Carmo and Jones in 2022 [ 1 ] proposed certain axioms 5(a)–(g) for a relation \(\operatorname{ob}\) that holds between sets of possible worlds \(X\) and \(Y\) if \(X\) is obligatory in the context \(Y\). It was the latest iteration in a sequence of systems [ 2 , 3 , 4 ] .

We will exhibit a paradox therein. Our paradox will be a weak form of conditional deontic explosion: given that something is somewhat desirable (passing a course with a grade of C, say) and given that the most desirable outcome (the grade of A) is unavailable, the somewhat desirable outcome becomes obligatory.

We then show that despite this paradox, the systems of Carmo and Jones have interesting mathematical content. For the strongest system we provide a full classification of its models; for weaker versions we characterize the least models (under inclusion) satisfying the axioms and basic contrary-to-duty assumptions.