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RE: Proposal to resolve ISSUE-118 (anonymous individual semantics)

From: Boris Motik <boris.motik@comlab.ox.ac.uk>
Date: Wed, 20 Aug 2008 19:28:41 +0200
To: "'OWL Working Group WG'" <public-owl-wg@w3.org>
Message-ID: <007a01c902ea$317abd20$1f01a8c0@wolf>

Hello,

In a private conversation, Alan asked be about the semantics of negative property assertions containing anonymous individuals: he
was unsure what the semantics of these would be and what the rationale for picking the semantics would be. He asked to report the
result of our discussion to the WG, and I'm doing this now.




BNodes are interpreted in RDF as big existentials that sit before the entire graph. If you're thinking in terms of the structural
syntax, an equivalent way of looking at this is to say that these existentials sit before the conjunction of all axioms in the
ontology. These existentials are thus global in both RDF and OWL 1.

Now in OWL 2 we extended the set of axioms by, amongst others, negative property assertions. The natural way to define semantics to
this is to leave the existentials before the conjunction of all axioms, and simply extend the types of axioms. Thus, the semantics
of

NegativePropertyAssertion( P _:x _:y )
PropertyAssertion( R _:y i )

would be (I hope you can read pidgn LaTeX)

\exists x,y:                  // this is the big existential sitting before the overall conjunction
  [\neg P(x,y)] \wedge R(y,i) // this is the conjunction of all axioms


Please let me know should you have further questions about this.

Regards,

	Boris

> -----Original Message-----
> From: public-owl-wg-request@w3.org [mailto:public-owl-wg-request@w3.org] On Behalf Of Boris Motik
> Sent: 20 August 2008 00:36
> To: 'OWL Working Group WG'
> Subject: Proposal to resolve ISSUE-118 (anonymous individual semantics)
> 
> 
> Hello,
> 
> Here is a proposal to resolve ISSUE-118. Basically, we'd make the semantics of anonymous individuals
> be true existential semantics;
> furthermore, to obtain decidability, we'd need to restrict at the syntactic level how anonymous
> individuals are to be used. More
> concretely, we'd need to perform the following changes:
> 
> 1. In the Semantics document, we'd need to extend the notion of satisfiability of axioms in an
> interpretation to respect an
> assignment of anonymous individuals to domain elements.
> 
> 2. In the Syntax document, we'd extend the General Restrictions on Axioms along these lines:
> 
> An ontology O is OK if
> 
> - no anonymous individual occurs in an axiom of type SameIndividual, DifferentIndividuals, or
> NegativePropertyAssertion, and
> - a forest F over the anonymous individuals in O exists such that, in each property assertion of the
> form PropertyAssertion( P ai1
> ai2 ) where both ai1 and ai2 are anonymous, either ai1 is a child of ai2 in F or vice versa.
> 
> 
> Please let me know how you feel about this.
> 
> Regards,
> 
> 	Boris
> 
Received on Wednesday, 20 August 2008 17:30:23 GMT

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