RE: ISSUE-3: REPORTED: Lack of anonymous individuals

Hello,

Anonymous individuals really are existentials, not just "unknown names". In fact, the anonymous individuals are exactly like bnodes
in RDF. Note that bnodes in RDF are the reason why checking entailment of RDF graphs is NP-complete: checking entailment of RDF
graphs then amount to checking containment of conjunctive queries, which is an NP-complete problem in the size of the query.


The approach that I proposed at the end of my first e-mail that started this discussion actually tries to formalize the notion of
"unknown names". In this case, we might have anonymous individuals however you want them (tree-like or non-tree-like); however, the
fact that the individuals are anonymous would not be reflected in the semantics. You would just be able to flag some individual as
"anonymous", which would be a signal to the editor to show it differently in the GUI. Still, it would be interpreted just as another
individual (albeit with an unknown name), and not as an existential. This seems to be a simple and practical solution.


Boris 

> -----Original Message-----
> From: Conrad Bock [mailto:conrad.bock@nist.gov]
> Sent: 08 November 2007 16:17
> To: 'Jim Hendler'; 'Boris Motik'
> Cc: 'OWL Working Group WG'
> Subject: RE: ISSUE-3: REPORTED: Lack of anonymous individuals
> 
> Boris,
> 
>  >  Let me give you a concrete example. Assume that O1 contains the
>  >  following ABox assertion:
> 
>  >  (13) hasParent(Bob,Mary)
> 
>  >  As long as O2 contains named individuals (Bob, Mary, and so on), you
>  >  will get exactly the same answers. Now let O2 be an ontology
>  >  containing the following ABox assertion:
> 
>  >  (14) hasParent(Bob,_:1)
>  >
>  >  Here the difference becomes important. Under the standard "true"
>  >  semantics, O2 follows from O1. This is because, in first-order
>  >  logic, hasParent(Bob,Mary) entails \exists x : hasParent(Bob,x).
> 
> So anonymous individuals translate to existentials?  I thought
> anonymnous just meant "has no name".  Then O2 would only follow from O1
> if sameAs(Mary, _:1).
> 
>  >  Under the approximative semantics, O2 *does not* follow from
>  >  O1. This is because (14) is actually equivalent to the following
>  >  ABox O2':
> 
>  >  (14) hasParent(Bob,some-invented-constant)
> 
>  >  Now in first-order logic, it is not the case that
>  >  hasParent(Bob,Mary) entails hasParent(Bob,some-invented-constant),
>  >  so O1 does not entail O2.
> 
> Though it would if =(Mary, some-invented-constant).
> 
> Conrad
>

Received on Thursday, 8 November 2007 17:03:41 UTC