There actually are formal imperative (and deontic, which may or may not be the same thing) logics.
And present-tense verbs are ambiguous as to whether they mean occasional or continuous action; if we know that Bob swims, do we know that he always swims, non-stop; or just that he sometimes swims, now and then? How about if Bob lives? Or if he owns something? If he eats? We judge from context because the grammar does not explicitly mark it.
It works just the same with imperatives. If you tell someone to eat green vegetables, are you telling them to always eat green vegetables? Continuously, non-stop? Or, eat green vegetables whenever they eat? Or just, eat green vegetables sometimes, maybe frequently?
So, it-is-imperative-that(you honk <-> you love formal logic) could very well (and contextually, given what honking means, probably does) mean that, if you love formal logic, you should sometimes honk (for instance, now, when you read this sticker), and that if you were for any other reason to honk, you should do so only if you love formal logic.
It does not mean that everyone who loves formal logic should continuously honk so long as they love formal logic.