- From: Jeremy Carroll <jjc@hplb.hpl.hp.com>
- Date: Wed, 17 Apr 2002 14:14:16 +0100
- To: <www-webont-wg@w3.org>
As my idea of the problem that we are trying to solve is clarifying (hopefully not too incorrectly) I am beginning to see problems with the dark triples solution to that problem. These are: 1: OWL syntax cannot be extended using RDF/RDFS/OWL mechanisms. 2: We still need a theory of classes. In order: Extensibility ============= The first ontology I wrote using DAML started by taking a subclass daml:Class, and subproperties of daml:Property etc, and a subclass of daml:Ontology. The motive was that the ontology I was creating was to represent the conceptualization of e-mail in Microsoft's Outlook product and I wished to extend the DAML+OIL mechanisms to include OLE mappings for the properties. From the point of view of computer science this seems a logical and natural thing to do; and a functionality that I hope that OWL can support. From the point of view of the semantic web I see extensibility in all possible directions as being a fundamental design obligation. This relied on *semantic* mechanisms such as subPropertyOf and subClassOf. If the semantics of OWL is defined directly on top of the graph syntax then this does not work. Rather, to have this work, we would need the conditions on an OWL interpretation to be essentially semantic constraints, like the additional constraints on RDFS interpretations in Pat's RDF Model Theory. Building on top of dark triples seems to be a commitment to not permitting this extensibility. If this is correct then I am unhappy with the proposal to use dark triples to address the semantic layering problems. Theory of Classes ================= (Summary dark triples ain't no magic wand). As we are all aware, a naive set theory is problematic. As Peter has shown, the theory of classes in DAML+OIL can be thought of as problematic if one presupposes that the ability to write a description of a class is sufficient to ensure its existence. It is at least plausible, that even without qualified cardinality constraints, a new version of Peter's paradox can be found. In axiomatic set theory, the class of syntactic expressions that actually correspond to sets that exist is restricted in some way. As a footnote I include a version from von Neumann-Bernays-Gödel set theory [1]. In a semantic web based theory such restrictions are very hard to state because they need to be robust against the open world assumption. As an example, in DAML+OIL we can have an innocuous looking qualified cardinality constraint: foo:r, rdf:type, owl:Restriction . foo:r, daml:onProperty, foo:bar . foo:r, daml:maxCardinalityQ, "0" . foo:r, daml:hasClassQ, :_3 . :_3, daml:oneOf, :_4 . :_4, daml:first, foo:singleton . :_4, daml:rest, daml:nil . when combined with another innocuous document rdf:type daml:samePropertyAs foo:bar . foo:singleton daml:sameInstanceAs foo:r . we have the Patel-Schneider paradox. I don't see this as a problem relating to RDF, but relating to the radical open world assumption that, for me, characterises the semantic web. At this stage my assumption is that an adequate theory of classes for the semantic web will be a major research undertaking, on a par with creating an adequate set theory. I believe that the latter took about 30 years. Given that we have the prior work to guide us, we may be able to look for a factor of 10 speed up. There appeared to be agreement at the f2f, that a first order theory (aka my solipsistic stuff [2]): - does clarify OWL semantics without contradicting our set theoretic intuitions - is the theory used by DAML+OIL - does not contain an adequate theory of classes capturing our set theoretic intuitions Personally I would feel happier with that solution than paying either of the prices that my analsysis suggests for a dark triple based theory of classes: viz: either: - a significant delay to the WG product in order for the SEM focus area to undertake a research project or: - the inability to meaningful take a subPropertyOf the properties used in constructing an owl ontology. Jeremy [1] Elliot Mendelson, Introduction to Mathematical Logic, 2nd edition, 1979, p 178. [Within a first-order theory NBG ... proposed by von Neumann and ... R. Robinson, Bernays and Gödel] PROPOSITION 4.4 Let phi(X1,....Xn,Y1,...Ym) be a well-formed formula the variables of which occur among X1,...Xn,Y1,....Ym and in which only set variables are quantified (i.e. phi can be abbreviated in such a way that only set variables are quantified). We call such a well-formed formula *predicative*. Then, turnstile (EZ)(x1)...(xn)(<x1,...,xn> memberOf Z iff phi(x1,...,xn,Y1,...,Ym)) Jeremy: I am trying to draw attention to the syntactic constraint to do with quantified variables in the wff; I see this constraint as alien in nature to how I perceive the open world of the semantic web. [2] http://lists.w3.org/Archives/Public/www-webont-wg/2002Mar/0179.html
Received on Wednesday, 17 April 2002 09:16:34 UTC