- From: pat hayes <phayes@ai.uwf.edu>
- Date: Wed, 29 Nov 2000 16:40:00 -0600
- To: Graham Klyne <gk-lists@dial.pipex.com>
- Cc: <www-rdf-logic@w3.org>

>At 09:44 AM 11/27/00 -0600, pat hayes wrote: >>The domain of a model theory, more or less by definition of the >>term "model theory", is the expressions of the language (or perhaps >>more exactly, the parsings of those expressions according to the >>syntactic rules of the language.) > >I'm not sure I'd know a model theory if it leapt up and bit me, but >that's a useful start for me. What would you say is the "range" of >a model theory? I'm glad you asked. The range is the interpretations. Thats what a model theory does: it defines (a mathematical model of) what counts as an interpretation of the language, and gives rules for how to interpret the expressions of the language in such an interpretation. (Other names for interpretations are 'possible world', 'set of circumstances' 'state of affairs' and 'model of the world'.) Exactly what counts as an interpretation, speaking now mathematically, depends on the language; more intricate langauges require more complicated notions of 'interpretation'. Propositional logic requires simply an assignment of truth-values to the basic proposition letters. First-order relational logic requires a set over which the quantifiers range, and denotations defined over this set for all the names and relation names in the language. Programming languages have traditionally required functional domains obeying certain fixpoint properties. Modal logics require more complicated interpretations with multiple domains linked by accessibility relations, and so on. 'Ontology' lanugages like DAML, which essentially describe a heirarchy but don't say anything much about it, seem to require only some sets with some relations between them as an interpretation, as in Peter Patel-Schneider's OIL semantics. Right now Im not yet sure what RDF really needs, but Im working on it. >>So I repeat: are you saying that the 'at' assertions are part of RDF, or not? > >I'd say not, but that it is possible to _model_ the 'at' assertions in RDF. The trouble with that answer is, I really do not know what it means. What sense of 'model' are you using? Do you mean it is possible to *describe* them in RDF? Or that it is possible to *simulate* them in RDF? Or that they are some kind of assertional *extension* to RDF? Or *axioms written in RDF syntax*? Any help would be appreciated. Pat Hayes --------------------------------------------------------------------- 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

Received on Wednesday, 29 November 2000 17:38:42 UTC