I've been feeling a bit under, but it's better now. Thanks for asking! I recognize you can define your logical axioms as you wish, just as you can mathematical

I've been feeling a bit under, but it's better now. Thanks for asking! I recognize you can define your logical axioms as you wish, just as you can mathematical systems. But the question is always going to be: how powerful is your system and what useful things can be derived from it? Judging from the Wikipedia article here, that logic excludes lots of useful things we have come to expect from (you know, useful) logics, starting first and foremost with Gödel's completeness theorem.