If A implies B then Not A implies Not B.
Apparently not everyone takes this for granted as I was surprised to find out. After making this claim on another forum, the claim was challenged and I immediately thought that I screwed up.
As a reach, I assumed the challenge was grounded in that fact that there are domains where logic has multiple values - not simply true or false.
My conjecture was and still is that in logic denying the excluded middle (an infinite valued logic) the first sentence, also called Modus Tollens, is no longer valid.
So here are my questions:
1) Is Modus Tollens valid in a logical system denying the excluded middle?
2) If not what is the minimum number of values in a logical system where Modus Tollens is valid?