- From: Michael Schneider <schneid@fzi.de>
- Date: Mon, 15 Oct 2007 18:12:46 +0200
- To: "Ian Horrocks" <horrocks@cs.man.ac.uk>
- Cc: "Ulrike Sattler" <sattler@cs.man.ac.uk>, "Owl Dev" <public-owl-dev@w3.org>, "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, "Swanson, Tim" <tim.swanson@semanticarts.com>, "Evren Sirin" <evren@clarkparsia.com>
Hi, Ian! Ian Horrocks wrote: >I don't believe that you have taken into account the non-structural >constraints relating to acyclicity. You certainly mean the part starting with "A strict partial order < on the object property expressions must exist such that each SubObjectPropertyOf(SUB PE) axiom in Ax fulfils the following conditions:" >Your axioms violate these >constraints as you have both SubObjectPropertyOf(brother sibling) and >SubObjectPropertyOf(SubObjectPropertyChain(sibling ...) brother). Now that you point me to it, I think that I can see it: I have to rewrite (in my mind) the axiom SubObjectPropertyOf(brother sibling) into the form: SubObjectPropertyOf( SubObjectPropertyChain(brother) sibling) This then matches the third of the acyclicity conditions "* SUB is of the form SubObjectPropertyChain(PE1 ... PEn) and PEi < PE for each 1 ? i ? n," with n = 1 in our case. So on the one hand, this condition demands that "brother(=PE1) < sibling(=PE)" must hold, while because of the other (the "real") sub property chain of my axiom set the same condition tells me that "sibling < brother" must hold. This is cyclic, so no strict partial order is possible. Huh, I did not see this before! (But it was pretty hidden! :)) >It is easy to see that allowing this kind of cycle would lead to >undecidability in the general case -- see page 10 of [1] for details. > >If you want to claim that these acyclicity restrictions are not very >clearly described in the OWL 1.1 spec, then I wouldn't want to argue >with you -- this section of the document clearly needs some work. An >alternative definition of these restrictions can be found in >Definition 2 of [2]. I will have a look at these papers. And (more importantly) I will further play around with sub property chains, and I will collect problems which I find when dealing with these acyclicity conditions in practice. I am going to report back to this list or the issues list, when I find problems which I think might be of general interest. Thanks for pointing me to the problems! So no perfect brother for now... Cheers, Michael > >Ian > >[1] http://web.comlab.ox.ac.uk/oucl/work/ian.horrocks/Publications/ >download/2004/HoSa04a.pdf >[2] http://web.comlab.ox.ac.uk/oucl/work/ian.horrocks/Publications/ >download/2006/HoKS06a.pdf > > >On 15 Oct 2007, at 09:19, Michael Schneider wrote: > >> [Also cc'ed to Tim Swanson, Ian Horrocks and Evren Sirin, because >> this mail >> can be regarded as a follow up to the thread "Inferring Properties >> based on >> Types"] >> >> Hi again, Ulrike! >> >>> -----Original Message----- >>> From: public-owl-dev-request@w3.org >>> [mailto:public-owl-dev-request@w3.org] On Behalf Of Ulrike Sattler >>> Sent: Friday, October 12, 2007 3:00 PM >>> To: Owl Dev >>> Subject: Re: Defining cross products in OWL-1.1 >>> >>> >>> On 12 Oct 2007, at 12:14, Michael Schneider wrote: >>> >>> >>> >>> [CC'ed Peter Patel-Schneider, because I cite him in this mail] >>> >>> Hi list! >>> >>> I have started to stroll around a little through the >>> OWL-1.1 issues list >>> this week, and I found this interesting one (issue 30) >>> yesterday evening: >>> >>> "Need a role descrption based on the "cross product" >>> of two concepts" >>> http://code.google.com/p/owl1-1/issues/detail?id=30 >>> >>> (Sorry, I cannot find out who the original author >>> "kashyap.vipul" was.) >>> >>> After reading this I was not really sure if this issue >>> is about specifying >>> cross products in general, or just about realizing a >>> specific scenario, with >>> or without the use of a cross product. But IMHO it /is/ >>> certainly a >>> noteworthy question if cross products can be specified >>> in OWL or not. >> >> After reconsidering both the original discussion in the issues list >> and your >> last mail, I am now pretty convinced that the focus of this >> discussion was >> *not* the question of defining cross products A X B. It seems that >> I was >> misled by the subject of this issue entry, so I >misunderstood the real >> issue. In this case, finding out that cross products can be >> specified in >> OWL-1.1 is, of course, not the interesting part anymore. :-/ >> >> Never mind, because I claim that even the real issue is solvable in >> OWL-1.1! >> >> Ulrike Sattler wrote: >> >>> Peter Patel-Schneider wrote: >>> >>> "You are asking for the ability to define roles. >>> >>> A similar definition would be >>> brother = sibling INTERSECTION range(Male) >>> using range(x) as a shorthand for crossProduct(owl:Thing,x) >>> >>> this is a confusing shorthand: >> >> If we forget about the "confusing shorthand" (this problem has been >> resolved >> now, I believe), the core question here seems to be: Can the >> 'brother' role >> be /fully/ defined in OWL to be a 'Male' 'sibling'? This question >> can be >> restated into the following task: Find a set of OWL-1.1 axioms >> which is >> equivalent to the two statements >> >> (1) FORALL x,y: brother(x,y) ==> sibling(x,y) AND Male(y) >> (2) FORALL x,y: sibling(x,y) AND Male(y) ==> brother(x,y) >> >> Ok, (1) is easy to translate: >> >> (A1) SubObjectPropertyOf(brother sibling) >> (A2) ObjectPropertyRange(brother Male) >> >> Because given a tuple (a,b) for which brother(a,b) is true. From >> (A1) we >> receive that sibling(a,b) is true. AND from (A2) we receive that >> Male(b) is >> also true, because: >> >> Ulrike Sattler wrote: >> >>> - if a property p has range X, say Male, then, whenever we >>> find a tuple (a,b) in p, we know that b must be an instance of >>> X. Eg, whenever a has a brother b, then b must be Male. >> >> Now to (2). I have already shown previously that a translation for >> this is >> possible: >> >> >> <http://lists.w3.org/Archives/Public/public-owl-dev/2007JulSep/ >> 0212.html> >> >> And by applying Ian Horrock's simplified version of such a >> translation, as >> given in >> >> >> <http://lists.w3.org/Archives/Public/public-owl-dev/2007OctDec/ >> 0065.html> >> >> we can translate (1) and (2) into the following set of >OWL-1.1 axioms: >> >> (A1) SubObjectPropertyOf(brother sibling) >> (A2) ObjectPropertyRange(brother Male) >> (A3) SubClassOf(Male ObjectSomeValuesFrom(_r owl:Thing)) >> (A4) SubObjectPropertyOf( >> SubObjectPropertyChain(sibling _r InverseObjectProperty >> (_r)) >> brother) >> >> where '_r' has to be some "fresh" role symbol, which isn't used >> anywhere >> else in the surrounding ontology (such is always available). >> >> The only thing to check is if these four axioms are allowed >> regarding the >> "nonstructural restrictions" chapter in the OWL-1.1 draft: >> >> <http://www.webont.org/owl/1.1/owl_specification.html#7> >> >> The role 'brother' is a "non-complex" role, because it is the super >> role of >> the sub property chain in (A4), so it is not allowed to occur in >> certain >> kinds of axioms. But 'brother' only occurs in an additional 'range' >> axiom >> and a sub property axiom, so there seems to be no danger here. >> >>> This expands expressive power (I'm pretty sure). >>> I don't know whether there is a reasoning algorithm >>> for this construct." >>> >>> no, there isn't. >> >> Well, there actually /is/, because by giving a translation into a >> set of >> OWL-1.1 axioms, any OWL-1.1 reasoner will do the job. Maybe you >> meant that >> there is no reasoning algorithm for /intersections/ of roles. But >> this isn't >> really needed here, because it is possible to encode the whole >> thing without >> using any kind of complex role operators, except sub property chains. >> >> So it turns out that the 'brother' relationship is even /exactly/ >> definable >> in OWL-1.1. >> >> Cheers, >> Michael >> >> -- >> 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=555 >> >> FZI Forschungszentrum Informatik an der Universität Karlsruhe >> Haid-und-Neu-Str. 10-14, D-76131 Karlsruhe >> Tel.: +49-721-9654-0, Fax: +49-721-9654-959 >> Stiftung des bürgerlichen Rechts >> Az: 14-0563.1 Regierungspräsidium Karlsruhe >> Vorstand: Rüdiger Dillmann, Michael Flor, Jivka Ovtcharova, Rudi >> Studer >> Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus > > -- 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=555 FZI Forschungszentrum Informatik an der Universität Karlsruhe Haid-und-Neu-Str. 10-14, D-76131 Karlsruhe Tel.: +49-721-9654-0, Fax: +49-721-9654-959 Stiftung des bürgerlichen Rechts Az: 14-0563.1 Regierungspräsidium Karlsruhe Vorstand: Rüdiger Dillmann, Michael Flor, Jivka Ovtcharova, Rudi Studer Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus
Received on Monday, 15 October 2007 16:13:16 UTC