From: Dmitry Tsarkov <dmitry.tsarkov@gmail.com>

Date: Mon, 1 Oct 2007 16:08:20 +0100

Message-ID: <7b84f3a00710010808x7991abc8te0a67c5a3b61da45@mail.gmail.com>

To: "Evren Sirin" <evren@clarkparsia.com>

Cc: "Michael Schneider" <schneid@fzi.de>, "Ian Horrocks" <horrocks@cs.man.ac.uk>, "Swanson, Tim" <tim.swanson@semanticarts.com>, "Owl Dev" <public-owl-dev@w3.org>

Date: Mon, 1 Oct 2007 16:08:20 +0100

Message-ID: <7b84f3a00710010808x7991abc8te0a67c5a3b61da45@mail.gmail.com>

To: "Evren Sirin" <evren@clarkparsia.com>

Cc: "Michael Schneider" <schneid@fzi.de>, "Ian Horrocks" <horrocks@cs.man.ac.uk>, "Swanson, Tim" <tim.swanson@semanticarts.com>, "Owl Dev" <public-owl-dev@w3.org>

[reply to the list this time] On 10/1/07, Evren Sirin <evren@clarkparsia.com> wrote: [skip] With these modifications we get the > following set of axioms to express the above rule in OWL 1.1: > > (R4) SubObjectPropertyOf( SubObjectPropertyChain(sibling manman) > brother) > (A1') ReflexiveObjectProperty( manman ) > (A3) ObjectPropertyDomain( manman Man ) > (A4) FunctionalObjectProperty( manman ) One could possibly define a macro that would translate a user-friendly > syntax into this set of axioms (and would generate the a unique property > like manman for different uses). I think this wouldn't work as expected. To be more precise, it would silently introduce additional restrictions to the model. As the semantics of the construction ReflexiveObjectProperty( manman ) is the following GCI SubClassOf ( owl:Thing ObjectExistsSelf(manman) ) and we have a domain of the property manman, than the (implicit) axiom SubClassOf (owl:Thing, Man) would be added to the ontology. The same would happen for every other reflexive property with either range or domain defined. So, every concept in the ontology would be a Man (in addition to all other supertypes). Best, Dmitry. Cheers, > Evren > > [1] http://webont.org/owl/1.1/owl_specification.html#7 > > > On 9/29/07 9:16 AM, Michael Schneider wrote: > > Hello, Ian! > > > > Ian Horrocks wrote on September 16, 2007: > > > > > >> On 15 Sep 2007, at 23:18, Michael Schneider wrote: > >> > >> > >>> Hi, Tim! > >>> > >>> > >>>> -----Original Message----- > >>>> From: public-owl-dev-request@w3.org > >>>> [mailto:public-owl-dev-request@w3.org] On Behalf Of Swanson, Tim > >>>> Sent: Saturday, September 15, 2007 12:18 AM > >>>> To: public-owl-dev@w3.org > >>>> Subject: Inferring Properties based on Types > >>>> > >>>> > >>>> Is there any way in OWL (or in any of the proposed extensions) to > >>>> express an inference rule like the following: > >>>> > >>>> (?x :P ?y) > >>>> :A(?y) > >>>> => > >>>> (?x :R ?y) > >>>> > >>>> > >>>> For a more concrete example: > >>>> > >>>> (?x :hasSibling ?y) > >>>> :Male(?y) > >>>> => > >>>> (?x :hasBrother ?y) > >>>> > >> It isn't possible in either OWL or OWL 1.1. > >> > > > > This is a late response, but it kept me wondering, if there is an easy > to > > understand reason for /why/ Tim's rule > > > > (R1) FORALL x,y: sibling(x,y) AND Man(y) ==> brother(x,y) > > > > is not possible to express in OWL-1.1. Now, I finally found the time to > > think about this question more deeply. And, to my surprise, it seems to > me > > that there still is a way to make it happen. Can this be the case? > > > > My idea is trying to simulate the class 'Man(.)' by a role > 'manman(.,.)', > > which is intended to "behave equivalently" to 'Man'. I formalize this > idea > > by the the following set of two statements: > > > > (S1) FORALL x: manman(x,x) <==> Man(x) > > (S2) FORALL x,y: manman(x,y) ==> x = y > > > > By (S1), I try to express that there is a "natural" one-to-one > > correspondence between instances of class 'Man', and "loop" instances of > > role 'manman' (by "loop" I mean role instances of the form > 'manman(x,x)'). > > And (S2) is meant to express that (S1) already fully specifies the > 'manman' > > role. > > > > Using (S1), I can restate Tim's original rule (R1) in the following way: > > > > (R2) FORALL x,y: sibling(x,y) AND manman(y,y) ==> brother(x,y) > > > > And I claim (see below for my argumentation) that from (S2) it follows > that > > (R2) is equivalent to: > > > > (R3) FORALL x,y: [ EXISTS z: sibling(x,z) AND manman(z,y) ] ==> > > brother(x,y) > > > > Then, (R3) can be translated into an OWL-1.1 "sub property chain": > > > > (R4) SubObjectPropertyOf( SubObjectPropertyChain(sibling manman) > brother > > ) > > > > And as you told me in a previous mail about the "uncle" problem, I am > really > > allowed to build such complex sub role chains, where the super role, > > 'brother' here, may be different from the chained roles, 'sibling' and > > 'manman' here. > > > > BTW: In this mail, I will always use for OWL-Axioms the (hopefully :)) > most > > current functional syntax and semantics as specified in [1]. > > > > So, /if/ my simulation of class 'Man' by role 'manman' is adequate, and > /if/ > > I were able to translate the statement set {(S1),(S2)} into an > equivalent > > OWL-1.1 axiom set {A1,...,An}, /then/ I were able to express Tim's rule > (R1) > > as the OWL-1.1 axiom set {(R4),A1,...,An}. > > > > Before I further discuss this question, I will first try to give an > argument > > for my claim that from (S2) I can infer the equivalence of (R2) and > (R3). > > For this to be true, AFAICS it suffices to show that the predicates p > and q, > > defined by > > > > p(x,y) := sibling(x,y) AND manman(y,y) > > q(x,y) := EXISTS z: sibling(x,z) AND manman(z,y) > > > > are equal under the condition (S2). This seems to be the case: > > > > * Case "(S2) ==> FORALL x,y: [p(x,y) ==> q(x,y)]": Given arbitrary > > instances x and y, for which sibling(x,y) and manman(y,y) both hold. I > > define z := y, which provides me the existence of some z, for which both > > sibling(x,z) and manman(z,y) hold. (Note that this direction of the > argument > > did not even use condition (S2)). > > > > * Case "(S2) ==> FORALL x,y: [q(x,y) ==> p(x,y)]": Given arbitrary > > instances x and y, and let's further assume that some instance z exists, > for > > which sibling(x,z) and manman(z,y) both hold. Then we can conclude from > (S2) > > that z = y. Hence, both sibling(x,y) and manman(y,y) hold. > > > > Thus, (R2) and (R3) really seem to be equivalent within the context of > the > > statement set {(S1),(S2)}. > > > > So the remaining question is: Can I express the statement set > {(S1),(S2)} in > > OWL-1.1 ? > > > > First, I split (S1) into the equivalent statement set > > > > (S1a) FORALL x: Man(x) ==> manman(x,x) > > (S1b) FORALL x: manman(x,x) ==> Man(x) > > > > Next, I claim that the statement set {(S1b),(S2)} is equivalent to the > > statement set {(S1b'),(S2)}, where (S1b') is given by: > > > > (S1b') FORALL x: [ EXISTS y: manman(x,y) ] ==> Man(x) > > > > Again, it suffices to show that the predicates P and Q, defined by > > > > P(x) := manman(x,x) > > Q(x) := EXISTS y: manman(x,y) > > > > are equal under the condition (S2). The argumentation for this is pretty > > analog to the argumentation for the "(S2) ==> [(R2) <==> (R3)]" claim > above. > > Well, I won't perform this a second time. :) > > > > So what I have to do now is to find a set of OWL-1.1 axioms, which are > > equivalent to the following set of three statements: > > > > (S1a) FORALL x: Man(x) ==> manman(x,x) > > (S1b') FORALL x: ( EXISTS y: manman(x,y) ) ==> Man(x) > > (S2) FORALL x,y: manman(x,y) ==> x = y > > > > Here is my proposed set of OWL-1.1 axioms: > > > > (A1) SubClassOf( Man ObjectExistsSelf(manman) ) > > (A2) SubClassOf( ObjectMinCardinality(1 manman owl:Thing) Man ) > > (A3) ObjectPropertyDomain( manman Man ) > > (A4) FunctionalObjectProperty( manman ) > > > > First, I deduce all statements from the axiom set: > > > > * Deduction of (S1a): (A1) is the equivalent translation of (S1a), > > because 'ObjectExistsSelf(R)' denotes the class {x:R(x,x)}. > > > > * Deduction of (S1b'): (A2) is the equivalent translation of (S1b'), > > because 'ObjectMinCardinality(1 R owl:Thing)' denotes the class {x: > > #{y:R(x,y)} >= 1}. > > > > * Deduction of (S2): Given arbitrary instances x and y, for which > > manman(x,y) holds. So, x is in the domain of manman. Thus, from (A3) it > > follows that Man(x) holds. This allows me to conclude from (A1) that > > manman(x,x) also holds. And by (A4), I get (x,y) = (x,x), hence x = y. > > > > Second, I deduce all axioms from the statement set: > > > > * Deduction of (A1): (A1) is the equivalent translation of (S1a). > > > > * Deduction of (A2): (A2) is the equivalent translation of (S1b'). > > > > * Deduction of (A3): From (S1a), I learn that for each Man x there > > exists a role instance manman(x,.), thus Man is a subset of > domain(manman). > > >From (S1b') I learn that whenever there is some role instance > manman(x,.), > > then x is a Man, thus domain(manman) is a subset of Man. Hence > > domain(manman) = Man. > > > > * Deduction of (A4): Given arbitrary instances x, y and z, for which > > manman(x,y) and manman(x,z) both hold. From (S2) it follows x = y, and x > = > > z. Hence y = z, i.e. manman is a functional role. > > > > So, it turnes out that the statement set {(S1a),(S1b'),(S2)} is > equivalent > > to the OWL-1.1 axiom set {(A1),(A2),(A3),(A4)}. And I showed before that > > {(S1a),(S1b'),(S2)} is equivalent to {(S1),(S2)}. And the latter > statement > > set had made it possible to express (R1) in the form of the OWL-1.1axiom > > (R4). So it seems to me that Tim's rule really is expressable in OWL-1.1, > as > > the axiom set > > > > { (R4), (A1), (A2), (A3), (A4) } (Tim's Rule expressed in OWL-1.1 > ) > > > > Did I make a mistake anywhere? > > > > > > Cheers, > > Michael > > > > [1] http://www.webont.org/owl/1.1/semantics.html#2 > > > > > > > >> The "work-around" given below by Michael is similar to what you would > >> get be using a suitable DL-safe rule -- intuitively, this is a rule > >> of a form such that it will only affect named individuals. An > >> arbitrary rule (such as the one you give above) can be transformed > >> into a DL-safe one by introducing a new unary predicate, say > >> NamedIndividual, that is true for all named individuals (this can be > >> achieved by adding the ground fact => NamedIndividual(i) for every > >> individual i occurring in the ontology), and by adding atoms > >> NamedIndividual(?v) to the body of the rule for each variable ?v used > >> in the rule. > >> > >> Of course using a DL-safe rule (or equivalently Michael's work- > >> around) with an ontology O will *not* (by itself) result in > >> entailments such as the class of people having a male sibling being a > >> subclass of the class of people having a brother. > >> > >> Regards, > >> Ian > >> > >> > >> > >>> I think, you can at least do the following: > >>> > >>> First, use the inverses of the roles 'hasSibling(.,.)' and > >>> 'hasBrother(.,.)', called 'isSiblingOf(.,.)' and isBrotherOf(.,.)', > >>> respectively. > >>> > >>> With this, the following rule is equivalent to yours: > >>> > >>> (1) isSiblingOf(y,x), Man(y) => isBrotherOf(y,x) > >>> > >>> This can be transformed into: > >>> > >>> (2) y IN {z|isSiblingOf(z,x)} AND Man(y) => y IN > >>> > >> {z|isBrotherOf(z,x)} > >> > >>> And this translates (and generalizes) into the following OWL/DL > >>> (1.0) axiom: > >>> > >>> (3) SubClassOf( > >>> intersectionOf( > >>> restriction( isSiblingOf value(x) ) > >>> Class(Man) > >>> ) > >>> Restriction( isBrotherOf value(x) ) > >>> ) > >>> > >>> Problem with this approach: You need one such axiom for each > >>> individual x > >>> (the variable 'x' appears free in (2)). > >>> > >>> 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, 1 October 2007 15:08:32 UTC

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