Research in Text-to-SQL conversion has been largely benchmarked against datasets where each text query corresponds to one correct SQL. However, natural language queries over real-life databases frequently involve significant ambiguity about the intended SQL due to overlapping schema names and multiple confusing relationship paths. To bridge this gap, we develop a novel benchmark called AmbiQT with over 3000 examples where each text is interpretable as two plausible SQLs due to lexical and/or structural ambiguity. When faced with ambiguity, an ideal top-$k$ decoder should generate all valid interpretations for possible disambiguation by the user. We evaluate several Text-to-SQL systems and decoding algorithms, including those employing state-of-the-art LLMs, and find them to be far from this ideal. The primary reason is that the prevalent beam search algorithm and its variants, treat SQL queries as a string and produce unhelpful token-level diversity in the top-$k$. We propose LogicalBeam, a new decoding algorithm that navigates the SQL logic space using a blend of plan-based template generation and constrained infilling. Counterfactually generated plans diversify templates while in-filling with a beam-search that branches solely on schema names provides value diversity. LogicalBeam is up to $2.5$ times more effective than state-of-the-art models at generating all candidate SQLs in the top-$k$ ranked outputs. It also enhances the top-$5$ Exact and Execution Match Accuracies on SPIDER and Kaggle DBQA.

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