From Tables to Quantified Statements: Evaluating LLM Inference Generation through Executable Verification

LLMs can generate fluent descriptions from tables, but their outputs may remain logically unsupported by the structured data. We introduce STAT-TO-TEXT, a controlled task in which LLMs generate quantified natural language inferences from statistical tables using quantified constructions such as all, some, no, and most. To evaluate these inferences, we use an LLM generated Python checker code which when executed verifies the corresponding truth conditions against the table. We compare four open-weight LLMs across model families and scales, evaluating faithfulness, logical accuracy, table coverage, and diversity. Our results show that model scale and family matter, with the largest model (GPT-OSS-120B) consistently producing the most faithful inferences without sacrificing greater table coverage and quantifier diversity, as opposed to smaller models. These findings are supported by human annotation, which shows that the automated checker closely aligns with human judgments.