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Your 'logic' is flawed. You are missing the implied direction of the 'is' statements - they go in towards the centre, but not out from the centre. This means that the diagram does not imply A is B, and B is C; rather it is implying A is B, and C is B (as well as D is B). 'Is' is not necessarily identity (and not in this case), it can also be used for ...

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