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Re: DAML+OIL - subsumption and multiple constraints on the same property

From: Thorsten Liebig <liebig@informatik.uni-ulm.de>
Date: Thu, 15 May 2003 10:11:48 +0200
Message-ID: <3EC34BC4.5060501@informatik.uni-ulm.de>
To: Matt Halstead <matt.halstead@auckland.ac.nz>
Cc: www-rdf-logic@w3.org

Matt Halstead schrieb:
> I am beginning to confuse myself with direct subClass relationships in 
> DAML+OIL.  The example follows :

If you transform your DAML+OIL code into Description Logics it will look

> Class A
>     subClassOf
>          hasObject    X  1*     ( means property hasObject  hasClass  X
>                                    with cardinality 1 or more)

(define-concept A (at-least 1 hasObject X))

> Class B
>     subClassOf        A
>     subClassOf
>          hasObject    Y   1=
>     subClassOf
>          hasObject    Z    1*

(define-primitive-concept B (and A
				 (exactly 1 hasObject Y)
				 (at-least 1 hasObject Z)))

> Class X

(define-primitive-concept X)

> Class Y
>      subClassOf       X

(define-primitive-concept Y X)

> Class Z
>      subClassOf       X

(define-primitive-concept Z X)

> What I am trying to do
> Class A has a property hasObject that can be one or more objects of 
> class X.  Now I want to make a more specialized form of Class A called 
> Class B that is a subclass of A, but has the restrictions that it needs 
> exactly one object of Class Y and at least 1 or more objects of Class Z. 
>  Class Y and Z are more specialized forms of Class X.  If I take away 
> the subClass of A restriction of Class B then I can still look at it and 
> say members of Class B are certainly members of Class A.

No, since A is defined with a necessary, but not sufficient condition
an object is of class A iff it is explicitly defined as an object of A.

>  But now I seem 
> to have lost the explicit feeling that subClass of A gave, especially 
> when using an editor such as OilEd.

I'm not sure about your question here, but if you remove the subClassOf
statement and define A with help of a necessary and sufficient condition
you can deduct that B is a subClassOf A.
(For example the Racer DL-reasoner will do that if you feed him with the
above by removing "A" from the definition of B and changing "define-primitive-
concept" with "define-concept" in the definition of A).

> The interpretation of multiple contraints on the same property
> I need to understand if my thinking is correct.  The way I interpret 
> Class B is as follows :
> There are 3 anonymous classes that Class B is some function of.
> 1) the class of all individuals that have at least 1 or more hasObject 
> properties of type X
> 2) the class of all individuals that have at exactly 1 property 
> hasObject of type Y
> 3) the class of all individuals that have at least 1 or more hasObject 
> properties of type Z
> 2) and 3) are subsets of 1)
> We now form the conjunction of these restrictions, so that Class B is 
> the class of individuals that have exactly one hasObject property of 
> type Y and at least one or more hasObject properties of type Z, and that 
> this forms a subset of the class of individuals that have 1 or more 
> hasObject properties of type X.  The fact I have used subclass say that 
> these are necessary, but not sufficient conditions for membership.
> Is my interpretation is correct?
> regards
> Matt

Received on Thursday, 15 May 2003 04:18:41 UTC

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