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My impression of this as a programmer is that if one is modelling a system in which different people may have different beliefs then one must design the model accordingly, otherwise there will be bugs.

But that doesn't mean there's anything wrong with logic itself. Whatever model you come up with is still going to be based on classical logic so at some point you still need to assume that that remains valid in order to do anything at all. And I've never heard of a case where this could fail, at least not within the finite worlds one can in practice model.




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