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

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. 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.

> 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.

> 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.
> 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."

Non-simple property definition in OWL 1.1 generalizes "transitive 
properties or their inverses or any of their superproperties" to 
consider subproperty chains. 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
 
[1] http://www.w3.org/TR/owl-ref/#OWLDL
[2] 
http://web.comlab.ox.ac.uk/oucl/work/ian.horrocks/Publications/download/2006/HoKS06a.pdf
> Cheers,
> Michael
>
> --
> Dipl.-Inform. Michael Schneider
> FZI Forschungszentrum Informatik Karlsruhe
> Abtl. Information Process Engineering (IPE)
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> Email: Michael.Schneider@fzi.de
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>
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>

Received on Friday, 5 October 2007 12:55:21 UTC