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In countries like the United States and England, where thought about law has focused primarily on adjudication, legal reasoning is often identified with the intellectual processes by which judges reach conclusions in deciding cases. [...] When legal reasoning is conceived of in these broader terms, it is seen to involve not only, and not primarily, the application of rules of formal logic but also other methods of exposition.

Definitions of rationale. (law) an explanation of the fundamental reasons (especially an explanation of the working of some device in terms of laws of nature) “the rationale for capital punishment”

Latin, "rationale for the decision." The term refers to a key factual point or chain of reasoning in a case that drives the final judgment. When considering earlier cases as precedent, courts often ask parties to be very clear about how they interpret the main guiding principle or ratio decidendi of the earlier case.