logic vs system of logic

logic and system of logic both are nouns.

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

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

Other synonyms of logic include logical system.

logic (noun)	system of logic (noun)
the branch of philosophy that analyzes inference	a system of reasoning
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