# Test Cases: Extended Cardinality Testing

From: Thorsten Liebig <liebig@informatik.uni-ulm.de>
Date: Fri, 16 May 2003 15:47:50 +0200
Message-ID: <3EC4EC06.7020209@informatik.uni-ulm.de>
To: Jeremy Carroll <jjc@hpl.hp.com>

```
I found two bugs in section 7.3.4 Extended Cardinality Testing:

<description-logic/Manifest902#test>:
The description says:
"This non-entailment can be replicated for any three natural numbers
i, j, k such that i+j < k. In this example, they are chosen as 2, 3 and 6."
but the conclusion is (in Racer syntax):

(define-primitive-concept nonconclusions902
(and (at-least 2 p)
(at-least 3 q)
(at-least 6 r)))

which is indeed satisfiable.
I suppose the following conclusion was intended:

(define-primitive-concept nonconclusions902
(and (at-least 2 p)
(at-least 3 q)
(at-most 4 r)))

But since at-most represents a "less or equal" condition
(http://www.w3.org/TR/owl-semantics/direct#owl_maxCardinality_semantics)
the description should then say "... i, j, k such that i+j =< k. In this
example, they are chosen as 2, 3 and 4."

The same is to <description-logic/Manifest904#test>.

BTW: the current tests are not very sophisticated. I suggest
to add more complex cardinality test.

E.g. the following entailments:

(define-primitive-concept conclusion-x1
(and (at-least 2 p)
(at-most 2 q)
(exactly 3 r)))

(define-primitive-concept conclusion-x2
(and (at-most 2 p)
(at-least 4 r)
(at-most 2 q)))

(define-primitive-concept conclusion-x3
(and (at-most 2 p)
(at-least 4 r)
(all r A)
(at-least 3 q)))

Or even more complex:

(define-primitive-concept C)
(define-primitive-concept A C)
(define-primitive-concept B (and C (not A)))
(define-primitive-concept D C)
(define-primitive-role r :range C)
(define-primitive-role p :parent r :range A)
(define-primitive-role q :parent r :range B)
(define-primitive-role s :parent r :range D)

(define-primitive-concept conclusion-x4
(and (exactly 3 p)
(exactly 3 q)
(exactly 3 s)
(at-most 6 r)))

And some corresponding non-entailments.

Thorsten

--
_____________________________________________________________
Thorsten Liebig              Abteilung Künstliche Intelligenz
Tel.: +49 731 502 4207                Fakultät für Informatik
Fax.: +49 731 502 4119                        Universität Ulm
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Received on Friday, 16 May 2003 09:47:55 UTC

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