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Re: bnodeification

From: Pat Hayes <phayes@ihmc.us>
Date: Wed, 11 Jan 2006 16:32:18 -0600
Message-Id: <p06230906bfeadbd5b654@[10.100.0.5]>
To: tessaris <tessaris@inf.unibz.it>
Cc: Enrico Franconi <franconi@inf.unibz.it>, Bijan Parsia <bparsia@isr.umd.edu>, souripriya.das@oracle.com, public-rdf-dawg@w3.org

>Hi Pat,
>
>Pat Hayes wrote:
>
>>  -----------
>>
>>  A binding on a pattern Q is a map from the variables and bnodes in Q to
>>  terms. The result B(Q) of applying the binding B to Q is the RDF graph
>>  obtained by replacing each variable or bnode in Q by its value under B.
>>
>>  An answer binding with respect to a scoping graph G' is a binding B such
>>  that:
>  > (1)  any bnodeIDs introduced by B occur in G'
>  > (2)  G entails (G' union B(Q)).
>
>It works for RDF(S), but I'm uneasy with the idea of extending mappings
>with bnode names. In this way all the the variables in the query became
>distinguished variables and no more true existentials.

Logically, there is no distinction between variables and existentials 
in a query (i.e. on the RHS of a Gentzen sequent), surely? Variables 
are just existentials that we are asking to see bindings for.

>It doesn't make any difference with RDF and RDF(S), but with OWL for
>example you don't get a true conjunctive query language.
>
>E.g. given the KB [:a rdf:type (Some :r :c)], the query { ?x :r _:b }
>has no answers.

It seems to me that SELECT ?x {?x :r ?b} should have an answer just 
when SELECT ?x {?x :r _:b} does, since we allow bnodes as binding 
values to variables. So this query should have an answer, which would 
simply utilize a binding of _:b to another bnodeID (conceptually, in 
the 'OWL-RDF comprehension closure' of the KB).

This is exactly why I am worried about imposing condition (1) on OWL 
entailment, which I tried to explain in the telecon. Seems to me that 
this strict condition (1) (which isn't, to repeat, logically 
necessary, but is there only to keep redundancy to a minimum) is not 
going to be reasonable past RDFS, since OWL/RDF has built-in semantic 
conditions stated as comprehension principles which effectively 
assert the existence of an infinite amount of OWL stuff which is not 
mentioned explicitly in, but logically required to exist by, an 
OWL/RDF graph. These include such things as the lists used to encode 
OWL syntax, and also in this case, the :r value from :a that must 
exist in order that the 'Some' be satisfied; and then a bnode 
representing this known-to-exist thing is a legitimate binding for 
the variable/bnode in the query.  Certainly any engine which is 
capable of inferring that _:b exists would surely be capable of 
generating an appropriate bnodeID for that thing and returning that 
as a binding, if required. But of course, we do not require it for 
query bnodes since they cannot be selected.

Once we have semantic conditions in the language which guarantee that 
things exist which are not mentioned by name in a KB, we will need to 
relax condition (1) to allow these 'necessary' existents to be 
referred to in answer bindings. The case seems to me to be exactly 
similar to the case of rdf: and rdfs: IRIs in axiomatic triples in 
RDF and RDFS, and even more similar to function symbols in FOL, where 
answers bindings can be terms in the Herbrand universe generated from 
skolem functions. If one forbids functions, the same condition 
becomes a requirement like this on the generation of existential 
'names' in relational argument positions. All this amounts to in 
practice is that we allow KBs to have a 'stock' of spare bnodeIDs 
they can use as answer bindings to denote things known to exist, and 
that are considered to occur in the dataset.

I agree this whole topic is potentially debateable, but it seems to 
me that we can (must?) leave any debates about exactly how to handle 
OWL queries to a later date. I have no confidence that ANY of our 
proposed definitions will work EXACTLY as stated for OWL queries 
without some changes, if only minor ones. OWL querying is still an 
open issue. In the meantime, let us try to keep the definitions as 
simple and clear and robust as we can. I am still very nervous of 
relying on the 'ordered merge' trick to keep bnode scopes aligned 
properly: it is too much like an algorithmic specification to be 
robust enough to seem comfortable.

>Moreover, the algebra definition gets more complicate since you need to
>project over the true variables all the times.

True, but this can be easily handled by a suitable definition of 
'variable binding' or some such which contains the projection, if 
required.

Pat

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Received on Wednesday, 11 January 2006 22:32:41 GMT

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