formal vs logical

formal is a noun but logical is not a noun.

Word	Noun	Adjective	Verb	Adverb
formal	Yes	Yes	No	No
logical	No	Yes	No	No

formal (noun)	logical (noun)
a gown for evening wear
a lavish dance requiring formal attire

formal (adjective)	logical (adjective)
being in accord with established forms and conventions and requirements (as e.g. of formal dress)	capable of or reflecting the capability for correct and valid reasoning
(of spoken and written language) adhering to traditional standards of correctness and without casual, contracted, and colloquial forms	marked by an orderly, logical, and aesthetically consistent relation of parts
refined or imposing in manner or appearance; befitting a royal court	capable of thinking and expressing yourself in a clear and consistent manner
logically deductive	based on known statements or events or conditions
represented in simplified or symbolic form
characteristic of or befitting a person in authority