Re: Proposed change to the OWL-2 Direct Semantics entailment regime

Pardon my naïve questions, but I'm having a hard time understanding why the
current OWL-2 Direct Semantics ER would not provide any answers to this
example.

On 11/30/10 4:57 AM, "Enrico Franconi" <franconi@inf.unibz.it> wrote:
> ..snip..
> A = R some Thing
> B = R max 0 Thing
> 
> Consider the following data:
> 
> :john :friend :mary
> :john friend :andrea
> :mary :loves :andrea
> :andrea :loves :paul
> 
> :mary rdf:type A
> :paul rdf:type B

Ok, I don't see any BNodes in the data.
 
> or, graphically:
> 
>       :john
>      /      \
>     /:f      \:f
>    v          v
> :andrea <--- :mary  ---> A
>    |     :l        :type
>    |:l
>    v
>  :paul  ---> B
>        :type
> 
> Consider the query:
> {?X friend _:y, _:y rdf:type A, _:y loves _:z, _:z rdf:type B}

> If the bnodes in the query are interpreted as genuine existential variables,
> the answer should be:
> {{?X -> :john}}.

I would expect this same answer even if _:y and _:z are treated as
variables.

> This is because there are two "alternative" completions of the data: one where
> (:andrea rdf:type A), and an alternative one where (:andrea rdf:type B).  This
> happens since A and B cover the universe, so for sure one of the two
> alternative completions has to be true. In both completions the evaluation of
> the query leads to {?X -> :john}, so this is the certain answer.

Ok.
 
> In the current spec the answer is empty, since bnodes can only bind to
> individuals or other bnodes, and in the data there is no binding that
> satisfies the query (since there is no unique "completion" of the data).

This my point of confusion, maybe if you spell it out further, I would see
something I'm currently missing.  In the first 'completion', _:y would be
bound to :Andrea and _:z to :Paul.  In the second, _:y would be bound to
:Mary and _:z to :Andrea.  In both cases, the Bnodes in the queries are
(consistently) bound to individuals and the instantiation of the solutions
WRT the query are entailed by the data and the OWL axioms.

So, my intuitive understanding is that there are two unique solutions (prior
to 'projecting out' the Bnodes from the solutions), but there is only one
(once you do).  Is it there something in this ER specification about how
this projection/stripping happens that is the culprit here?

I'm not sure I understand what bearing the lack of a unique 'completion' of
the data has on the restriction in this ER that bnodes can only bind to
individuals or other bnodes (since this restriction doesn't seem relevant to
the example as the only thing the bnodes can bind to are individuals).  Am I
missing something?

P.S., it would probably help an outsider's understanding of the substance of
the issue if the (overall) tone of this thread wasn't so belligerent.  Just
a friendly observation :)

-- Chime


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Received on Tuesday, 30 November 2010 16:59:39 UTC