In this paper, the reportive construction sollen+infinitive is treated as merely agnostic, with the negative epistemic component emerging qua conversational implicature. The paper aims to test whether the interrogative sentence type can be seen as a contextual trigger for this implicature. It concludes that the negative epistemic implicature can be triggered or strengthened by proper questions and mirative questions, but not by rhetorical or unresolvable questions as defined by Celle (2018).