On the Subject of Leveraging through Logic

“Okay, so I know that each door has to lead somewhere, which means that somewhere at the place where we're trying to go there must be a reverse door that leads here. ... Another victory for logic. Come, Stanley, our destiny awaits!”

Instructions:

These tables are designed such that you can work out which letters are true quickly and easily, given the edgework. These conditions must be met exactly (unless otherwise specified) in order for the letter to be true.