Definitions of formal:

• adjective:   logically deductive

  Example: "Formal proof"

• adjective:   characteristic of or befitting a person in authority

  Example: "Formal duties"

• adjective:   being in accord with established forms and conventions and requirements (as e.g. of formal dress)

  Example: "Pay one's formal respects"

• adjective:   (of spoken and written language) adhering to traditional standards of correctness and without casual, contracted, and colloquial forms

  Example: "The paper was written in formal English"

• adjective:   represented in simplified or symbolic form
• adjective:   refined or imposing in manner or appearance; befitting a royal court