RE: A proposal for the fragments document

Hi Boris!

>Hello Michael,
>
>Thanks for these corrections! I've corrected most of them, 
>apart from the ones I mention below; for some I have additional
>questions.
>
>> -----Original Message-----
>> From: Michael Schneider [mailto:schneid@fzi.de]
>> Sent: 11 March 2008 13:04
>> To: Boris Motik
>> Cc: public-owl-wg@w3.org; bcg@cs.man.ac.uk
>> Subject: RE: A proposal for the fragments document
>> 
>
>[snip]
>
>> * Table 2 and 3: For the rules with a list as an argument 
>("intersectionOf", unionOf): The list head
>> should be the RHS, but currently is the LHS. e.g.: 
>Currently: "T(?x1 intersectionOf ?c)" but should
>> be "T(?c intersectionOf ?x1)" ("x1" denotes the list head).
>> 
>
>I'm not sure I understand this comment. If C is an 
>intersection of C1 and C2, then this is serialized as
>
>classID owl:intersectionOf T(SEQ description1 ... descriptionn) .
>
>In the rules, ?x1 is matched to the list, and ?c is matched to 
>the class, so we need in the rule the triple "T(?c,
>owl:intersectionOf, ?x1)", 

Yes.

>and this is what we indeed have.

I see that it is ok now for intersections and unions.

But the problem still remains for sub property chains, even *after* you have updated the syntax:

  T(?x1, rdf:first, ?p1)
  ...
  T(?sc, rdfs:subPropertyOf, ?p)
  T(?x1, owl11:propertyChain, ?sc)
  ^^^^^^                      ^^^^
  swap RHS and LHS !

>> * Table 2 and 3: It is "rdf:subPropertyOf" ("rdf:*"!) but 
>should be "rdfs:subPropertyOf". Ditto (but
>> with "owl:") for "intersectionOf" and "unionOf".
>
>I'm not sure I understand this comment.

It's ok now, too.

>> * Perhaps not really editorial: There is no rule for 
>"owl11:ReflexiveProperty", but the other new
>> property characteristics of OWL-1.1 have rules. Was this 
>ommission intended?
>> 
>
>OWL-R cannot safely support reflexive properties: such 
>properties depend on the entire domain, so this means that we 
>potentially
>cannot consider just the explicitly mentioned objects.

Ok. At least, now that you say this, I would believe that the following entailment(s) must hold in the case of true reflexivity of some property p (although I am not quite sure, since it looks a bit esoterical ;-)):

  { p rdf:type owl11:ReflexiveProperty }
  |= 
  <someArbitraryURI> p <someArbitraryURI>

This would essentially mean that any approach which is *only* based on triple entailment rules will *never* be able to capture reflexivity to its full extend. You would also need some "URI string generator", at least for forward reasoning (not talking about the question of usefulness here).

But then I see another issue. How does this compare to 'owl:sameAs'? In the introduction to table 1 ("The Semantics of Equality") you write:

  "it defines the equality relation [...] owl:sameAs as being reflexive, [...]" 

The respective entailment rule is

  IF
    T(?x ?p ?y)
  THEN
    T(?x owl:sameAs ?x)
    T(?p owl:sameAs ?p)
    T(?y owl:sameAs ?y)

Of course, this rule will only produce triples with an LHS and RHS which are mentioned as names in the regarded RDF graph. So this rule does not provide real reflexivity according to what I said above (provided that this was right). 

On the other hand, the model-theoretic semantics of 'owl:sameAs' in OWL-R-Full is

  IF
    <x,y> in EXT_I(S_I(owl:sameAs))
  THEN
    x = y

In comparison with OWL-Full, this is only an "IF" and not an "IFF" semantic condition. But how do I come from this model-theoretic "IF" semantic condition to the entailment rule above? For example, I do not see how I can gain the following model-theoretic entailment from an arbitrary triple "x p y" within the RDF graph:

  { x p y } |= { x owl:sameAs x }

Maybe the 'sameAs' entailment rule is actually too strong?

BTW: I notice that pD* lists (nearly) the same entailment rules for 'owl:sameAs' as your proposal. But unlike your proposal, pD* gives a different model-theoretic semantics to 'owl:sameAs'. pD* does not map 'owl:sameAs' to real equality ("="), but defines it to be an equivalence relation on the domain, together with a substitution principle.

Cheers,
Michael

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
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Email: Michael.Schneider@fzi.de
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