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*We will host an informal discussion session in relation to the topic of this talk during the lunch time on Thursday the 20th (12:30-13:00 ET) at If you have any questions, comments, ideas, pointers to the literature, or suggestions for additional languages to consider, please join! If you have feedback to us but can’t make it to the session, please email us!* ---------- One of the central questions in semantic research is whether there are any **universal constraints on the possible denotations of lexical items** of a certain grammatical category. In this paper, we will consider a number of recent proposals which put forward possible constraints that relate the meaning of a **clause-embedding predicate** when it takes an interrogative complement to its meaning when it takes a declarative complement. We will argue that each of these proposals has counterexamples and identify a new constraint, **P-to-Q distributivity**, which rules in the counterexamples to the existing proposal, and yet rules out many conceivable denotations which have so far not been attested in cross-linguistic research.