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RE: Unclear about Nonstructural Restriction [WAS: Inferring Properties based on Types]

From: Michael Schneider <schneid@fzi.de>
Date: Fri, 5 Oct 2007 17:42:05 +0200
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A040A6A6@judith.fzi.de>
To: "Evren Sirin" <evren@clarkparsia.com>
Cc: "Owl Dev" <public-owl-dev@w3.org>

Hi, Evren!

Evren Sirin wrote on Friday, October 05:

>On 10/5/07 7:04 AM, Michael Schneider wrote:
>>
>> When I tried to verify this for my own understanding, I had 
>difficulties to
>> understand the respective paragraph in this chapter. The first
>> "nonstructural restriction" says (at the end of the chapter):
>>
>>     * Only simple object properties are allowed to occur 
>>       in [the axiom closure] Ax in
>>
>>       * ObjectMinCardinality, ObjectMaxCardinality, 
>ObjectExactCardinality, 
>>         and ObjectExistsSelf classes, 
>>         and
>>
>>       * ObjectPropertyFunctional, InverseFunctionalObjectProperty, 
>>         ObjectPropertyIrreflexive, ObjectPropertyAsymetric, 
>>         and DisjointObjectProperty axioms.
>>
>> Let's assume for this discussion that it is clear what a 
>"simple" object
>> property is in this context, because this is not the 
>important bit here. 
>>
>> What I do not understand from this text is, what actually is 
>allowed for
>> "simple" properties, and what actually is not allowed for non-simple
>> properties. Does the above paragraph say that simple 
>properties can occur in
>> /all/ of the above axioms together (all axiom from both items '*')? 
>
>Yes, simple properties can occur in any of the class expressions and 
>axioms in any combination. 

Thanks! This is what I had supposed.

>Note that, the only reason having two 
>distinct lists in the above definition is to group class 
>expressions (or 
>in this case more specifically restrictions) and axioms separately for 
>presentation purposes. Other than that there is no significance to 
>having two lists.

Ah, ok, this was one of the things which have confused me. Thanks for
clarifying this! 

>> Or just
>> in one of the first item and one of the second item? And for 
>non-simple
>> properties: Aren't they allowed to occur in /any/ of the 
>above axioms, or
>> are they only allowed in e.g. a 'ObjectMinCardinality' 
>(first item), but
>> then not also in a 'AsymmetricObjectProperty' (second item)? 
>
>Similarly non-simple properties cannot occur in any of the 
>restrictions 
>or axioms mentioned above.

Ok, I understand, it's really that restrictive. Thanks.

>> And if a
>> non-simple property is allowed to occur in an 
>'ObjectExistsSelf' restriction
>> (first item), is it then also allowed to occur in another of the
>> restrictions of the first item, e.g. in an 'ObjectMinCardinality'
>> restriction? 
>>   
>I guess it is clear by now that non-simple properties are not 
>allowed to 
>occur in self restrictions.

Yes!

>> Ok, a lot of confusing questions, but this just results from me being
>> confused by this paragraph. :) I hope you see my problem. 
>From what you
>> wrote above, I belive that you have more background 
>knowledge about how
>> these nonstructural restrictions are meant. But for me, who 
>only has this
>> single excerpt from the OWL-1.1 draft, it is hard to see 
>what the correct
>> intention is. 
>>   
>
>Yes, the non-structural restrictions are a little bit tricky. 
>Note that, 
>there was a similar restriction on OWL-DL but there were far fewer 
>language constructs interacting which made the definition simpler. 
>Section 8.2 of OWL reference [1] describes this restriction as follows:
>
>"OWL DL requires that no cardinality constraints (local nor 
>global) can 
>be placed on transitive properties or their inverses or any of their 
>superproperties."

I had never heard about this restriction on transitive properties before.
But when I read through the "Nonstructural" chapter for OWL-1.1 yesterday, I
found this out myself, and this came to a big surprise to me:

  "An object property expression PE 
  [which is an object property P or its inverse]
  is /composite/ in [the axiom closure] Ax [of some ontology] 
  if Ax contains an axiom of the form
    [...]
    * ObjectPropertyTransitive(PE), [...]

And later in the chapter it is explained that if such a composite object
property P is (for instance) a sub property of some other property Q, then Q
gets non-simple, i.e. it cannot occur in any of those axioms listed in the
nonstructural restriction conditions. Well, such a sub property relationship
only has to exist in the /axiom closure/ Ax of some ontology. But the axiom
closure Ax of any ontology, which has a property P, always contains the
trivial sub property axiom

  SubObjectPropertyOf(P P)

So this means that the transitive property P /itself/ is a non-simple object
property. And so I really cannot put cardinality restrictions (and more) on
P. I hope that I have understood the chapter correctly in this way, because
it is not that easy to understand.

>Non-simple property definition in OWL 1.1 generalizes "transitive 
>properties or their inverses or any of their superproperties" to 
>consider subproperty chains. 

I think that these nonstructural restrictions might become an ugly problem
in practice. For example, when I define an 'uncle' property via a
SubPropertyChain of the form:

  SubObjectPropertyOf(subObjectPropertyChain(parent brother) uncle)

Then 'uncle' is a non-simple property, because it's composite. But this
means that I cannot declare it to be

  * an IrreflexiveObjectProperty
  * a DisjointObjectProperty to, for example, another property 'aunt'

These would normally be natural property characteristics for an 'uncle'
property, but they are not possible under the nonstructural restriction
conditions. And every super property of 'uncle', e.g. an additional
'relative' property, will also be hit by the nonstructural restrictions.
Pretty bad IMHO!

>Disallowed constructs are also extended 
>from cardinality constraints to include some of the new constructs 
>introduced in OWL 1.1. More technical details about these restrictions 
>and why they are required to ensure decidability can be found in [2].
>
>Hope this helps,
>
>Evren

Yes, this was very informative! Many thanks, Evren!

Cheers,
Michael

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
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Fax  : +49-721-9654-727
Email: Michael.Schneider@fzi.de
Web  : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555

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Received on Friday, 5 October 2007 15:42:18 GMT

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