Searching for a universal constraint on the possible denotations of clause-embedding predicates

We propose a new universal constraint on the relationship between the meaning of a clause-embedding predicate when it takes an interrogative complement and its meaning when it takes a declarative complement. According to this proposal, every clause-embedding predicate V satisfies a constraint that we refer to as P-to-Q Entailment. That is, for any exhaustivity-neutral interrogative complement Q, if there is an answer p to Q such that "x Vs p" is true, then it follows that "x Vs Q" is true as well. We discuss empirical advantages of this proposal over existing proposals and explore potential counterexamples to P-to-Q Entailment.