Formal - relating to form.

For example, 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. We can see the soundness of this argument by substituting in symbols to make the form clear.

If

S is a P

and

all P are M,

then S is M

Other examples

• 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.
• 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. See Formal Hall
• In British English, the formal is the same as the event referred to by American English speakers as the prom.

Compare with

• Informal -- Casual -- Intuitive