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Re: AllDisjoint in RDF mapping

From: Pat Hayes <phayes@ihmc.us>
Date: Mon, 26 Feb 2007 17:10:44 -0600
Message-Id: <p06230906c20916e80bb0@[10.100.0.26]>
To: Michael Schneider <m_schnei@gmx.de>, public-owl-dev@w3.org

>Holger Knublauch wrote on Mon, 26 Feb 2007:
>
>>The goal should be to have some mechanism that allows users to 
>>enter and display a disjoint union, e.g. in
>>
>>    A = B xor C xor D
>>
>>assuming xor represents disjoint union.
>
>Hi, Holger!
>
>Just a side note (a little offtopic): I believe that the above is 
>not the best way to describe a disjoint union.

Yeh, this is an old trap. Binary xor is not associative, and n-ary 
xor is not a composition of the binary operation.

BTW, I would strongly urge that y'all follow Jim Hendlers advice and 
treat the assertion of the union and the assertion of disjointness as 
two separate items. Note that in standard mathematical terminology, 
disjoint union does not imply disjointness of the sets; a disjoint 
union, standardly indicated by the plus sign, is also called a 
discriminated union or a tagged union, and it contains two 'copies' 
of anything that is in the intersection of the two sets being 
unioned. Note that this (unlike what y'all are here calling a 
disjoint union) makes no assertions about the sets, is a genuine 
set-theoretic function, i.e. it is defined for any two sets, and it 
is associative, so the n-ary case is gotten by composing the binary 
case. These are all very desirable properties, which (I suggest) you 
should not abandon casually.

Pat Hayes


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Received on Monday, 26 February 2007 23:11:01 GMT

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