- From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
- Date: Wed, 13 Mar 2002 10:04:03 -0500
- To: www-webont-wg@w3.org
- Cc: Guus Schreiber <schreiber@swi.psy.uva.nl>
I have put together a short, informal note on the layering landscape. For a more formal derivation of the layering problem itself, see http://lists.w3.org/Archives/Public/www-webont-wg/2002Mar/0018.html Peter F. Patel-Schneider Bell Labs Research The Layering Landscape Peter F. Patel-Schneider The layering discussion is about the relationship between OWL and other formalisms. As a formalism is about syntax and semantics, the layering discussion is about both syntax and semantics. The Landscape To hopefully make some things clearer, I present a quick overview of RDF(S), OIL, and DAML+OIL as they relate to the layering discussion. 1/ RDF(S) The syntax of RDF(S) is triples, serialized in XML (or not). The semantics of RDF(S) is a slightly non-standard model-theoretic semantics. The main semantic relationship in RDF(S) is a fairly standard version of entailment. In the semantics of RDF *everything* mentioned denotes. What this means is that there are objects in the domain of interpretations for individuals, classes, and properties. Further, classes and properties are linked to their extension. Even things that might be considered to be syntax, such as instance and subclass, are properties or whatever. So in RDFS there is a property rdf:type that is the relationship between resources and their types; there is a class rdfs:Resource that is the class of all resources; and there is a class rdfs:Class that is the class of all classes. 2/ OIL A syntax of OIL is a subset of XML, unrelated to the syntax of RDF(S). The semantics of OIL is a standard DL model-theoretic semantics. In the semantics of OIL only individuals denote objects in the domain. Classes have an extension, which is a subset of the domain. The extension of properties is a set of pairs. Descriptions have no status in interpretations; the extension of descriptions is built up from the extension of its components. In OIL, the structural relationships are not properties. That is there is no property that corresponds to the type relationship, nor is there a property that correspons to the subclass relationship. 3/ DAML+OIL The syntax of DAML+OIL is RDF syntax. The model-theoretic semantics of DAML+OIL is a slightly non-standard combination of DL semantics and the RDFS semantics. Entailment is not used in the semantics of DAML+OIL. In fact, the semantics of DAML+OIL does not include any semantic relationships. (This is a bug, not a feature.) The Problem The problem, in a nutshell, is that making OWL an extension of RDFS in the same way that RDFS is an extension of RDF produces semantic paradoxes. (By this I mean that OWL's syntax would be triples and everything would denote.) Why do these semantic paradoxes arise? If everything has to denote, then lots of classes and restrictions have to exist in OWL interpretations, or else there will be too few valid entailments. Because classes and restrictions need to have links back to themselves, some of these ``built-in'' classes and restrictions have links back to themselves. Because rdf:type is a property, and because of the expressive power needed in OWL, a ``built-in'' restriction that cannot be given a class extension thus exists in all OWL interpretations, and thus there are no OWL interpretations. This restriction is, informally, a restriction that is defined as having as instances those resources who have no rdf:type relationship to itself. If a resource is an instance of this restriction, then it can't have an rdf:type relationship to the restriction, and thus is not an instance of the restriction. If a resource is not an instance of this restriction, then it must have an rdf:type relationship to the restriction, and thus is an instance of this restriction. Caveat Pat Hayes disagrees with me on some portion of this. I believe that what he is disagreeing with is the idea of doing the extension in this way, not on the result of doing the extension this way. Solutions Any solution to this problem will have to either: 1/ Use RDF syntax (N-triples) for OWL but change the semantics, perhaps by making some things not denote. 2/ Use a different syntax for the portions of OWL that should not denote, and give that syntax its own meaning. The N-triples portion of the syntax can have the same meaning as in RDFS. 3/ Not use (standard) entailment for determining consequences. (I'm not sure if this would result in a viable approach.) Each of these options can be realized in several different ways. For example, in the different-semantics option, making all restrictions and OWL-defined classes not denote might be sufficient. However, it might also be sufficient to make rdf:type not denote. In the different-syntax option, it might be possible to use a different syntax only for restrictions. Using a different syntax for all class and property definitions is definitely a viable approach. In this option, there are also a number of approaches to providing semantics for the extra syntax.
Received on Wednesday, 13 March 2002 10:06:01 UTC