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Re: Inverse property on classes

by Uli Sattler :: Rate this Message:

On 15 May 2009, at 16:09, Cédric Thiébault wrote:

Would you use allValuesFrom <http://www.w3.org/TR/owl-guide/#owl_allValuesFrom> to create this weird pizza class that has all mozzarella as topping?
:Pizza_mozzarella_class :hasTopping all :Mozzarella_class

No. That's why I said that it wouldn't be that trivial. Here you're saying that "all toppings of Pizza_mozzarella_class's instances are instances of Mozzarella_class". But you need something else: "any instance of Pizza_mozzarella_class has *all* instances of Mozzarella_class as toppings". Do you see the difference? The second does imply that *any* instance of Mozzarella_class is a topping of an instance of the Pizza_mozzarella_class (provided the latter is non-empty) while the first does not.

So I need to define both sides of the relation?
:Pizza_mozzarella_class :hasTopping all :Mozzarella_class
:Mozzarella_class :isToppingOf all :Pizza_mozzarella_class

if this is what you want to say...? The above second axiom says that each instance of Mozzarella_class can *only* be a topping of Pizza_mozzarella_class...i.e., *if* a mozzarella is the topping of something, then this something is a Pizza_mozzarella....so you

- disallow other Pizzas to have mozzarella toppings, and

- you still can have mozzarellas that aren't toppings of anything (notice the *if* above)

In this case, I don't use anymore the inverse property?

hm, you use :hasTopping and :isToppingOf , so you should have an axiom saying that :isToppingOf is the inverse of :hasTopping, thus you still use inverse properties...indirectly.

I have the feeling that property characteristics like inverse and transitivity are useful on instances, not on classes.

why?! If I say that all children of Turtles only have parents who are Green (assuming that 'hasChild' is the inverse of 'hasParent'), then the class 'Turtle and hasChild some Thing' will be inferred to be a subclass of 'Turtle and Green'...so inverse properties *have effects* of the entailments regarding classes, if this is what you mean by 'are useful'

If we add an ingredient class to our ontology and a transitive property hasPart that is parent of hasTopping.
:Ingredient rdf:type owl:Class
:hasPart rdf:type owl:TransitiveProperty
:hasTopping rdf:type :hasPart

:Cheese_class rdf:type :Ingredient

:Pizza_mozzarella_class :hasTopping all :Mozzarella_class
:Mozzarella_class :hasPart some :Cheese_class

Would it be possible to know if my pizza has some cheese as ingredient?

assuming that you pizza is 'Pizza_mozzarella', no: because you only use :hasTopping *all* :Mozzarella_class

Actually, I want to use classes and not individuals because I need to reason on them and it seems that reasoners can only work on classes...

I'm not sure what you mean by "it seems that reasoners can only work on classes...". It is often a highly non-trivial modeling decision (to use classes or individuals to model certain things).

When I tried to find inferred classes from my instances it did not work...

how did you do this?

But when I used classes instead of instances, the reasoner created the inferred model.
In fact, if I was able to 'navigate' threw my ontology using the inverse and transitive properties on classes, it would be great. But for the moment, I can't.

I don't understand what you mean...what tool do you use?

Cheers, Uli

But I can do it easily with instances... that's why I'm stuck with individuals :-(

Thanks again Pavel!

Cedric

On Wed, May 13, 2009 at 4:40 PM, Pavel Klinov <klinovp@... <mailto:klinovp@...>> wrote:

Hello,

Cédric Thiébault wrote:

Hi,

[snip]

When I create an individual :Pizza_mozzarella and add a
property :hasTopping on :Mozzarella individual, I can work
with the inverse property on the topping and I see that
:Mozzarella :isToppingOf :Pizza_mozzarella. It works great
with individual.

But when I try to do the same test with classes:
:Pizza_mozzarella_class :hasTopping some :Mozzarella_class

But I cannot use the inverse property: :Mozzarella_class does
not know anything about :Pizza_mozzarella_class.

Is this normal ?

Yes. Notice that you are not making any claim here about
Mozzarella_class in general. You're only saying that all instances
of Pizza_mozzarella_class are related to *some* instance of
Mozzarella_class. Imagine a model in which there are 10,000
mozarrellas and only one of them is used as a topping on all
pizzas (it would be a satisfying model). Would you want to be able
to conclude something general about 9,999 mozarellas basing on
only one instance?

Are inverse properties usable only on individuals ?

Well, it depends on what you mean by "using". For example, you can
define a class (and an instance) of pizzas which has *all*
instances of Mozzarella as toppings (although it's not that
trivial). Then, of course, you'll be able to infer that
:Mozzarella_class :isToppingOf some :that_weird_pizza_class.

Cheers,
Pavel

Thanks for your help :-)

Cedric

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