logical system vs logic

logical system and logic both are nouns.

Word	Noun	Adjective	Verb	Adverb
logical system	Yes	No	No	No
logic	Yes	No	No	No

As nouns, logical system and logic are synonyms defined as:

Other synonyms of logical system include system of logic.

logical system (noun)	logic (noun)
a system of reasoning	the branch of philosophy that analyzes inference
	a system of reasoning
	reasoned and reasonable judgment
	the principles that guide reasoning within a given field or situation
	the system of operations performed by a computer that underlies the machine's representation of logical operations