Ramya Keerthy Thatikonda

Ramya Keerthy Thatikonda, Jiuzhou Han, Wray Buntine et al.

Logical reasoning is a fundamental task in natural language processing that presents significant challenges to Large Language Models (LLMs). The inherent characteristics of logical reasoning makes it well-suited for symbolic representations such as first-order logic (FOL). Research in symbolic logical reasoning explored FOL generation using state-of-the-art LLMs (i.e., GPT-4) to produce FOL translations of natural language (NL) statements, but errors in translation are usually not the focus. We address this by categorizing the translation errors in FOL statements generated by LLMs. To make progress towards improving the quality of FOL translations for smaller language models such as LLaMA-2 13B and Mistral 7B, we create ProofFOL, a high-quality FOL-annotated subset of ProofWriter dataset using GPT-4o. The models fine-tuned on this silver standard data achieve a significant gain in performance when compared to larger language models such as LLaMA-2 70B. In addition to improving the model using large data, we also tackle the issue of data scarcity and introduce an incremental framework encompassing of data augmentation and verification steps. In the augmentation process, a single pair of (premises, conclusion) is split into multiple new instances based on the predicates and FOLs. This data is used for fine-tuning, and the inference on this model generates FOLs with fewer errors over the model trained on the original data. Our investigation on the translation errors leads to generation of a perturbation dataset, which is used to train a verifier that corrects potential syntactic and semantic FOL translation errors. We demonstrate an efficient method for making the most of a limited existing human-annotated dataset. Our results show state-of-the-art performance for ProofWriter and ProntoQA datasets using ProofFOL on LLaMA-2 and Mistral models.

Ramya Keerthy Thatikonda, Jiuzhou Han, Wray Buntine et al.

The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore reliable reasoning system. However, smaller LMs often struggle with this translation task, frequently producing incorrect symbolic outputs due to formatting and translation errors. Existing approaches typically rely on self-iteration to correct these errors, but such methods depend heavily on the capabilities of the underlying model. To address this, we first categorize common errors and fine-tune smaller LMs using data synthesized by large language models. The evaluation is performed using the defined error categories. We introduce incremental inference, which divides inference into two stages, predicate generation and FOL translation, providing greater control over model behavior and enhancing generation quality as measured by predicate metrics. This decomposition framework also enables the use of a verification module that targets predicate-arity errors to further improve performance. Our study evaluates three families of models across four logical-reasoning datasets. The comprehensive fine-tuning, incremental inference, and verification modules reduce error rates, increase predicate coverage, and improve reasoning performance for smaller LMs, moving us closer to developing reliable and accessible symbolic-reasoning systems.

Ramya Keerthy Thatikonda, Wray Buntine, Ehsan Shareghi

Logical reasoning is a critical benchmark for evaluating the capabilities of large language models (LLMs), as it reflects their ability to derive valid conclusions from given premises. While the combination of test-time scaling with dedicated outcome or process reward models has opened up new avenues to enhance LLMs performance in complex reasoning tasks, this space is under-explored in deductive logical reasoning. We present a set of Outcome Reward Models (ORMs) for deductive reasoning. To train the ORMs we mainly generate data using Chain-of-Thought (CoT) with single and multiple samples. Additionally, we propose a novel tactic to further expand the type of errors covered in the training dataset of the ORM. In particular, we propose an echo generation technique that leverages LLMs' tendency to reflect incorrect assumptions made in prompts to extract additional training data, covering previously unexplored error types. While a standard CoT chain may contain errors likely to be made by the reasoner, the echo strategy deliberately steers the model toward incorrect reasoning. We show that ORMs trained on CoT and echo-augmented data demonstrate improved performance on the FOLIO, JustLogic, and ProverQA datasets across four different LLMs.

Ramya Keerthy Thatikonda, Wray Buntine, Ehsan Shareghi

The recent successful paradigm of solving logical reasoning problems with tool-augmented large language models (LLMs) leverages translation of natural language (NL) statements into First-Order Logic~(FOL) and external theorem provers. However, the correctness of FOL statements, comprising operators and text, often go unverified due to the lack of a reliable evaluation metric for comparing generated and ground-truth FOLs. In this paper, we conduct a comprehensive study on the sensitivity of existing NL-, FOL-, and graph-based metrics to capture differences between a sampled FOL and its corresponding ground-truth. We then measure the alignment between a metric-based ranking of FOL outputs and a strong LLM as-a-judge. To do this, we first apply operator and text-based perturbations to ground-truth FOL statements to assess metric sensitivity. We then evaluate metric robustness by comparing the metrics against LLMs judgment. Our empirical findings highlight a clear oversensitivity in the n-gram metric BLEU for text perturbations. The operator perturbation affects the semantic graph metric Smatch++ for structural changes, and the FOL metric for specific operator changes. We observe a closer alignment between BertScore and LLM judgement, proving the importance of semantic evaluation. Additionally, we show that combining metrics enhances both robustness and sensitivity compared to using individual metrics.

Long Hei Matthew Lam, Ramya Keerthy Thatikonda, Ehsan Shareghi

The emergence of Large Language Models (LLMs) has demonstrated promising progress in solving logical reasoning tasks effectively. Several recent approaches have proposed to change the role of the LLM from the reasoner into a translator between natural language statements and symbolic representations which are then sent to external symbolic solvers to resolve. This paradigm has established the current state-of-the-art result in logical reasoning (i.e., deductive reasoning). However, it remains unclear whether the variance in performance of these approaches stems from the methodologies employed or the specific symbolic solvers utilized. There is a lack of consistent comparison between symbolic solvers and how they influence the overall reported performance. This is important, as each symbolic solver also has its own input symbolic language, presenting varying degrees of challenge in the translation process. To address this gap, we perform experiments on 3 deductive reasoning benchmarks with LLMs augmented with widely used symbolic solvers: Z3, Pyke, and Prover9. The tool-executable rates of symbolic translation generated by different LLMs exhibit a near 50% performance variation. This highlights a significant difference in performance rooted in very basic choices of tools. The almost linear correlation between the executable rate of translations and the accuracy of the outcomes from Prover9 highlight a strong alignment between LLMs ability to translate into Prover9 symbolic language, and the correctness of those translations.