Dissecting Logical Reasoning in LLM s: A Fine-Grained Evaluation and Supervision Study (2025)

Abstract: Logical reasoning is a core capability for large language models (LLMs), yet existing benchmarks that rely solely on final-answer accuracy fail to capture the quality of the reasoning process. To address this, we introduce FineLogic, a fine-grained evaluation framework that assesses logical reasoning across three dimensions: overall accuracy, stepwise soundness, and representation-level probing. Leveraging this framework, we conduct a comprehensive study on how different supervision formats in fine-tuning shape reasoning abilities. We fine-tune LLMs on four supervision styles—one in natural language and three symbolic variants—and find a key trade-off: natural language supervision excels at generalization to out-of-distribution and long-chain problems, whereas symbolic supervision is superior at instilling structurally sound, atomic reasoning steps. Furthermore, our probing analysis indicates that fine-tuning primarily refines the model’s step-by-step generation process, rather than improving its ability to converge on an answer early. Together, our framework and analysis provide a more rigorous lens for evaluating and improving logical reasoning in LLMs. The code is available at https://github.com/YujunZhou/FineLogic.

## introduction large language models (llms) are rapidly emerging as transformative tools across a wide array of applications @xcite @xcite @xcite @xcite . among these, reasoning serves as a core capability underpinning tasks such as problem-solving @xcite , scientific question answering @xcite , and code analysis @xcite . consequently, a growing body of research has sought to evaluate and enhance the reasoning abilities of llms from multiple perspec-tives @xcite @xcite @xcite @xcite . within this broader landscape, logical reasoning stands out as a particularly challenging and intellectually demanding domain @xcite . it requires a synthesis of natural language understanding, formal logical interpretation, and multi-step inferential processing @xcite @xcite . despite growing interest in the logical reasoning capabilities of llms, most existing benchmarks focus narrowly on whether a model produces the correct final answer @xcite @xcite . this binary evaluation, typically assessing only the correctness of a "true" or "false" output, can be misleading, as it fails to determine whether the model arrived at the answer through valid multi-step reasoning @xcite . consequently, correct answers may reflect guesswork rather than genuine logical inference. we are thus motivated to address rq1: how to rigorously evaluate llms' step-by-step correctness in logical reasoning tasks, beyond the binary evaluation of the final answer? in parallel with benchmarking efforts, numerous methods have been proposed to enhance the multistep logical reasoning abilities of llms. while many leverage inference-time strategies @xcite , in-context learning @xcite , or external logical verifiers @xcite to guide the model toward more rigorous reasoning, some recent studies explored supervised fine-tuning (sft) as a more direct approach to enhancing logical reasoning @xcite . for example, @xcite proposes a synthetic logic corpus designed to offer broad and systematic coverage of logical knowledge. however, it remains unclear for this important question, rq2: what style of question: given the facts that (1) every cat drinks milk, and (2) tom is a cat, can we conclude that tom drinks milk? which is better for sft data design? training data, natural language or formal logical symbols, better facilitates the learning of multistep logical reasoning through sft? addressing this research question is important for understanding how to most effectively instill logical reasoning capabilities in llms. to address rq1, we propose finelogic, a diagnostic framework designed to offer a multidimensional evaluation of llms' reasoning processes, moving beyond binary final-answer correctness. rather than creating another leaderboard, finelogic serves as a tool for llm practitioners to pinpoint specific weaknesses in reasoning chains, such as flawed logic, redundancy, or nonatomic steps. our framework evaluates models along three complementary dimensions: (1) overall benchmark accuracy: this metric captures a model's ability to perform multi-step logical reasoning and its generalizability across problems from diverse domains. (2) stepwise soundness: inspired by @xcite , we assess the quality of each intermediate reasoning step using three criteria-validity (whether the step is logically valid), relevance (whether its conclusion is used in later steps), and atomicity (whether it applies a single, minimal inference rule). these metrics aim to evaluate the model's ability to generate human-interpretable and logically coherent reasoning chains. to address rq2, we systematically investigate how different supervision formats affect the reasoning capabilities of llms. specifically, we examine both natural language-based training data and logicsymbol-based representations, including several structured variants. our analysis shows that natural language supervision is particularly effective in conveying core reasoning patterns, leading to strong performance across a wide range of evaluation benchmarks. notably, it exhibits impressive generalizability even on out-of-distribution test sets that require long reasoning chains. however, a deeper examination of stepwise soundness and internal representation probing reveals certain limitations. models trained with natural language supervision tend to struggle with producing strictly minimal reasoning chains (e.g., more likely including redundant steps and applying multiple inference rules in a single step, as shown in figure 5 ). in contrast, models trained with symbolic reasoning styles are better at filtering out irrelevant information, generating atomic steps aligned with individual deduction rules, and maintaining cleaner, logically grounded reasoning trajectories. to summarize, our contributions are as follows: ## finelogic evaluation framework as illustrated in figure 2 , finelogic builds on existing benchmarks and evaluates logical reasoning ability from three complementary perspectives ## supervision format and style: sft data design in this section, we examine how different supervision styles for sft affect the logical reasoning abilities of llms. our training data is based on fld and prontoqa, both of which include gold reasoning chains suitable for constructing diverse supervision styles. for fld, we generate 500 problems for each reasoning depth from 0 to 15, plus 1500 unknown samples, totaling 9500 training instances. for pron-toqa, we use 3200 3-hop problems. during evaluation, fld covers depths 0-19, while prontoqa uses only the hardest 5-hop samples. we compare four supervision styles across two categories: natural language-based and symbolic reasoning. each style reflects a different level of abstraction and clarity in reasoning structure. a small portion of translations, connective phrases, and intermediate steps are generated using gpt-4.1. prompt examples are shown in figure 4 (appendix e). ## conclusion we introduce finelogic, a unified and fine-grained framework for evaluating the logical reasoning capabilities of large language models. by integrating overall benchmark accuracy, stepwise soundness, and representation-level probing, finelogic enables more interpretable and rigorous assessment beyond final-answer correctness. leveraging this framework, we conduct a systematic investigation of how different fine-tuning supervision formats impact reasoning ability. our experiments demonstrate that while natural language supervision leads to strong generalization and benchmark gains, symbolic styles better support minimal, rule-aligned reasoning structures. furthermore, representationlevel probing reveals that sft primarily affects how models generate stepwise solutions rather than their ability to predict answers directly. these findings offer practical guidance for designing supervision strategies tailored to different reasoning objectives and highlight the importance of evaluating both behavioral and internal reasoning quality when advancing llm reasoning systems.