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Re: ISSUE: OWL-DL compatibility

From: Michael Kifer <kifer@cs.sunysb.edu>
Date: Thu, 19 Nov 2009 15:24:23 -0500
To: Jos de Bruijn <debruijn@inf.unibz.it>
Cc: Chris Welty <cawelty@gmail.com>, RIF WG Public list <public-rif-wg@w3.org>
Message-ID: <20091119152423.19565b20@kiferdesk>


On Thu, 19 Nov 2009 12:15:53 +0100
Jos de Bruijn <debruijn@inf.unibz.it> wrote:

> Michael Kifer wrote:
> > On Wed, 18 Nov 2009 16:06:06 +0100
> > Jos de Bruijn <debruijn@inf.unibz.it> wrote:
> >
> >   
> >>>>> 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:
> >>>>         
> >>> Thanks Jos.
> >>> Please see questions within.
> >>>
> >>>       
> >>>> - 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.
> >>>>         
> >>> Can you elaborate? How does this introduce universal quantification? 
> >>>       
> >> The semantic correspondence between subclasses in OWL and ## in RIF is
> >> defined as follows [1]:
> >>
> >> C(c) is a subset of C(d) whenever Itruth(Isub(IC(<c>),IC(<d>))) = t, for
> >> any two IRIs c and d
.....
> >> Now, since there is a strict separation between the interpretation of
> >> individuals and classes in the OWL direct semantics, we cannot objects
> >> in Dind to represent classes. Thus, like we did for frame formulas, we
> >> need to change the interpretation of subclass formulas [2]:
> >>
> >> Isub is a mapping D × D → D
> >>
> >>
> >> If we now want to embed this modified RIF into standard RIF [3] the only
> >> embedding I can come up with for b##c is
> >> (a)  Forall ?x (tr'(c)(?x) :- tr'(b)(?x))
> >>     
> >
> > So, where is the universal quantifier in the body?
> > What you have here is an axiom schema in RIF of the form:
> >
> > Forall ?x (tr'(c)(?x) :- tr(b)##tr(c) and tr'(b)(?x))
> >   
> 
> I was also originally thinking about such an axiom schema, but that will
> not work, since class identifiers are not in Dind.
> This axiom schema would create unwanted connections between individuals
> in Dind and classes.
> 
> Consider for example an OWL ontology with the statements:
> a=b
> a subclass c
> 
> This ontology does not entail b subclass c. When adding the mentioned
> axiom and a##c to the ontology, b subclass c is entailed.

Hold on! a,b, and c are predicates. How can you write a=b in BLD?
If you meant a=b in OWL-DL, then it means a subclass b and b subclass a, isn't
it? So, b subclass c is entailed. If you mean a=b in RDF then this cannot be
even mapped to BLD.

In any case, I don't see how any of your arguments support your assertion that
## in the rule body somehow bring universal quantification into the rule bodies
of BLD.
To me this all looks like a non-sequitur. If you can provide a formal argument,
please do.

regards
michael

 
> Cheers, Jos
> 
> > It does not mean that this axion is substituted in the body of a rule whenever
> > c##b appears there. Otherwise, you would be claiming that Horn F-logic is not
> > Horn, for example.
> >
> > michael 
> >
> >   
> >> [1]
> >> http://www.w3.org/2005/rules/wiki/SWC#Semantics_of_RIF-OWL_DL_Combinations
> >> [2]
> >> http://www.w3.org/2005/rules/wiki/SWC#Modified_Semantics_for_RIF_Subclass.2C_Membership.2C_and_Frame_Formulas
> >> [3]
> >> http://www.w3.org/2005/rules/wiki/SWC#Embedding_RIF_DL-document_formulas_into_RIF_BLD
> >>
> >>     
> >>> And why
> >>> does it matter anyway?
> >>> We already have universal quantification on the OWL side, so any OWL
> >>> predicate that occurs in a rule body potentially brings in universal
> >>> quantification. A combination of OWL+Horn is not Horn, so I don't understand
> >>> your concerns.
> >>>       
> >> A combination of OWL 2 RL (which is Horn) with Horn should be Horn as
> >> well, IMHO.
> >> Besides, full OWL 2 DL does not introduce arbitrary universal
> >> quantification. In particular, formulas of the form (a) cannot appear
> >> inside axioms. If formulas of the form (a) would be allowed to appear in
> >> the bodies of rules, known techniques for reasoning with DL-safe
> >> OWL+Horn cannot be used for RIF-OWL DL combinations.
> >>
> >>     
> >>>> Besides, having subclass statements in rules without allowing variables
> >>>> does not seem all that useful.
> >>>>         
> >>> We don't really know that. If there is a legitimate concern -- then yes. But I
> >>> don't understand your concern, so please elaborate.
> >>>       
> >> To summarize: my main concerns are that if a##b is allowed in rule bodies:
> >>
> >> - it is not possible to use rules reasoning with RIF-OWL2RL combinations
> >> - it is not possible to use know techniques for reasoning with DL-safe
> >> OWL+Horn for DL-safe RIF-OWL DL combinations
> >>
> >>
> >>
> >> Cheers, Jos
> >>
> >>     
> >>> cheers
> >>> michael
> >>>
> >>>       
> >>>> 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
> >>>>>>>>>
> >>>>>>>>>                   
> 
> 
Received on Thursday, 19 November 2009 20:25:00 GMT

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