Formal

The term formal has a number of uses

In logic, formal logic reasons about a logical argument based only on the form and not on the meaning.

If Socrates is a man and all men are mortal, then Socrates is mortal

The conclusion follows from propositional logic. The soundness of this argument can be seen by substituting in symbols to make the form clear.

If S is a P and all P are M, then S is M

Formal verification works in a formal language to attempt to prove formal properties hold for a formal specification of a formal system
Formal power series extend the notion of a power series by removing the requirement for convergence. Thus they have the same form as a power series, but their more abstract interpretation, not implying a meaningful sum of the series, can be applied more generally.
A formal calculation is one involving manipulation of symbols.
Formal grammar – formal system – formal set theory
Formal occasions such as a formal dinner party or high tea might require one to wear formal attire such as an evening gown or tuxedo. An example is Formal Hall.
In British & Australian English, the formal is the same as the event referred to by American English speakers as the prom.
In American English, the formal most often refers to an event similar to the above, but organized by a college or university organization, typically but not always a fraternity or sorority.
As an adjective, formal means being in accord with established forms or the antonym of informal (or casual).
In histology, a short form for formalin or formaldehyde often used as a prefix in compound expressions.

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