DAML+OIL model theory stance on classes as instances

From: Peter F. Patel-Schneider (pfps@research.bell-labs.com)
Date: 07/10/02

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    As there was some discussion yesterday about whether classes had properties
    in the DAML+OIL model theory, I reread the model theory document to see
    exactly what it said.
    The result - a definite no, shading to maybe.  :-)
    The model theory has three mappings, each of which map the nodes of a
    collection of RDF triples into something else
    	IC, which maps classes (nodes) to their extensions
    	IR, which maps relationships (nodes) to their extensions, which are
    	    (roughly) 2-place relationships over the domain of discourse
    	IO, which (roughly) maps individuals (nodes) to their extensions,
    	    which are (roughly) elements of the domain of discourse
    So classes are nodes in the RDF graph, and do not participate in the
    extension of relationships, which interrelate things in the domain of
    However, IO maps nodes into the domain of discourse.  Thus the IO mapping
    of classes do participate in the extensions of relationships, leading to
    the ``maybe'' shading.

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