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shellac/int-vs-ext.txt

Created July 2, 2009 12:59
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int-vs-ext.txt
Given
a subclass of b
b subclass of c
* If <x,y> is in IEXT(I(rdfs:subClassOf)) then x and y are in IC and ICEXT(x) is a subset of ICEXT(y)
hence extension(a) subset of extension(b)
similarly extension(b) subset of extension(c)
thus extension(a) subset of extension(c) (transitivity of subset)
HOWEVER to complete this we need the extensional condition:
* <x,y> is in IEXT(I(rdfs:subClassOf)) if and only if x and y are in IC and ICEXT(x) is a subset of ICEXT(y)
(note if and only if)
extension(a) subset of extension(c), thus a subclass of b
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