So if I removed the lungs of chicken, you would no longer consider it a bird? Or if I surgically modified some other creature (e.g. a pig) to have circulatory lungs, you would consider this to be a bird?

Different people's concepts of "bird" agree on most real-world examples, but I see no reason why they should agree on all conceivable hypothetical examples, so the task of "defining" a word is futile.

Warrigal gave a good recognition algorithm: it inspects a small subset of properties and gives an answer that accords with our judgment in most real-world cases. That's about as far as one can or should go when "defining" something outside of mathematics.