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Possible semantic bugs concerning domain and range

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Tue, 24 Sep 2002 17:26:34 +0100
Message-ID: <15760.37434.214548.647023@merlin.horrocks.net>
To: pat hayes <phayes@ai.uwf.edu>, www-webont-wg@w3.org

Pat,

DAML+OIL, and I hope OWL, can be viewed a fragment of FOL, with atomic
classes and properties corresponding to unary and binary predicates
respectively. According to this correspondence, subClassOf axioms
become implications, e.g., A subClassOf B corresponds to:

forall x . A(x) -> B(x)

Similarly, a property range axiom P range A corresponds to:

forall x,y P(x,y) -> A(y).

What could be simpler and clearer than that?

The combination of these two sentences entails 
forall x,y P(x,y) -> B(y).

What could be simpler and clearer than that?

If you want some alternative semantics, could you please explain in
similar terms what it is?

Ian

p.s. In DAML+OIL, and I hope in OWL, it has long been recognised (I'm
sure it is written down in the documentation somewhere) that range is
just syntactic sugar, and that P range A could be re-written as:

Thing subClassOf Restriction (onProperty P) (allValuesFrom A)

with the same result as above, i.e., this axiom plus A subClassOf B
clearly entails:

Thing subClassOf Restriction (onProperty P) (allValuesFrom B)
Received on Tuesday, 24 September 2002 11:29:36 GMT

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