With regard to the law of the excluded middle you have it correctly. However it is frequently not used in normal speech (e.g. "I do not beleive that God exists" often means "I do not beleive that God exists" - in a formal two-valued logic this violates the law of the excluded middle).
With regard to wave-particle duality there is a contradiction between the behaviour of a particle and that of a wave. That is, light must formally speaking be neither but instead something that bheaves in some ways like both. And this points again to logic being an issue of semantics, since the resolution of the contradiction is to point out that light neither fully fits the definition of a wave nor of a particle.
As to the idea of "non-contradiction" having a source I wouldn't even try to explain it. I reject the idea on the grounds that it makes no sense to me. That's why I asked you fro your explanation to see if you had thought of something I'd missed.