely deep lists which have no loops, i.e. structures of the >form <s1 <s2 <...<sn <>>...>>. On this view, every list defines a >finite sequence of elements of S. Other lists are possible, however, >which would also satisfy the recursive definition: infinitely deep >lists, for example, or looping lists of the form l = <s, l>. > >Although it is possible to axiomatize a recursive 'definition' as a >logical assertion, there is no way to finitely axiomatize the least >fixed-point solution. We could impose it as a semantic condition; but >this condition, although intuitively sensible and in correspondence >to the usual semantics for computational languages, may have some >regrettable consequences when used, as here, in the context of a >descriptive language. In particular, there would be no way to >establish the completeness of any finitary inference process relative >to such a semantics. We therefore avoid making this stipulation, and >simply require that the set of lists in any interpretation be *some* >set which satisfies the recursive definition. Note that this means >that any set of lists will at least contain all the finite >non-looping lists. > >The semantics of the rdf list vocabulary is then straightforward. In >any RDF interpretation I, we assume that > >ICEXT(I(rdf:List)) is a set of lists over IR @@Note the use of 'a' >rather than 'the'.@@ > >I(rdf:nil) = <> > ><x, y> in IEXT(I(rdf:first)) iff x = <y, l> for some l in >ICEXT(I(rdf:List)) > ><x, y> in IEXT(I(rdf:rest)) iff x = <s, y> for some s in IR > >We note in passing that this semantics requires that the universe IR >is closed under the operation of constructing lists. > >Any interpretation I of any RDF graph of the form > >A1 rdf:type rdf:List . >A1 rdf:first B1 . >A1 rdf:rest A2 . >A2 rdf:first B2 . >A2 rdf:rest A3 . >... >An rdf:first Bn . >An rdf:rest rdf:nil . > >has I(A1) = <I(B1), <I(B2), <... <I(Bn), <> >...>>. We will describe >this as a sequence and write it as [I(B1), ... , I(Bn)]. Sequences >are the ordered multisets of the elements of finite lists. > >-------- > > >-- >--------------------------------------------------------------------- >IHMC (850)434 8903 >home >40 South Alcaniz St. (850)202 4416 >office >Pensacola, FL 32501 (850)202 4440 fax >phayes@ai.uwf.edu >http://www.coginst.uwf.edu/~phayes -- --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola, FL 32501 (850)202 4440 fax phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayesReceived on Friday, 20 September 2002 09:59:02 EDT

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