illogic vs invalidity

illogic and invalidity both are nouns.

Word	Noun	Adjective	Verb	Adverb
illogic	Yes	No	No	No
invalidity	Yes	No	No	No

As nouns, invalidity is a hyponym of illogic; that is, invalidity is a word with a more specific, narrower meaning than illogic:

illogic: invalid or incorrect reasoning
invalidity: illogicality as a consequence of having a conclusion that does not follow from the premisses

Other hyponyms of illogic include invalidness.

illogic (noun)	invalidity (noun)
invalid or incorrect reasoning	illogicality as a consequence of having a conclusion that does not follow from the premisses