From: Michael Kifer <kifer@cs.sunysb.edu>

Date: Thu, 19 Nov 2009 15:29:29 -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: <20091119152929.75186437@kiferdesk>

Date: Thu, 19 Nov 2009 15:29:29 -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: <20091119152929.75186437@kiferdesk>

Yes, mapping classes using I_C is incorrect. As I mentioned in a previous email, a=b among classes cannot be mapped into an equality in BLD because predicates are not individuals, and equality is defined only among individuals. michael On Thu, 19 Nov 2009 12:52:35 +0100 Jos de Bruijn <debruijn@inf.unibz.it> wrote: > I realized there was a problem in the definition of the semantics of > RIF-OWL DL combinations. Individual, class, and property identifiers > were all mapped to objects in the domain D using the same mapping > function I_C. This means that if two individuals a,b were equated (a=b), > their class interpretations would be equated as well (i.e., a(?x) <-> > b(?x) would follow from). This is not in line with the OWL direct semantics. > Therefore, I added a mapping function I_C' to the definition of > dl-semantic structures that is used in the context of class and property > identifiers, i.e., b and c in a#b, b##c, a[b -> d], and a[rdf:type -> c]. > > This change does not impact the embedding in section 9.2. In fact, the > embedding is incorrect for the old (buggy) definition, but is correct > for the new definition. > > > Best, Jos > > Jos de Bruijn 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 > >>> > >>> > >> Just to be clear: "whenever" means "if" here, right? > >> > >> > > > > Yes. > > > >> > >> > >>> 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. > > > > > > 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 20:30:02 UTC

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