invalidity vs illogicalness

invalidity and illogicalness both are nouns.

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

As nouns, illogicalness is a hypernym of invalidity; that is, illogicalness is a word with a broader meaning than invalidity:

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

Other hypernyms of invalidity include illogic, illogicality, inconsequence.

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