Daily Papers

We present FOLIO, a human-annotated, open-domain, and logically complex and diverse dataset for reasoning in natural language (NL), equipped with first order logic (FOL) annotations. FOLIO consists of 1,435 examples (unique conclusions), each paired with one of 487 sets of premises which serve as rules to be used to deductively reason for the validity of each conclusion. The logical correctness of premises and conclusions is ensured by their parallel FOL annotations, which are automatically verified by our FOL inference engine. In addition to the main NL reasoning task, NL-FOL pairs in FOLIO automatically constitute a new NL-FOL translation dataset using FOL as the logical form. Our experiments on FOLIO systematically evaluate the FOL reasoning ability of supervised fine-tuning on medium-sized language models (BERT, RoBERTa) and few-shot prompting on large language models (GPT-NeoX, OPT, GPT-3, Codex). For NL-FOL translation, we experiment with GPT-3 and Codex. Our results show that one of the most capable Large Language Model (LLM) publicly available, GPT-3 davinci, achieves only slightly better than random results with few-shot prompting on a subset of FOLIO, and the model is especially bad at predicting the correct truth values for False and Unknown conclusions. Our dataset and code are available at https://github.com/Yale-LILY/FOLIO.

Accurate translation from Natural Language to First-Order Logic (NL-to-FOL) underpins neurosymbolic AI systems and Natural Language Inference (NLI), making the quality of NL-to-FOL benchmarks essential -- yet these datasets have never been rigorously audited. Our first contribution is to present a systematic human inspection of the validation split of FOLIO and a subset of MALLS test instances, finding that approximately 39% and 36% of entries, respectively, contain incorrect FOL formalizations (i.e., ground truth labels), with additional rates of ambiguous NL sentences (16.4% and 48%) and incorrect NLI labels in FOLIO (8.4%). Our second contribution is to develop and release corrected ground truths for such datasets, showing that annotation errors distort model evaluation on a reference benchmark task: testing three state-of-the-art LLMs (Gemma~4 31B-it, Qwen3-30B-A3B, and GPT-4o-mini) with the corrected ground truths yields accuracy gains from +9 to +22 percentage points. Motivated by these findings, we propose an LLM-based framework to support humans in manual reviewing NL-to-FOL datasets. By directing reviewers toward the most error-prone instances, we empirically show that it is possible to achieve 90% dataset accuracy after reviewing fewer than 24% of instances, compared to over 70% required by unguided review. We release all human-verified annotations and the code for our framework.

Existing methods on understanding the capabilities of LLMs in logical reasoning rely on binary entailment classification or synthetically derived rationales, which are not sufficient for proper investigation of model's capabilities. We present P-FOLIO, a human-annotated dataset consisting of diverse and complex reasoning chains for a set of realistic logical reasoning stories also written by humans. P-FOLIO is collected with an annotation protocol that facilitates humans to annotate well-structured natural language proofs for first-order logic reasoning problems in a step-by-step manner. The number of reasoning steps in P-FOLIO span from 0 to 20. We further use P-FOLIO to evaluate and improve large-language-model (LLM) reasoning capabilities. We evaluate LLM reasoning capabilities at a fine granularity via single-step inference rule classification, with more diverse inference rules of more diverse and higher levels of complexities than previous works. Given that a single model-generated reasoning chain could take a completely different path than the human-annotated one, we sample multiple reasoning chains from a model and use pass@k metrics for evaluating the quality of model-generated reasoning chains. We show that human-written reasoning chains significantly boost the logical reasoning capabilities of LLMs via many-shot prompting and fine-tuning. Furthermore, fine-tuning Llama3-7B on P-FOLIO improves the model performance by 10% or more on three other out-of-domain logical reasoning datasets. We also conduct detailed analysis to show where most powerful LLMs fall short in reasoning. We will release the dataset and code publicly.