What Is a Clarification? Estimating Model-Dependent Input Ambiguity

Ambiguous inputs can admit multiple valid interpretations, each potentially yielding a different answer. Existing work largely treats this ambiguity as a property of the input, but for a particular language model, only some alternatives may be known and answerable. We therefore distinguish world ambiguity, capturing all alternatives admitted by an input, from model ambiguity, capturing those accessible to the responding model. To characterize these alternatives, we formalize natural-language clarifications through three desiderata—uniqueness, faithfulness, and answer equivalence—and show that they induce a one-to-one correspondence between valid answers and equivalence classes of clarifications. Thus, an interpretation can be represented either by its answer or by the clarifi- cations that uniquely express it. Leveraging this correspondence, we introduce CIRCLECLAR, a black-box method that estimates which answers are available to a model through an answer–clarification–answer cycle. Across open-domain QA and executable Text-to-SQL, CIRCLECLAR achieves strong recovery of these answer sets. In QA, the recovered support yields the strongest overall performance in model-dependent ambiguity detection and enables effective selection among answering, clarifying, and abstaining. Together, these results demonstrate the practical value of a model-dependent view of ambiguity and it’s characterization through an answer-clarification correspondences