On 7/8/2012 11:11 AM, Pat Hayes wrote:
> OWL Full does indeed treat classes intensionally. OWL-DL, however, treats
> them extensionally. See the 'direct semantics' (which is normative) for OWL-DL
> inhttp://www.w3.org/TR/owl-semantics/direct.html, where the interpretation
> of a class name is simply a subset of the universe. That is an extensional
> meaning for classes. (01)
In every version of model theory for every version of logic, the
denotation of a relation is a subset of the universe of discourse. (02)
But two different relations (or OWL classes) can be specified by axioms
that are not logically equivalent. They might have the same extension
in one universe, but different extensions in a different universe. (03)
The direct model theory (by Patel-Schneider & Horrocks) acknowledges that: (04)
From http://www.w3.org/TR/owl-semantics/direct.html
> Definition: A collection O of abstract OWL ontologies and axioms and
> facts entails an abstract OWL ontology or axiom or fact O' with respect
> to a datatype map D if each interpretation with respect to map D that
> satisfies each ontology and axiom and fact in O also satisfies O'. (05)
They are talking about different "interpretations" in which the same
a given set of axioms can specify a class that may have different
extensions in different universes. (06)
It is much cleaner and simpler just to say that every OWL class
has a defining relation (specified by axioms) and a extension that
varies from one universe of discourse to another. (07)
John (08)
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