RE: Action-67 some examples on b-nodes issues and their impact on users

Hi, Ivan!

Ivan Herman wrote on Wednesday, January 23:

>1. Scope of skolemization
>
>I am not sure I fully understand the proposal in terms of the 
>'skope' of 
>the skolemization. By that I mean: what are the 'units' (I do not know 
>how to call this) within which two 'identical' blank nodes are 
>skolemized with the same new URI? For OWL:
>
>  - are we speaking about an 'ontology' as being one 'unit'? 
>Or are the 
>ABox and TBox separated in this sense? I heard different 
>remarks used on 
>the calls, that is why I ask (I may have misunderstood something).
>
>  - how does this affect the import mechanism? Is skolemization done 
>after or before all imports? (I would expect 'after', but I 
>just wanted 
>to be sure...)

That's an interesting question. In the case that skolems will be RDF-mapped to bNodes, then I would say that the scope of a skolem is a single ontology, *without* the imported ontologies, and independent on the TBox/ABox question. Here is my argumentation:

Imagine we have two ontologies O1 and O2, which are represented in FS-syntax, and O1 imports O2, and both O1 and O2 contain a skolem named '_:x'. There shouldn't be a change in semantics if all the axioms of O1 and O2 are integrated into a new ontology O3. The question is, what happens with the skolem(s) named '_:x' when such a "merge" is performed?

To answer this question, I would say that there shouldn't also be a change in semantics if the merge is done through the following sequence of operations:

  (1) RDF-map both ontologies O1 and O2 to respective RDF graphs G1 and G2.
  (2) Merge the RDF graphs G1 and G2 into a new RDF graph G3.
  (3) FS-map graph G3 to an ontology O3 in FS syntax.

In step (1), all the skolems named '_:x' are mapped to RDF-bNodes with the same name. In step (2), in order to correctly merge the two RDF graphs, all occurrences of '_:x' in G2 (w.l.o.g.) have to be renamed to a new bNode name which does not yet occur in G1 and G2, for example '_:y'. In (3), all occurrences of '_:x' and '_:y' are mapped to skolems in O3 of the same names. It is clear that, if in O3 the skolems named '_:y' would instead be named '_:x' (no renaming while merging), then we would get name clashes, and this would change the meaning of such an ontology.

Just for completeness, here are two additional points to consider:

 (A) This "scope" question isn't restricted to skolem constants alone, but would also occur for existential variables.

 (B) In OWL-1.1-Full we will have the same scope question (but there for existentials), and this scope question did already exist in OWL-1.0-Full -- with the same answer as given above, AFAIK. 

Cheers,
Michael

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
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