RE: A proposal for the fragments document

Hi, Boris!

>Hello,
>
>Thanks for the correction; I've updated the document.
>
>You're right in that the reflexivity of a property might be 
>treated in the same way as the reflexivity in the case of equality. As
>you've rightly noticed, this is an approximation in the sense 
>that we consider only the URIs that are explicitly in the RDF graph;
>however, I believe this should be more than sufficient for 
>practical applications. 

I agree.

>I've added the appropriate rule and 
>have modified
>the grammar accordingly.

Ok.

>As for your last comment about equality, I believe that OWL-R 
>handles equality in exactly the same way as pD* in that it partitions
>the domain into a set of equivalence classes. (BTW, pD* does 
>not at all talk about model theory: it merely lists a bunch of rules.)

But here I have to object. At least in the paper [1] that I know, pD* is
explictly introduced as an extention to the model-theoretic semantics of
RDFS, for which *additionally* exists a set of "entailment rules" (that's
not the best of terms, I think btw.). From the introduction chapter:

  This paper has several purposes. It aims to:
  [...]
  extend the semantics and the complete set of simple
  entailment rules for RDFS, with the results relating
  to decidability and complexity, so as to apply to the
  OWL vocabulary.

Actually, most of the paper talks about model-theoretic aspects. Def. 5.1
talks about "pD* interpretations" and introduces all model-theoretic
semantic conditions except those derived from RDFS. Def 5.2 explains what
"pD* entailment" is based on the notion of a "satisfying interpretation".
And Def. 5.8 gives a Herbrand interpretation for pD*, which is then used in
Lemma 5.10 to prove that pD* is satisfiable (actually a much stronger result
is proved). 

The "entailment rules" for pD* are then listed in Table 7, and a certain
completeness result for these rules w.r.t. model-theoretic entailment based
on the model-theoretic semantic conditions is given in Theorem 5.11.

So ter Horst clearly distinguishes between the model-theoretic foundation of
pD* and the set of practical entailment rules.

For the semantic equivalence of OWL-R-Full and pD* on owl:sameAs: I still
have doubts, but I will think about this further.

>Regards,
>
>	Boris

Cheers,
Michael

[10] <http://linkinghub.elsevier.com/retrieve/pii/S1570826805000144>

>
>> -----Original Message-----
>> From: Michael Schneider [mailto:schneid@fzi.de]
>> Sent: 11 March 2008 21:30
>> To: Boris Motik
>> Cc: public-owl-wg@w3.org
>> Subject: 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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