Modus Tollendo Tollens with obligation conditionals: Towards a deontic inheritance logic respecting the Stoic criterion

We know that Modus Tollendo Tollens is a difficult rule to apply. We also know that there are circumstances in which people easily use it. One of those circumstances is whenever the conditional premise is an obligation conditional. On the other hand, the Stoic criterion of the conditional, that is, the proposal Chrysippus of Soli gave for the latter logical connective, has been related to Non-Axiomatic Logic and Inheritance Logic. My aim here is to try to show that obligation conditionals can be deemed as deontic inheritance statements in Non-Axiomatic Logic or Inheritance Logic. I will attempt to argue that it is possible to build a deontic inheritance logic with two essential characteristics. First, it respects the Stoic criterion of the conditional. Second, in consistence with the literature, it leads to the conclusion expected by classical logic when the conditional is an obligation.