system of logic vs logical system

system of logic and logical system both are nouns.

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

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

Other synonyms of system of logic include logic.

system of logic (noun)	logical system (noun)
a system of reasoning	a system of reasoning