Re: ISSUE: OWL-DL compatibility

> Unless anyone else has an opinion, Jos are you willing to make that change?
> 

I updated the syntax and semantics of RIF-OWL DL combinations, as well
as the embedding of RIF-OWL 2 RL combinations accordingly:
- in class membership formulas a#b, b must be a constant symbol
- in subclass formulas b##c, c,b must be constant symbols
- subclass formulas may only occur as facts

I imposed the last restriction, because I believe that in BLD-OWL 2 RL
combinations, using subclass statements in rule bodies necessarily
amounts to have been to introduce universal quantification in the body,
making such combinations outside horn, which I think is undesirable.
Besides, having subclass statements in rules without allowing variables
does not seem all that useful.

Best, Jos

> 
> 
> Michael Kifer wrote:
>> Yes, I agree that 3a is a reasonable fix. 3b is too big of a change,
>> and I was
>> not suggesting it for this round.
>>
>> michael
>>
>>
>> On Tue, 10 Nov 2009 10:53:32 -0500
>> Chris Welty <cawelty@gmail.com> wrote:
>>
>>> I read this a little more carefully.
>>>
>>> Basically, the issue is whether to add some correspondence between
>>> rif:subclass and rdf:subclass and between rif:type and rdf:type *in
>>> the OWL compatibility section* of SWC.  Such a correspondence is
>>> already there for RDF compatibility, but Michael noted that it is not
>>> "inherited" by the "OWL-DL" (now know as OWL Direct Semantics)
>>> section.  So, currently in SWC, the OWL-DL compatibility has no
>>> correspondence between the rather obvious type/subclass relations in
>>> the two languages.
>>>
>>> I agree this is a problem and should be fixed, and option #1 in
>>> Michael's analysis, copied below (to leave it as is) is unacceptable.
>>>
>>> Option #2 is to just add a sentence to the text saying there is no
>>> correspondence between owl and rif type/subclass.  This is less than
>>> satisfactory.
>>>
>>> Option #3 is to "fix" it somehow, and there are two variations there,
>>> I'll call them 3a (just repeat the correspondences from RDFS in
>>> OWL-DL) and 3b (do the best possible job mapping between owl and rif
>>> subclass).
>>>
>>> </chair>I prefer option 3a.  I agree with Jos' analysis of option 3b
>>> and think it is too big a change.<chair>
>>>
>>> As chair, I am also willing to accept 2 or 3a as an oversight and bug
>>> fix (I personally thought the correspondence between type and
>>> subclass were "inherited" from the RDF correspondence, so 3a would
>>> just make it the way I thought it was), however 3b seems to me,
>>> procedurally, to be much more significant and requires a new last
>>> call for SWC.
>>>
>>> -Chris
>>>
>>> Jos de Bruijn wrote:
>>>>> In today's telecon I was asked to reanimate the issue of OWL
>>>>> compatibility,
>>>>> which was discussed 1 month ago.
>>>>>
>>>>> Here is the relevant message:
>>>>>
>>>>> http://lists.w3.org/Archives/Public/public-rif-wg/2009Sep/0017.html
>>>>>
>>>>> The current situation is a bug, IMO. If it isn't a bug then at
>>>>> least that part
>>>>> of the document is very unsatisfactory and obscure. Jos proposed 3
>>>>> solutions:
>>>>>
>>>>> 1- leave things as they are, assuming that # and ## are not of
>>>>> interest
>>>>>    to users of RIF-OWL DL combinations
>>>>> 2- explain the use of # and ## in the document (this would
>>>>> certainly not
>>>>>    be a substantive change, so we should not run into procedural
>>>>> problems)
>>>>> 3- define the semantics of # and ## in RIF-OWL DL combinations in a
>>>>>    similar fashion as in RIF-RDF combinations: a one-to-one
>>>>> correspondence
>>>>>    between # and OWL class membership statements and implication
>>>>> between ##
>>>>>    and OWL subclassing.
>>>>>
>>>>> The easiest for him would be to do nothing (1), thus leaving things
>>>>> unsatisfactory and obscure. His next choice is (3), which is also
>>>>> my choice and
>>>>> the "right thing to do."  (3) stretches things a little, but it can
>>>>> be argued
>>>>> that it is a simple fix.
>>>> In my earlier e-mail to Michael referred to I did not say what my
>>>> preference is among the mentioned options.  I guess arguments can be
>>>> made for all three options, so in fact I do not have a strong
>>>> preference, but I do have a concern about option (3): implementation
>>>> might be harder.  If, for example, implementation is done through
>>>> embedding in other rules system, like the embedding of RIF-OWL2RL
>>>> combination in the appendix of the document, quite a few rules need to
>>>> be added for the ## construct.
>>>> In particular, for every pair of distinct class names (A,B), we need to
>>>> add the rule:
>>>>
>>>> Forall ?x (?x[rdf:type -> B] :- And(?x[rdf:type -> A] A##B))
>>>>
>>>> This means adding a quadratic number of rules.
>>>>
>>>> Dealing with # is easy: in the mapping of RIF DL-document formulas to
>>>> RIF documents [1] we simply map a#b to tr'(b)(a). Clearly, we would
>>>> restrict b in formulas a#b to constant symbols.
>>>>
>>>>
>>>> [1]
>>>> http://www.w3.org/TR/rif-rdf-owl/#Embedding_RIF_DL-document_formulas_into_RIF_BLD
>>>>
>>>>
>>>>
>>>>> Solution (2) is more work. It fixes the obscurity aspect, not the
>>>>> unsatisfactory aspect of the definitions. So, (3) seems like the
>>>>> best way to
>>>>> proceed.
>>>>>
>>>>> Solution (3) still leaves some problems, which are unrelated to the
>>>>> above
>>>>> issues. In the current semantics, subclassing in RIF implies
>>>>> subclassing in
>>>>> OWL/RDF, but not vice versa.
>>>>>
>>>>> In this regard, I would like to point to my follow-up message
>>>>> http://lists.w3.org/Archives/Public/public-rif-wg/2009Sep/0019.html
>>>>> Here I proposed a stronger semantics, which fixes this
>>>>> non-entailment problem.
>>>> Michael proposed the following semantics:
>>>>
>>>> {(A,B) | A rdfs:subclassOf B and A != B on the RDF side}
>>>>                 = {(A,B) | A##B on the RIF side}
>>>>
>>>> I feel that this would take us out of Horn, even when considering
>>>> Simple
>>>> entailment, because implementation would require (classical) negation.
>>>> At least, that is the only way I current see how this could be
>>>> implemented. As we know, classical negation in the body amounts to
>>>> disjunction in the head, so we would end up adding the following
>>>> rule to
>>>> the embedding of RDF-RDF combinations:
>>>>
>>>> Forall ?x, ?y (Or(?x##?y ?x=?y) :- ?x[rdfs:subClassOf -> ?y])
>>>>
>>>> For RIF-OWL DL combinations such a semantics is even more problematic,
>>>> because subclass in OWL DL means subset relation between class
>>>> extensions, so the condition would look something like (X^C is the
>>>> class
>>>> extension of X):
>>>>
>>>> {(A,B) | A^C subset B^C and A^C != B^C on the RDF side}
>>>>                 = {(A,B) | A##B on the RIF side}
>>>>
>>>> (Actually, we will need to apply some tricks here, since A and B are
>>>> not
>>>> constants on the OWL side, but I guess we can come up with a definition
>>>> that kind-of achieves this semantics)
>>>>
>>>> A formula implementing the => direction of the condition for a pair of
>>>> class names A,B would look something like (again, negation in the body
>>>> becomes disjunction in the head):
>>>>
>>>> Forall ?x (
>>>>   Or(A##B
>>>>      And(Forall ?x(?x[rdf:type -> B] :- ?x[rdf:type -> A])
>>>>          Forall ?x(?x[rdf:type -> A] :- ?x[rdf:type -> B])))
>>>>   :-
>>>>   Forall ?x(?x[rdf:type -> B] :- ?x[rdf:type -> A]))
>>>>
>>>>
>>>> So, I would not be in favor of extending either the semantics of RDF or
>>>> the semantics of OWL DL combinations with such a condition.
>>>>
>>>>
>>>> Best, Jos
>>>>> This would certainly be a substantive change semantically (although
>>>>> not
>>>>> significant textually). If we don't have the energy to do it this
>>>>> time,
>>>>> maybe for RIF 1.1.
>>>>>
>>>>> michael
>>>>>
>>
> 

-- 
Jos de Bruijn            debruijn@inf.unibz.it
+390471016224         http://www.debruijn.net/