- From: Ian Horrocks <horrocks@cs.man.ac.uk>
- Date: Fri, 9 Aug 2002 15:48:17 +0100
- To: "Jonathan Borden" <jonathan@openhealth.org>
- Cc: <www-webont-wg@w3.org>
On August 8, Jonathan Borden writes: > > This back and forth between axiomatic and model theoretic semantics is > confusing me a bit. I take it that the RDF model theory is being developed > as a model theoretic semantics. Pat Hayes and Guha have proposed Lbase as a > framework to integrate various model theories for semantic web languages. Is > this the right question? It may be interesting from a theoretical perspective, but it wont change any of the issues we have been debating or solve any of the problems. > Does the choice of axiomatic vs. model theoretic semantics affect this? Is > it possible to extend a model theoretic semantics via axiomatization? It is > possible to develop the OWL semantics as an extension of Lbase? How are the > RDF and OWL semantics intended to be related? The question we need to ask ourselves is what we want semantics for and what we want to do with them. My idea is that they should be a declarative specification of the meaning of the language that is both simple enough for people to understand and agree that it really does capture the intended meaning, and precise enough to act as yardstick against which algorithms and implementations can be measured. If we choose a language that has a natural mapping to standard FOL then we can satisfy these requirements by using either (or both) a standard MT or a direct mapping into standard FOL, i.e., a mapping where classes (resp. properties) map to unary (resp. binary) predicates, intersection maps to and, union maps to or, negation maps to not, etc. If we choose a language without a natural mapping to standard FOL, e.g., a language that attempts a complete integration with RDF and includes classes of classes, then our job becomes much tougher. We can devise a MT for the language, one that extends the RDF MT, but it will be much more complex, e.g., including comprehension principles. We may be able to devise a complete axiomatisation of the language in FOL, but the axiomatisation will be complex. We may even be able to map the language into a different logic, such as Lbase, but then we would be dependant on the properties of this other logic. Apart from the fact that it may not even be possible to generate a coherent specification (i.e., one free from paradoxes), the difficulty with the first two of these is that they become sufficiently complex that it is no longer easy to be sure that they correctly capture the intended meaning. We then have the problem Chris described, where we have to be concerned not only with possible errors in our implementations of the specification but also with possible errors in our model of the specification. Regards, Ian > > Jonathan
Received on Friday, 9 August 2002 10:50:36 UTC