From: Dan Connolly <connolly@w3.org>

Date: 30 May 2002 15:16:19 -0500

To: patrick hayes <phayes@ai.uwf.edu>

Cc: connolly@jammer.dm93.org, www-webont-wg@w3.org

Message-Id: <1022789779.25651.210.camel@dirk>

Date: 30 May 2002 15:16:19 -0500

To: patrick hayes <phayes@ai.uwf.edu>

Cc: connolly@jammer.dm93.org, www-webont-wg@w3.org

Message-Id: <1022789779.25651.210.camel@dirk>

On Thu, 2002-05-30 at 14:37, patrick hayes wrote: [...] > >The following closure rules apply: > > > > ?l ont:first ?x. ==> ?l ont:item ?x. > > > > ?l ont:rest ?r. > > ?r ont:first ?x. ==> ?l ont:item ?x. > > ?Should that be > > ?l ont:rest ?r. > ?r ont:item ?x. ==> ?l ont:item ?x > > in order to recurse? Yes. You guys are reading closely! > >cardinality: > >if ?nl is a numeral for ?n (i.e. ?nl is a string that is a lexical > >representation of the integer ?n), and <IS(?p), ?nl> is in > >IEXT(I(ont:cardinality)) and <?s, ?o> is in IEXT(?p), then > >the size of the set { ?x: <?s, ?x> is in IEXT(?p) } is ?n. > > Why not just say... that numerals denote numbers as a blanket > assumption, umm... because sometimes they're movie titles? I don't think I understand. > and then state the condition in the interpretation? The > numbers part is kind of automagical, but at least you are being open > about that (and it can be handled by assuming that numerals have a > fixedpont semantics in any case.) > > The condition is then > > If <?p, ?n> in IEXT(I(ont:cardinality)) then > |{?x: <?x,?s> in IEXT(?p)}| = ?n > > > > >complementOf: > >if <?s, ?o> is in IEXT(I(ont:complementOf)), > >then ICEXT(?s) is the complement of ICEXT(?o) > >relative to IR. > > > >differentIndividualFrom: > >if <?s, ?o> is in IEXT(I(ont:differentIndividualFrom)), > >then ?s is not equal to ?o. > > > > > >disjointUnionOf: > >1. if <?s, ?l> is in IEXT(I(ont:disjointUnionOf)), > >and <?l, ?a> is in IEXT(I(ont:item)), > >then ICEXT(?a) is a subset of ICEXT(?s). > > > >2. if <?s, ?l> is in IEXT(I(ont:disjointUnionOf)), > >and <?l, ?a> is in IEXT(I(ont:first)), > >and <?l, ?r> is in IEXT(I(ont:rest)), > >and <?x, ?s> is in IEXT(I(rdf:type)), > >then either ?x is in ICEXT(?a) or > >there is a ?b where <?r, ?b> is in IEXT(I(ont:item)). > > > >3. if <?s, ?l> is in IEXT(I(ont:disjointUnionOf)), > >then ?l is a pairwise-disjoint list, defined > >recursively > > Whoa. If this really is a same-syntax extension then in order for > this to be meaningful you need to show how recursion can be expressed > in RDF (good luck). Huh? In the DAML+OIL model theory, the prose appeals to all sorts of traditional set theoretic notions when expressing constraints on interpretations... it uses stuff like |{...}| to denote the cardinality of sets and such. > If you want to be able to say: look, I *know* the > lists are finite since they are part of the graph, so obviously I can > tail-recurse along them; then fine: but now you have built the lists > into your syntax, No, ?l refers to something in IR, i.e. in the semantic domain, not something in V, i.e. in the syntax. > so you aren't describing a same-syntax extension. > Which is fine with me, let me say at once; but let's keep our > terminology clear. You can use recursion on syntax, but you can't use > it on things in the semantic domain unless you first show that the > domain satisfies the fixpoint condition for the basic recursion > theorems. (Same point, differently expressed: how do you know that > the lists in the semantic domain, denoted by your list expressions, > are finite? Finiteness isn't expressible in any RE language.) I don't think I understand. If there's an infinite list, or a cycle, it just won't satisfy the definition I gave for pairwise-disjoint list. I don't care if there are such things in the domain; they just can't be objects of disjointUnionOf triples. Constraints on interpretations are expressed using semi-formal writing, no? If there's some rule that says one can express contraints on interpretations thus: x in IC(?R) iff IR(?P)({x}) <= IC(?C) but one cannot inductively/recursively define sets in the domain, I'd like to know more about these rules. By the way... 'the fixpoint condition for the basic recursion theorems'... I'm not familiar with that; how about a reference? I don't see anything about it my favorite "crash course" source... http://www.earlham.edu/~peters/courses/logsys/lshome.htm Ugh... this page nominated by google is completely greek http://nl.ijs.si/~damjan/kleene.html it points toward Kleene... This isn't much help, except suggesting Cantor is the author I should be looking for... http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?General+Recursion+Theorem This seems to be the course I'm missing... 15-453 Formal Languages, Automata, and Computation (FLAC) http://www-2.cs.cmu.edu/~lblum/courses/flac/schedule.html > You could give RDF a different semantics (eg use minimal models) like > the logic programmers do for Horn logic, but then it probably > wouldn't mean what you want it to mean for other purposes. I hope I don't need to go there. -- Dan Connolly, W3C http://www.w3.org/People/Connolly/Received on Thursday, 30 May 2002 16:16:42 UTC

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