For example, formal logic reasons about an 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

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