If you think of the prefix as 'iN-', then you can use these transformations:
'iN- + <word>' -> 'in + word. (e.g. inactive, incapable, indecent, inequitable, infamous, ingratitude, inhospitable... etc)
UNLESS the following word or morpheme starts with one of these:
- bilabial consonant, then 'iN- + <word>' -> 'im + <adj>' (improbable,imbecile, immaculate etc)
- 'l', then 'iN- + <word>' -> 'il + <word>' (illogical, illegal etc.)
- 'r', then 'iN- + <word>' -> 'ir + <word>' (irregular, irredeemable, etc)
The apparent counter-example 'inbred' isn't, because its 'in-' prefix isn't the same as the polarity-reversing 'iN-' prefix.
Sorry, I should have made it clear that I was not connecting "illogic" to "ill logic". I simply meant in the original post that, when spoken, the two sound very similar. I also should have pointed out that I have not heard "ill logic" used since about 1987 when my A Level English teacher used to use it quite regularly. I too wouldn't encourage its use. "Flawed logic" is indeed much better.
I shouldn't post when I haven't had much sleep!