From Wikipedia, we have:
In natural languages, an indicative conditional is the logical operation given by statements of the form "If A then B". Unlike the material conditional, an indicative conditional does not have a stipulated definition. The philosophical literature on this operation is broad, and no clear consensus has been reached.
Is it not just a case of disallowing certain rules of inference in propositional logic, e.g. disallowing $\neg A \to A \implies B$ or some other rule(s) of inference that allows you do make such an inference?
I routinely use such rules (as above) in writing formal proofs. Would mathematics as we know it even be possible if we implemented such restrictions?