formally

Formally is an adverb used to indicate that something is done according to established forms, rules, or conventions, or in an official or ceremonious manner. It is often used to contrast with informal or casual approaches and to emphasize adherence to procedure, protocol, or standard practices.

Etymology and sense development: Formally derives from the adjective formal, which comes from Latin forma meaning shape or form. The adverbial form, formed with the -ly suffix, broadened to cover both the social sense of propriety and the technical sense of rigorous, rule-bound contexts.

Usage: In everyday language, formally can describe courteous or ceremonial behavior, official processes, or structured writing. For example, a meeting may be formally opened by a chair, a document may be formally adopted, or a grievance filed formally through a prescribed process. In contrast to informal settings, formality often signals respect for rank, tradition, or legal requirements.

Technical and academic uses: In mathematics, computer science, and logic, formally often precedes phrases like "prove formally" or "verify formally," signaling reasoning conducted within a specified formal system with explicit axioms and rules. In law and diplomacy, decisions and communications are described as formally valid or formally recognized when they meet established legal or procedural criteria.

See also: formality, formal language, formal method, formal verification.