From: pat hayes <phayes@ai.uwf.edu>

Date: Mon, 22 Jan 2001 15:36:46 -0800

Message-Id: <v04210108b69272e1e1cd@[130.107.66.237]>

To: Miles Sabin <MSabin@interx.com>

Cc: www-rdf-logic@w3.org

Date: Mon, 22 Jan 2001 15:36:46 -0800

Message-Id: <v04210108b69272e1e1cd@[130.107.66.237]>

To: Miles Sabin <MSabin@interx.com>

Cc: www-rdf-logic@w3.org

>Working on the assumption that there's at most a countably >infinite set of URI(-refs) ... each is a finite sequence of >charaters drawn from a finite alphabet ... and similarly for >Literals, am I right to infer that, > >1. there is at most a countable infinity of resources: because > every resource has a URI(-ref) and no two distinct resources > share a URI(-ref). > >hence that, > >2. the set Resources from rdfms 5.1, is at most countably > infinite, > >3. the set Properties from 5.3 is at most countably infinite: > because a (proper) subset of Resources. > >and hence that, > >4. RDF models can contain at most countably many statements: > becauce they're subsets of, > > Properties x Resources x (Resources U Literals) > > which is at most countably infinite because Properties, > Resources and Literals are. Yes, you are right to infer that. However, your question raises another, related, issue: according to several members of the group which developed RDF, the 'graph model' of a set of RDF triplets is intended itself to be *the* model (in the sense from model theory) of those triplets. It follows that all RDF models of any RDF ontology (that could be stored on any web page, at any rate) must be not only countable, but finite. Now, since the finite-model restriction is not expressible in first-order (or any complete semi-decideable) logic, this would appear to indicate that RDF must have a semantics which has no semidecision procedure (and hence no proof procedure.) 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/~phayesReceived on Monday, 22 January 2001 18:34:12 UTC

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