Hmmm.... the opposite of logical? Like dysfucntional is the opposite of functional, one the opposite of logical is dyslogical?
That word I know from my days as part of the free Mandela movement, it means expressing censure or disapproval.
The definition I have is "uncomplimentary."
Wow, see that word has two meanings depending on which side of the pond we are, yes I looked it up in my husband dictionary from the 1980 after I read your post and the says the same as I said.
I love the English language, it so varied and words means different things between all the English speaking countries.
That why we sometimes don't understand each other, we mean the same thing but use different words or we mean the different things and use the same words.
The same happens over here too, in Swedish rar is kind and Norwegian it is crazy and the Danish word for boy means farmhand in Swedish.