formally

This adverb describes adherence to established structures, whether they are social, legal, or logical. In social contexts, it refers to a level of decorum and dress that is ceremonial or stiff, often contrasting with "informally" or "casually." In legal or administrative contexts, it indicates that a specific required procedure has been followed to make an action valid.

In technical fields like mathematics, logic, or linguistics, the term shifts toward a meaning of rigorous precision. Here, it describes a system where the form or structure of the argument is more important than the intuitive meaning, ensuring that a proof is logically airtight and follows a strict set of axioms.