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At Wikipedia, I read:

Logic arose (see below) from a concern with correctness of argumentation. Modern logicians usually wish to ensure that logic studies just those arguments that arise from appropriately general forms of inference. For example, Thomas Hofweber writes in the Stanford Encyclopedia of Philosophy that logic "does not, however, cover good reasoning as a whole. That is the job of the theory of rationality. Rather it deals with inferences whose validity can be traced back to the formal features of the representations that are involved in that inference, be they linguistic, mental, or other representations".

By contrast, Immanuel Kant argued that logic should be conceived as the science of judgment, an idea taken up in Gottlob Frege's logical and philosophical work, where thought (German: Gedanke) is substituted for judgment (German: Urteil). On this conception, the valid inferences of logic follow from the structural features of judgments or thoughts.

I can't say that I've read much (e.i., any) Kant, so I'm asking from a position of ignorance. So far I haven't even discovered where I might read Kant's own expression of the relationship between logic and reason in general.

Does Kant say that whenever we are using good reasoning, we are following logic whether we know it or not? (That's what I get from the Wikipedia quote above.)

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The main source would be The Critique of Pure Reason, but an accesible book is his Prolegomena which goes straight to the point.

Aristotle had stumbled upon the structure of the syllogisms and invented the traditional logic, which alone was in use up until modern times. Kant in turn wasn't arguing against or trying to outperform Aristotelean logic, but was instead arguing against the empiricist view, that experience alone counts on the one hand - and on the other against the metaphysicians, who opposed to the empiricists, held reason in high regard. The former group led by great philosopher David Hume, who was close to willing to abolish fundamental concepts such as causality, was a serious threat to religion, ethic and science as Kant saw it. The latter considered reason as an all to valid source of knowledge - Kant is trying to justify how metaphysics itself can be valid at all and why. Kant wasn't trying to modify the Aristotelian logic itself as mentioned before, but grounded it's source as a active process, where the brain has the ability to schematize what ever goes through it like a stamp, producing judgements. His major insight was that the logic stems from reason itself, also termed the Copernican revolution.

Thinking itself involves judging in Kant's regard. Judging is an innate ability, which is why reason and logic are so closely intertwined.

To ease it up, a judgement is simply a sentence like "This is a horse". Let's analyze this sentence, which surely involves some forms of judging. "This" is something particular, "is" refers to existence, and "a horse" refers to one or more of the pool of horses. Simply gazing out, dozing off or experiencing without giving thougths to it, does is contrast not necessarily rely on judging things. The oneness or particularity of the horse may or may not exist in reality, it could be a fatamorgana or not, but the distinct logical concepts themselves is no longer up for questioning in the way the empiricists had done. Kant limited and narrowed the scope of reason and in turn the nature of metaphysics.

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