Summary: A semantic relation between a family of sets of formulas and a set of formulas, dubbed generalized entailment, and its subrelation, called constructive generalized entailment, are defined and examined. Entailment construed in the usual way and multiple-conclusion entailment can be viewed as special cases of generalized entailment. The concept of constructive generalized entailment, in turn, enables an explication of some often used notion of interrogative entailment, and coincides with inquisitive entailment at the propositional level. Some interconnections between constructive generalized entailment and Inferential Erotetic Logic are also analysed.