What does [a, b] mean in your opinion? In boost interval it means that the resulting value of a computation involving intervals is somewhere in that range. That is quite universal statement. Problem is boost interval itself conflicts with it.
As on that example value in interval [-inf, -1] U [1, inf] cannot be in the range (-1, 1). And boost interval class tells it can (on the example suggested by mine and implemented as test example by Mark)
It's not set theory, it's not multi-inverval. You can different results if you do operations in differen order... that's all fine because it's not about math but about numerical computations. So please stick to the boost definition is you want to discuss that. If you do that then I'll reply. That is the reason for function not able to return correct result MUST throw exception and MUST NOT return corrupted result instead. What kind of boost definition you need to discuss such an obvious practice?