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Re: An inconsistency or not?

From: Chris Purcell <cjp39@cam.ac.uk>
Date: Thu, 31 Mar 2005 00:28:37 +0100
Message-Id: <7cb088a212cb2b0330a8db03a26ac146@cam.ac.uk>
Cc: (wrong string) <minsu@etri.re.kr>
To: (wrong string) <50263336@student.cityu.edu.hk>

You assert:

     card({...}) = 2

This is only true if John != Johnny, which we do not know. Your 
argument is invalid.

> It is my second reply. Consider the interpretation of the cardinality 
> restriction..
>
> {x ∈ O | card({y ∈ O∪LV : <x,y> ∈ ER(p)}) = n}
>
> Substitute n = 1, x = Harry, p = hasFather into the interpretation..
>
> {Harry ∈ O | card({y ∈ O∪LV : <Harry,y> ∈ ER(hasFather)}) = 1}
>
> Then..
>
> {y ∈ {S(John),S(Johnny)} | card({John ∈ O∪LV : <Harry,y> ∈ 
> ER(hasFather)}) = 2 <> 1}
>
> Therefore the restriction (class axiom?), restriction(hasFather 
> cardinality(1)), is not satisified. Hence the collection of axioms is 
> not consistent.
Received on Wednesday, 30 March 2005 23:28:42 UTC

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