# Re: yet another non-entailment (was Re: another revision of semantics document)

From: pat hayes <phayes@ai.uwf.edu>
Date: Fri, 6 Sep 2002 00:31:12 -0700
Message-Id: <p05111b0eb99e0956f5cb@[65.212.118.251]>
To: "Jeremy Carroll" <jjc@hplb.hpl.hp.com>

```
>I found one two, or rather an infinite set ...
>
>for any three natural numbers iii, jjj, kkk such that
>    iii+jjj>=kkk
>
>following Peter's semantics we have:
>
>
>:p rdfs:subPropertyOf :r .
>:q rdfs:subPropertyOf :r .
>
>entails
>
>_:x rdf:type rdfs:Class .
>_:x owl:intersectionOf [
>    <<:p owl:minCardinality iii>>
>    <<:q owl:minCardinality jjj>>
>] .
>_:x rdfs:subClassOf
>    <<:r owl:minCardinility kkk>> .
>
>(using notation from
>http://www.coginst.uwf.edu/users/phayes/RDFS2OWL-C.html
>)
>
>Since this entailment uses rather more arithmetic than I feel confortable
>with, I prefer it being a non-entailment.

I need to look at this example more closely (dont quote see why we
need the plus sign in the inequality) but the general point is well
taken. There is a danger in introducing arithmetic comparisons into
any logic. I think we need to be careful to state the cardinality
conditions with 'guards' on them so that the 'integers' involved are
restricted in some way, eg maybe totally ordered by < but not, say,
an arithmetic field.

Pat

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```
Received on Friday, 6 September 2002 04:58:24 GMT

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