The same real-life questions posed to different individuals may lead to different answers based on their unique situations. For instance, whether a student is eligible for a scholarship depends on eligibility conditions, such as major or degree required. ConditionalQA was proposed to evaluate models’ capability of reading a document and answering eligibility questions, considering *unmentioned* conditions. However, it is limited to questions on single documents, neglecting harder cases that may require *cross-document reasoning* and *optimization*, for example, “What is the maximum number of scholarships attainable?” Such questions over multiple documents are not only more challenging due to more context to understand, but also because the model has to (1) explore all possible combinations of unmentioned conditions and (2) understand the relationship between conditions across documents, to reason about the optimal outcome. To evaluate models’ capability of answering such questions, we propose a new dataset MDCR, which can reflect real-world challenges and serve as a new test bed for complex conditional reasoning that requires optimization. We evaluate this dataset using the most recent LLMs and demonstrate their limitations in solving this task. We believe this dataset will facilitate future research in answering optimization questions with unknown conditions.

Retrieving relevant tables containing the necessary information to accurately answer a given question over tables is critical to open-domain question-answering (QA) systems. Previous methods assume the answer to such a question can be found either in a single table or multiple tables identified through question decomposition or rewriting. However, neither of these approaches is sufficient, as many questions require retrieving multiple tables and joining them through a join plan that cannot be discerned from the user query itself. If the join plan is not considered in the retrieval stage, the subsequent steps of reasoning and answering based on those retrieved tables are likely to be incorrect. To address this problem, we introduce a method that uncovers useful join relations for any query and database during table retrieval. We use a novel re-ranking method formulated as a mixed-integer program that considers not only table-query relevance but also table-table relevance that requires inferring join relationships. Our method outperforms the state-of-the-art approaches for table retrieval by up to 9.3% in F1 score and for end-to-end QA by up to 5.4% in accuracy.