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Re: Can an object property be both functional and transitive?

From: Jie Bao <baojie@gmail.com>
Date: Mon, 26 Jan 2009 15:17:42 -0500
Message-ID: <b6b357670901261217r5ce80c2fqf1a193e8339964d8@mail.gmail.com>
To: Bijan Parsia <bparsia@cs.man.ac.uk>
Cc: W3C OWL Working Group <public-owl-wg@w3.org>

Thanks Bijan for the reference

On Mon, Jan 26, 2009 at 2:50 PM, Bijan Parsia <bparsia@cs.man.ac.uk> wrote:
> On 26 Jan 2009, at 19:36, Jie Bao wrote:
>> I come across this issue when update the Quick Reference. This issue
>> may already have been discussed, as I was not in the WG from the very
>> beginning. I just need a confirmation.
>> In OWL 1 DL, This is not allowed, for decidability considerations.
>> http://www.w3.org/TR/owl-semantics/syntax.html#
>> In OWL 2 DL, it is allowed, i.e., an object property CAN be both
>> functional and transitive
>> http://www.w3.org/2007/OWL/wiki/Syntax#Object_Property_Axioms (Figure 15)
> No. See the global restrictions:
>        http://www.w3.org/2007/OWL/wiki/Syntax#Global_Restrictions_on_Axioms
> """Each axiom in Ax of a type from the following list contains an object
> property expression that is simple in Ax:
> FunctionalObjectProperty, InverseFunctionalObjectProperty,
> IrreflexiveObjectProperty, AsymmetricObjectProperty, and
> DisjointObjectProperties."""
It looks the same as the OWL 1 case. However, we need to be careful
with the definition of ObjectPropertyAxiom after Figure 15 :

ObjectPropertyAxiom :=
    SubObjectPropertyOf | EquivalentObjectProperties |
    DisjointObjectProperties | InverseObjectProperties |
    ObjectPropertyDomain | ObjectPropertyRange |
    FunctionalObjectProperty | InverseFunctionalObjectProperty |
    ReflexiveObjectProperty | IrreflexiveObjectProperty |
    SymmetricObjectProperty | AsymmetricObjectProperty |

It very likely to give users a wrong impression that
FunctionalObjectProperty axiom and TransitiveObjectProperty axiom (as
well as for some other simple, non-simple cases) can co-exist for the
same property. A note to "Global Restrictions on Axioms" may be needed
here to draw users' attention.

In OWL 1 DL, it is directly clear from its definitive text

'ObjectProperty(' individualvaluedPropertyID ['Deprecated'] { annotation }
                { 'super(' individualvaluedPropertyID ')' }
                [ 'inverseOf(' individualvaluedPropertyID ')' ] [ 'Symmetric' ]
                [ 'Functional' | 'InverseFunctional' | 'Functional'
'InverseFunctional' | 'Transitive' ]

Another issue is that, if the UML diagrams are meant to be a normative
definition of OWL 2, can the "Global Restrictions on Axioms" be part
of the UML definition, or they are out of the expressivity of UML,
thus no standard UML tool can actually accept a complete OWL 2

>> As far as I can guess, this may reflect the recent progress on
>> undecidability results of DL with number restrictions.
>> Yevgeny Kazakov, Ulrike Sattler, and Evgeny Zolin. How many legs do I
>> have? Non-simple roles in number restrictions revisited. In Proc. of
>> the 14th Int. Conf. on Logic for Programming, Artificial Intelligence,
>> and Reasoning (LPAR'2007), Yerevan, Armenia October 15-19, 2007.
>> http://www.cs.man.ac.uk/~ezolin/pub/zolin_2007_RBox.pdf
> [snip]
>> Since OWL 2 has  inverse properties (role), is there any restriction
>> on its use to ensure the decidability of OWL 2 DL?
> Since that condition is even more complex, I'm not sure it's a good idea to
> add it at this time. (Simple vs.  non-simple is much easier.) I do hope
> implementations will go beyond the coarser restriction over time.
How implementor can be aware of this?

> Cheers,
> Bijan.

Received on Monday, 26 January 2009 20:18:18 UTC

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