In contrast to declaratives, it is not clear whether imperatives denote propositions or more generally what role truth and falsity play in their semantics.
While this problem was first noted in a footnote by Frege, it received a more developed formulation by Jørgensen.
Alf Ross observed that applying the classical rule of disjunction introduction under the scope of an imperative operator leads to unintuitive (or apparently absurd) results.
Consider: Ross's paradox highlights the challenge faced by anyone who wants to modify or add to the standard account of validity.
For valid declarative inference, the premises give you a reason to believe the conclusion.
The semantics for deontic logic requires that all obligations in the domain of discourse be fulfilled in an acceptable possible world.
Some strands of this debate connect it to Hans Kamp's paradox of free choice, in which disjunction introduction leads to absurd conclusions when applied under the scope of a possibility modal.
[6] There is no consensus among logicians about the truth or falsity of these (or similar) claims and mixed imperative and declarative inference remains vexed.