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Re: A Model Theoretic Semantics for DAML-ONT

From: Jeff Heflin <heflin@cs.umd.edu>
Date: Mon, 13 Nov 2000 13:53:48 -0500
Message-ID: <3A1038BC.64061305@cs.umd.edu>
To: www-rdf-logic@w3.org
Deborah,

Here are a few more comments on your proposed semantics for DAML-ont:

1) The "imports" statement is lacking semantics. The intent of "imports"
is so that you can say the current ontology or document includes the
rules and definitions from some other ontology. I imagine in order to
define this formally in KIF, you would need to add something like the
"ist" predicate (meaning "is true in") from context logic (see
McCarthy's and Guha's work). Assuming you had such a predicate, where
the first argument was an ontology, the second a predicate name, and the
rest arguments of that predicate, you might add this rule:

(=> (imports ?o1 ?o2)(ist ?o2 ?p ?a1 ?a2)
    (ist ?o1 ?p ?a1 ?a2))

Note that we could also add a rule that says imports is transitive, but
this can be deduced from the above rule and the definition of ist.

2) The following is used for the definition of "domain":

%% The object in an RDF statement of the form "(object property
resource)"
%% must be an instance of the domain of property.
(=> (Property ?p)(domain ?p ?d)(holds ?p ?x ?y)(type ?x ?d))

This implies that if there is more than one domain stated for a
property, that the "object" must be an instance of the intersection of
these domains.
However, the RDF Schema spec states "If there is more than one domain
property, the constrained property can be used with instances of ANY of
the classes..." That is, the "object" must be an instance of the union
of the domains.

Personally, I like your definition better. If you use the RDF schema
definition, then it becomes possible to extend an ontology in such a way
that content marked up with respect to new ontology is incompatible with
the extended ontology. Also, the RDF definition is meaningless (i.e.,
you cannot deduce anything from it or perform type checking) unless you
can close the world and guarantee that there do not exist any more
domain statements for the property in question elsewhere on the Web.

I think this is a case where it is worth deviating from RDF, but would
like to hear the opinions of others.

Jeff
Received on Monday, 13 November 2000 13:53:51 UTC

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