I don't think we need to redefine reasoning. Here's the definition of "reason" (the verb): "think, understand, and form judgments by a process of logic"

If Claude 4 provides a detailed, logical breakdown in its "reasoning" (yeah, that usage is overloaded), then we could say that there was logical inference involved. "But wait!", I already hear someone saying, "That token output is just the result of yet another stochastic process, and isn't directing the AI in a deterministic, logical way, and thus it is not actually using logic; it's just making something that looks convincingly like logic, but is actually a hallucination of some stochastic process". And I think this is a good point, but I find it difficult to convince myself that what humans are doing is so different that we cannot use the word "reasoning".

As a sidenote, I am _very_ tired of the semantic quagmire that is the current AI industry, and I would really appreciate a rigorous guide to all these definitions.