From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>

Date: Mon, 15 Sep 2008 09:43:49 -0400 (EDT)

Message-Id: <20080915.094349.131894469.pfps@research.bell-labs.com>

To: schneid@fzi.de

Cc: baojie@cs.rpi.edu, public-owl-wg@w3.org

Date: Mon, 15 Sep 2008 09:43:49 -0400 (EDT)

Message-Id: <20080915.094349.131894469.pfps@research.bell-labs.com>

To: schneid@fzi.de

Cc: baojie@cs.rpi.edu, public-owl-wg@w3.org

The treatment of axioms with main blank nodes is somewhat a matter of taste. I see no particular technical issues with their current treatment in the core OWL 2 Full semantic and will thus not vote against going forward in this manner. peter From: "Michael Schneider" <schneid@fzi.de> Subject: RE: Comment on OWL 2 Full Semantics Date: Mon, 15 Sep 2008 15:34:20 +0200 > Hi Peter and Jie, > > finally, here is my answer to your review comments concerning those > semantic conditions, which are split into two "IF" conditions, and where > the second part has an existential variable. > > Jie Bao wrote as a review comment: > > """ > I found many conditions in this section are defined > as comprehension rules (usually in the "iff" form). > Will it be better to move all the comprehension ones > into section 6, together with existing comprehension > conditions? > """ > > And Peter F. Patel-Schneider wrote per email on September 09, 2008: > > >I noticed that there are some (partial) comprehension principles in > >Section 4 of the OWL 2 Full Semantics document. > > (The rest of the mail follows below.) > > All these are not meant to be comprehension principles, although they > look so, because they contain an existentially quantified variable. Sub > property chains, the n-ary axioms ("All*"), and the negative property > assertions are axioms in OWL 2 DL, and I wanted to define IFF conditions > for them in Full just as for every other DL axiom. But these particular > axioms have a "root node" in their RDF syntax, which has to be provided > somehow. I "create" it by the existential. That's a simple and effective > approach, which keeps the treatment local (no need to deal with it in > different parts of the document), and which doesn't hurt too much the > main structure of the semantic condition. > > For the latter claim to see, imagine that the RDF syntax of sub property > chains would not contain a root node, as in > > q owl:subsumesPropertyChain (p1...pn) > > I would define the following IFF semantic condition for this alternative > form: > > IF l sequence of p1...pn in IR THEN > <q,l> in IEXT(IS(owl:subsumesPropertyChain)) > IFF > q, p1, ..., pn in IP, > IEXT(p1) o ... o IEXT(pn) sub IEXT(q) > > This can be equivalently split into the following two semantic > conditions: > > - IF > l sequence of p1...pn in IR, > <q,l> in IEXT(IS(owl:subsumesPropertyChain)) > THEN > q, p1, ..., pn in IP, > IEXT(p1) o ... o IEXT(pn) sub IEXT(q) > > - IF > l sequence of p1...pn in IP, > q in IP, > IEXT(p1) o ... o IEXT(pn) sub IEXT(q) > THEN > <q,l> in IEXT(IS(owl:subsumesPropertyChain)) > > Now compare this with the current two semantic conditions for the > multi-triple RDF encoding: > > - IF > l sequence of p1...pn in IR, > <x,q> in IEXT(IS(rdfs:subPropertyOf)), > <x,l> in IEXT(IS(owl:propertyChain)) > THEN > q, p1, ..., pn in IP, > IEXT(p1) o ... o IEXT(pn) sub IEXT(q) > > - IF > l sequence of p1...pn in IP, > q in IP, > IEXT(p1) o ... o IEXT(pn) sub IEXT(q) > THEN > EXISTS x in IR, > <x,q> in IEXT(IS(rdfs:subPropertyOf)), > <x,l> in IEXT(IS(owl:propertyChain)) > > These two IF semantic conditions have almost the same basic form as the > split semantic condition for the single-triple variant, except for the > additional "EXISTS x in IR" premise. IMHO, that's a pretty small > difference, and the "EXISTS x" just does enough to treat the "missing > root node" issue. Also, this approach will probably work in the same > form for every case where there is a root node for some axiom; at least, > it does work this way for all current cases in OWL 2. Btw, I don't see a > technical reason for not having two separate "IF" conditions instead of > a single "IFF" condition /always/. The reason for the single "IFF" > conditions is purely editorial: It takes less space to write them down, > and it keeps those things together, which belong to the same language > construct. > > Compared with this, Peter's proposal below seems more complicated and > not less unusual looking to me: > > (1) It is a "non-local" treatment which affects three different parts of > the document: The main semantic condition for the language feature, the > "Classes" and "Properties" tables, and the comprehension principles. > > (2) It introduces a sort of IFF condition, which does not occur > elsewhere in the Full Semantics: Denotations of triples containing the > language feature's vocabulary occur on both sides of the semantic > condition, e.g.: > > > x in ICEXT(IS(owl:NegativePropertyAssertion)) > > <x,u> in IEXT(IS(owl:sourceIndividual)) > > <x,p> in IEXT(IS(owl:assertionProperty)) > > <x,w> in IEXT(IS(owl:targetIndividual)) > > IFF > > <x,u> in IEXT(IS(owl:sourceIndividual)) > > <x,p> in IEXT(IS(owl:assertionProperty)) > > <x,w> in IEXT(IS(owl:targetIndividual)) > > <u,w> not in IEXT(p) > > I don't say that this is wrong, because it's technically perfectly > allowed. But I followed a design idea to have the semantic conditions > look similar to typical interpretations, where you have a syntactic > expression on the LHS, and its set-theoretic interpretation on the RHS > (as, for example, in the DL semantics). Of course, the Full Semantics > works a bit different, since in OWL Full semantic conditions have their > consequent /and/ their antecedent in the interpretation space. But I > find the above approach at least confusing. Also, having the "triples" > on the RHS makes it hard for the right-to-left side to fire. In > practice, if the regarded RDF graph does not already contain these > triples, the right-to-left side needs the help of a comprehension > principle to fire. And if these triples are already in the graph, then > the right-to-left side isn't needed anyway. Well, /almost/ not > necessary, this brings us to my next point. > > (3) The semantic conditions in the "Properties" class are weakened in > order to help make the proposed IFF conditions into "real" IFF > conditions. In the example cited above, if the domain of > owl:sourceIndividual would be ICEXT(IS(owl:NegativePropertyAssertion)), > as it is the case at the moment, then the IFF condition would > effectively be an ONLY-IF condition, since the right-to-left implication > would be trivially true. I don't think that we should change the domain > and range of the vocabulary denotations, just to receive "real" iff > conditions, but maybe I missed something here? > > I would also have some trouble with having the right-to-left sides as > comprehension principles, as they differ from the current comprehension > principles for lists and class expressions in that their premises are > more demanding. But I don't want to extend this mail any more. My claim > is that the current approach is more simple and straightforward, > although I agree that it is a bit ugly and might even be confusing. To > at least address the problem of possible confusion, I have now added > some introductory text to the beginning of the "Semantic Conditions" > section, which in particular addresses the "existential" semantic > conditions. Here is the diff: > > <http://www.w3.org/2007/OWL/wiki/index.php?title=RDF-Based_Semantics&diff=12926&oldid=12913> > > Please tell me whether this is ok for you or not. > > Cheers, > Michael > > >This would require the following changes: > > > >1/ Remove all partial comprehension principles from Section 4, i.e., > > remove the second halves of Table 4.11, 4.13, and 4.17. The > > comprehension principles in Section 6 would have to be augmented to > > make up for these removals. > > > >2/ Change the domain of owl:distinctMembers, owl:assertionProperty, > > owl:sourceIndividual, owl:targetIndividual, and owl:targetValue to > > IR, to allow for comprehension-free IFF semantic conditions for their > > axioms. > > > >3/ Provide comprehension-free IFF conditions for n-ary axioms, somewhat > > similar to the one already existing for disjointUnionOf: > > > > Table 4.13 N-ary Axioms > > if l sequence of u1, ..., un in IR then > > - x in ICEXT(IS(owl:AllDifferent)) > > <x,l> in IEXT(IS(owl:members)) > > IFF > > <x,l> in IEXT(IS(owl:members)) > > u1 /= uk for 1<=i<k<=n > > - same for owl:distinctMembers > > - x in ICEXT(IS(owl:AllDisjointClasses)) > > <x,l> in IEXT(IS(owl:members)) > > IFF > > <x,l> in IEXT(IS(owl:members)) > > ICEXT(ci) ^ ICEXT(ck) = {} for 1<=i<k<=n > > - similarly for AllDisjointProperties > > > >4/ Provide comprehension-free IFF conditions for negative property > > assertions: > > > > Table 4.17: Negative Property Assertions > > - x in ICEXT(IS(owl:NegativePropertyAssertion)) > > <x,u> in IEXT(IS(owl:sourceIndividual)) > > <x,p> in IEXT(IS(owl:assertionProperty)) > > <x,w> in IEXT(IS(owl:targetIndividual)) > > IFF > > <x,u> in IEXT(IS(owl:sourceIndividual)) > > <x,p> in IEXT(IS(owl:assertionProperty)) > > <x,w> in IEXT(IS(owl:targetIndividual)) > > <u,w> not in IEXT(p) > > - x in ICEXT(IS(owl:NegativePropertyAssertion)) > > <x,u> in IEXT(IS(owl:sourceIndividual)) > > <x,p> in IEXT(IS(owl:assertionProperty)) > > <x,w> in IEXT(IS(owl:targetValue)) > > IFF > > <x,u> in IEXT(IS(owl:sourceIndividual)) > > <x,p> in IEXT(IS(owl:assertionProperty)) > > <x,w> in IEXT(IS(owl:targetValue)) > > p in IDP > > <u,w> not in IEXT(p) > > > >5/ Provide comprehension-free IFF semantic conditions for reifications > > needed for annotations: > > > > Table 4.18: Reification for Annotation > > - x in ICEXT(IS(owl:Axiom)) > > <x,u> in IEXT(IS(owl:subject)) > > <x,p> in IEXT(IS(owl:predicate)) > > <x,w> in IEXT(IS(owl:object)) > > iff > > <x,u> in IEXT(IS(owl:subject)) > > <x,p> in IEXT(IS(owl:predicate)) > > <x,w> in IEXT(IS(owl:object)) > > <u,w> in IEXT(p)) > > - x in ICEXT(IS(owl:Annotation)) > > <x,u> in IEXT(IS(owl:subject)) > > <x,p> in IEXT(IS(owl:predicate)) > > <x,w> in IEXT(IS(owl:object)) > > iff > > <x,u> in IEXT(IS(owl:subject)) > > <x,p> in IEXT(IS(owl:predicate)) > > <x,w> in IEXT(IS(owl:object)) > > p in IAP > > <u,w> in IEXT(p)) > > -- > Dipl.-Inform. Michael Schneider > FZI Forschungszentrum Informatik Karlsruhe > Abtl. Information Process Engineering (IPE) > Tel : +49-721-9654-726 > Fax : +49-721-9654-727 > Email: Michael.Schneider@fzi.de > Web : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555Received on Monday, 15 September 2008 13:44:59 UTC

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