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Are Large Language Models Really Good Logical Reasoners? A Comprehensive Evaluation and Beyond

Fangzhi Xu, Qika Lin, Jiawei Han, Tianzhe Zhao, Jun Liu, Erik Cambria

arXiv:2306.09841v4cs.CLcs.AI

TL;DR

Whether LLMs can effectively perform logical reasoning remains an open question, despite their progress in NLP. The paper evaluates models across reasoning settings and introduces finer-grained measures and a content-neutral benchmark. Its evaluations find relative strength in deductive reasoning but continued struggles in inductive settings, and motivate a six-property capability scheme.

  • Problem

    Whether LLMs can effectively address logical reasoning remains an open question, while existing evaluations lack comprehensive coverage, fine-grained process analysis, content-neutral testing, or a complete capability framework.

    Source: §1 · pp. 1–2

  • Method

    The paper evaluates LLMs across four reasoning settings and fifteen datasets, assesses answers and explanations with four metrics, classifies errors, and introduces the content-neutral NeuLR dataset.

    Source: §1 · pp. 2–3, §3.3 · p. 4

  • Results

    Across reasoning settings, LLMs show relative strength in deductive reasoning but evident struggles in inductive settings.

    Source: §7 · p. 13

  • Takeaways & Limitations

    The paper proposes evaluating logical reasoning capability through six dimensions: Correct, Rigorous, Self-aware, Active, Oriented, and No Hallucination.

    Source: §7 · p. 12

    Current evaluation benchmarks, which primarily depend on objective metrics, are not sufficient to comprehensively evaluate LLMs.

    Source: §7 · p. 13

Abstract

from arXiv · show

Logical reasoning consistently plays a fundamental and significant role in the domains of knowledge engineering and artificial intelligence. Recently, Large Language Models (LLMs) have emerged as a noteworthy innovation in natural language processing (NLP). However, the question of whether LLMs can effectively address the task of logical reasoning, which requires gradual cognitive inference similar to human intelligence, remains unanswered. To this end, we aim to bridge this gap and provide comprehensive evaluations in this paper. Firstly, to offer systematic evaluations, we select fifteen typical logical reasoning datasets and organize them into deductive, inductive, abductive and mixed-form reasoning settings. Considering the comprehensiveness of evaluations, we include 3 early-era representative LLMs and 4 trending LLMs. Secondly, different from previous evaluations relying only on simple metrics (e.g., \emph{accuracy}), we propose fine-level evaluations in objective and subjective manners, covering both answers and explanations, including \emph{answer correctness}, \emph{explain correctness}, \emph{explain completeness} and \emph{explain redundancy}. Additionally, to uncover the logical flaws of LLMs, problematic cases will be attributed to five error types from two dimensions, i.e., \emph{evidence selection process} and \emph{reasoning process}. Thirdly, to avoid the influences of knowledge bias and concentrate purely on benchmarking the logical reasoning capability of LLMs, we propose a new dataset with neutral content. Based on the in-depth evaluations, this paper finally forms a general evaluation scheme of logical reasoning capability from six dimensions (i.e., \emph{Correct}, \emph{Rigorous}, \emph{Self-aware}, \emph{Active}, \emph{Oriented} and \emph{No hallucination}). It reflects the pros and cons of LLMs and gives guiding directions for future works.

1 INTRODUCTION

The introduction frames whether LLMs can reason logically as an open question and presents a broad evaluation designed to address gaps in coverage, explanation analysis, and content neutrality. It also proposes a six-property scheme for describing reasoning capability.

1 INTRODUCTION

  • The paper positions its evaluation architecture as addressing gaps in systematic coverage, fine-level assessment, content neutrality, and a complete capability framework.The introduction describes those gaps in prior evaluation work and identifies the architecture’s main components.Source: §1 · pp. 1–2
  • The evaluation spans four reasoning settings, fifteen datasets, and seven representative LLMs, including early-era and up-to-date models.The settings are deductive, inductive, abductive, and mixed-form.Source: §1 · p. 2
  • Four metrics assess answer correctness, explanation correctness, explanation completeness, and explanation redundancy, while five error types distinguish evidence selection from reasoning flaws.The system is described as applicable under human-annotation and automatic modes.Source: §1 · p. 2
  • NeuLR provides 3,000 content-neutral samples for deductive, inductive, and abductive reasoning to reduce dependence on input content when benchmarking logical reasoning.The paper presents content neutrality as a response to benchmarks whose reasoning may be affected by text content or overlap with training data.Source: §1 · pp. 2–3
  • The proposed capability scheme uses six properties: Correct, Rigorous, Self-aware, Active, Oriented, and No Hallucination.The properties are quantified from the evaluation experiments and used to visualize ability maps across reasoning settings.Source: §1 · pp. 2–3

2 PRELIMINARY

The preliminary section distinguishes logical reasoning by the direction and certainty of inference: deduction applies premises and rules, induction generalizes from observations, and abduction seeks likely explanations. It also treats combinations of these forms as mixed-form reasoning.

2 PRELIMINARY

  • Logical reasoning uses one- or multi-step inference from premises to generate implications containing new facts.The paper describes premises and logical rules as typical elements of reasoning.Source: §2 · p. 3
  • Deduction applies premises and logical rules or commonsense to reach certain conclusions, moving from general knowledge toward specific facts.The Jordan example pairs the rule that eight-year-olds attend primary school with the fact that Jordan is eight.Source: §2 · p. 3
  • Induction generalizes a rule from specific observations, so its conclusion is probable rather than certain.The paper contrasts this bottom-up direction with deduction.Source: §2 · p. 3
  • Abduction seeks the simplest and most likely explanation for observations, treating the inferred cause as probable.The paper illustrates the direction as premise2 plus rule leading to premise1.Source: §2 · p. 3
  • Fig. 2 illustrates an LLM answering a reasoning question, with generated results shown in red and explanations in blue.Source: Figure 2 · p. 3
  • Mixed-form reasoning combines at least two reasoning types across multiple steps, such as inducing a general rule and then applying it deductively.The crow example infers that all crows are black from two observations, then applies that rule to Emily.Source: §2 · p. 3

3 EVALUATION DETAILS

The evaluation details specify the models, datasets, and metrics used to assess logical reasoning. The design covers multiple reasoning settings and task formats, with measures of answers, explanations, and error types.

3 EVALUATION DETAILS

  • The evaluation is organized across deductive, inductive, abductive, and mixed-form settings, with prompts detailed in the appendix.Source: §3 · p. 3

3.1 Evaluated Models

  • Seven models are selected: three early-era representatives and four up-to-date LLMs, since including every rapidly emerging model is not realistic.The early-era models are text-davinci-003, ChatGPT, and BARD; the up-to-date models are LLaMA3.1-Chat, Mistral-Instruct-v0.3, Claude-3, and GPT-4.Source: §3.1 · p. 3

3.2 Evaluated Datasets

  • Fifteen popular datasets cover four reasoning settings and include both generation and classification tasks.For ChatGPT, some datasets use all test examples while larger datasets are sampled to 1,000 examples; text-davinci-003 and BARD use 100 examples per dataset.Source: §3.2 · pp. 3–4

3.3 Selected Metrics

  • Four metrics assess answer correctness, explanation correctness, explanation completeness, and explanation redundancy from objective and subjective perspectives.Completeness concerns whether the explanation contains the elements needed to infer the answer; redundancy concerns unnecessary information beyond what is needed.Source: §3.3 · p. 4
  • Five error types separate evidence-selection failures—wrong selection and hallucination—from reasoning failures—no reasoning, perspective mistake, and process mistake.The first group concerns selected facts; the second concerns how the model reasons from those facts.Source: §3.3 · p. 4

4 OVERALL EXPERIMENTS

Across fifteen logical-reasoning datasets, evaluated LLMs generally lag state-of-the-art metrics, with performance varying by reasoning mode, task form, and prompting. The experiments compare three early-era and four trending LLMs across these settings.

4 OVERALL EXPERIMENTS

  • Most evaluated LLM results fall short of state-of-the-art metrics across the fifteen datasets.The experiments cover three early-era LLMs and four trending LLMs.Source: §4 · p. 4, Table 1 · p. 5, Table 2 · p. 5
  • BARD is consistently strongest in deductive, inductive, and abductive settings, while ChatGPT performs better in mixed-form reasoning; LLMs do best deductively and mostly struggle inductively.The cross-setting comparison uses zero-shot results.Source: §4 · p. 4
  • Classification scenarios generally yield better performance than generation, where ChatGPT performs particularly poorly on several listed tasks.The authors suggest ChatGPT’s chat-oriented design may contribute to its generation-task weakness.Source: §4 · pp. 5–6
  • Few-shot in-context learning does not consistently improve performance, especially in inductive and mixed-form reasoning.The authors report gains on only some deductive and abductive datasets for the three discussed models.Source: §4 · p. 6

5 FINE-LEVEL EVALUATIONS

The fine-level evaluations show that answer accuracy alone misses whether LLMs reason correctly, completely, actively, and with appropriate evidence. Results vary by model and reasoning setting, while longer inputs and reasoning chains often challenge performance and prompting strategies do not help uniformly.

5.1 Are LLMs Rigorous Logical Reasoning?

  • BARD leads rigorous reasoning across four reasoning manners, but all selected LLMs drop from answer-only accuracy when explanations must also be correct and complete.LLMs are strongest at rigorous reasoning in abductive settings and weaker in deductive and inductive settings; ChatGPT often keeps explanations correct but incomplete, while text-davinci-003 more often maintains completeness.Source: §5.1 · p. 6, Table 3 · p. 7

5.2 Are LLMs Self-aware Logical Reasoners?

  • text-davinci-003 shows notable self-awareness in inductive, abductive, and mixed-form reasoning, while generation tasks tend to produce more redundant answers than classification tasks.BARD performs poorly in several settings; the authors relate redundancy in open-ended generation to responses covering diverse perspectives and conditions.Source: §5.2 · pp. 6–7

5.4–5.5 Are LLMs Active and Oriented Logical Reasoners?

  • BARD is the most active reasoner across deductive, inductive, and abductive settings, while ChatGPT is lazier in deductive and inductive tasks.ChatGPT is better oriented in deductive and inductive tasks but often misses the direction in abductive and mixed-form reasoning; the models therefore differ in activity and orientation.Source: §5.4 · p. 8, §5.5 · p. 8

5.6 Are LLMs Easy to Induce Hallucination in Logical Reasoning?

  • ChatGPT ranks first in avoiding hallucinations in deductive, inductive, and mixed-form settings, while BARD ranks last across all four settings.The paper counts context-contradicting or context-unverified facts as hallucinations; hallucinations occur in 27.46% of failure cases on average.Source: §5.6 · pp. 8, 10

5.3 Do LLMs Have Obvious Logical Flaws?

  • Across problematic cases, wrong evidence selection accounts for 33.26%, hallucination for 27.46%, perspective mistakes for 44.47%, and process mistakes for 36.20%.No-reasoning errors cover 19.33% of selected cases; the authors identify evidence and perspective selection as central challenges.Source: §5.3 · pp. 7–8, Figure 6 · p. 9

5.7 How Does the Number of Statements Affect the LLMs’ Performances?

  • With more input statements, performance generally drops, although five of six datasets show gains at certain statement counts; increasing context tokens also generally lowers ChatGPT performance.ChatGPT remains relatively stable as token counts rise on the EntailmentBank and Leap-of-Thought deductive datasets.Source: §5.7 · p. 10

5.8 How Does the Number of Reasoning Hops Affect the LLMs’ Performances?

  • More reasoning hops reduce ChatGPT’s deductive performance and sharply weaken induction beyond two hops, while abductive performance improves slightly with more hops.For three to nine inductive hops, performance stays stable at a relatively low level; most abductive test samples require one hop.Source: Figure 10 · p. 11, §5.8 · p. 11

5.9 Does Chain-of-Thought or Program-of-Thought Help Logical Reasoning?

  • Chain-of-thought does not consistently improve logical reasoning and often harms abductive results, while program-of-thought benefits stronger models but challenges many current LLMs.The paper evaluates program-of-thought using generated first-order logic and an external solver; open-source models benefit more from chain-of-thought but fail with program-of-thought.Source: §5.9 · pp. 11–12

6 NEUTRAL-CONTENT LOGICAL REASONING

The authors introduce NeuLR, a 3,000-sample neutral-content benchmark, and evaluate it under zero-shot, one-shot, and chain-of-thought settings. Results differ from the classical datasets: prompting improves performance in most cases, and inductive reasoning is generally stronger than deductive and abductive reasoning.

6 NEUTRAL-CONTENT LOGICAL REASONING

  • NeuLR contains 3,000 neutral-content samples, evenly divided among deductive, inductive, and abductive reasoning.The benchmark is proposed to reduce knowledge-bias influences in logical-reasoning evaluation.Source: §6 · p. 12
  • Few-shot and chain-of-thought prompting boost LLM performance in most NeuLR cases, with chain-of-thought helping accuracy most.text-davinci-003 shows consistent gains with both prompting strategies.Source: §6 · p. 12
  • BARD performs best and ChatGPT worst in zero-shot NeuLR results, but text-davinci-003 surpasses BARD with chain-of-thought prompting.The paper reports significant differences among zero-shot results and says overall NeuLR performance still has substantial room for improvement.Source: §6 · p. 12
  • On NeuLR, LLMs generally perform better in inductive than deductive or abductive reasoning, unlike the ordering reported for fifteen classical datasets.The authors identify an obvious weakness in abductive reasoning and suggest content neutrality can enhance strategies for inductive performance.Source: §6 · p. 12

7 CONCLUSION

The paper evaluates LLM logical reasoning across four reasoning settings and proposes a six-dimension evaluation scheme. Its results show model-specific strengths and weaknesses, with inductive reasoning a common challenge.

7 CONCLUSION

  • The evaluation covers fifteen datasets, four reasoning settings, three representative LLMs, and fine-level answer, explanation, and error analyses.The paper also proposes NeuLR, a neutral-content dataset covering deductive, inductive, and abductive settings.Source: §7 · p. 12
  • The proposed evaluation scheme measures LLM reasoning across Correct, Rigorous, Self-aware, Active, Oriented, and No hallucination dimensions.The paper visualizes ability maps across deductive, inductive, abductive, and mixed-form settings.Source: §7 · p. 12, Figure 11 · p. 13
  • Text-davinci-003 performs in a balanced way in deductive and mixed-form settings, but struggles with orientation in inductive tasks and laziness in abductive tasks.The paper characterizes its limitations as especially apparent in more complex settings.Source: §7 · p. 12, Figure 11 · p. 13
  • ChatGPT is weakest on common evaluations of correct and rigorous reasoning across deductive, inductive, and abductive settings, yet has advantages in orientation and avoiding hallucinations.It also shows comprehensive capability in mixed-form reasoning; the paper visualizes latest-model comparisons separately.Source: §7 · pp. 12–13, Figure 12 · p. 13
  • BARD is the most active reasoner and remains competitive in correctness and rigor, but shows weaknesses in self-awareness, orientation, and avoiding hallucinations.The authors also report redundant content and difficulty finding correct reasoning directions.Source: §7 · p. 13
  • All evaluated LLMs show specific reasoning limitations, with relative strength in deductive reasoning but evident struggles in inductive settings.The paper also finds objective-metric benchmarks insufficient for comprehensive evaluation.Source: §7 · p. 13
  • Supplementary automatic evaluations of four trending LLMs are presented as a check on the evaluation system’s scalability.The appendix provides visualizations of these models across six dimensions.Source: §7 · p. 13, Figure 12 · p. 13

8 FUTURE DIRECTIONS

The future directions target reasoning weaknesses identified in the evaluation, including inductive performance, capability awareness, rigor, hallucination, multi-hop reasoning, and explainability. The appendix also documents selected models and evaluation materials.

8 FUTURE DIRECTIONS

  • LLMs perform poorly at inductive reasoning, motivating work on pre-training or fine-tuning strategies, including inductive instructions.The passage contrasts inductive reasoning’s abstraction demands with deductive and abductive reasoning.Source: §8 · p. 13

Enhance the LLM’s perception of its capability bound-

  • Future work could strengthen LLMs’ awareness of their capability bounds so they can recognize when to refrain from answering.The passage notes that outputs may include irrelevant information or fabrications.Source: Enhance the LLM’s perception of its… · p. 13

Strengthen the rigorous reasoning to apply to real-world

  • Current LLMs are not sufficiently rigorous in deductive, inductive, and abductive reasoning, limiting their readiness for applications requiring detailed intermediate explanations.The passage names mathematical problem solving and precise educational Q&A as examples.Source: Strengthen the rigorous reasoning to… · p. 13
  • The paper calls for reducing hallucinations, improving multi-hop reasoning especially in inductive and abductive settings, and increasing explainability.It suggests more comprehensive hallucination metrics and strategies, question decomposition, and commonsense-based neuro-symbolic frameworks.Source: Strengthen the rigorous reasoning to… · pp. 13–14

APPENDIX

  • The appendix describes the study’s models, evaluation methodology, prompt engineering, NeuLR dataset, supplementary analyses, and dataset case studies.It presents this material as a detailed account of the methods and results.Source: APPENDIX · p. 16

APPENDIX A DETAILS OF LARGE LANGUAGE MODELS

  • The appendix lists three previously representative LLMs and four up-to-date LLMs selected for evaluation and analysis.Table 6 includes model affiliation, usage charge, pre-training data, and size.Source: Appendix A · p. 16, Table 6 · p. 16

APPENDIX B DETAILS OF EVALUATIONS

  • Appendix B supplements details of the evaluation.The supplied passage does not specify those details further.Source: Appendix B · p. 16

B.1 Evaluated Datasets

The appendix describes dataset sampling and evaluation modes for the study. It also reports the fact-length distribution in mixed-form reasoning datasets.

B.1 Evaluated Datasets

  • For large datasets, sample caps range from 600 to 1,000 cases, while text-davinci-003 and BARD use 100 randomly sampled examples per dataset.The four latest LLMs also use 100 randomly sampled cases per dataset; ChatGPT uses full datasets except for the listed large-scale datasets.Source: §B.1 · p. 16
  • Most samples in the four mixed-form datasets contain 1–2 or 3–4 facts.Table 7 reports the fact-length distributions as percentages.Source: §B.1 · p. 16, Table 7 · p. 16

B.2 Evaluation Modes

  • The evaluation uses four answer and explanation metrics, plus five metrics for attributing error cases.The three representative LLMs are manually annotated by ten NLP graduate students, while four trending LLMs are scored automatically by GPT-4o as an LLM judge.Source: §B.2 · p. 16

APPENDIX C SUPPLEMENTARY RESULTS ON LATEST LLMS

The appendix checks automatic judging against human annotation and supplements results for four trending LLMs. It also notes that the evaluation implementation considers both zero-shot and few-shot settings.

APPENDIX C SUPPLEMENTARY RESULTS ON LATEST LLMS

  • LLM-as-judge aligns well with human performance in the evaluation settings, based on a pilot comparison of 300 samples.The comparison covers four answer and explanation metrics and two error categories.Source: Figure 13 · p. 16, Appendix C · p. 16
  • The appendix presents automatic evaluation results for four trending LLMs across six dimensions, using heatmaps for correctness, rigorousness, self-awareness, activity, orientation, and no-hallucination.The supplied passages identify the result visualizations but do not state specific outcomes.Source: Appendix C · p. 17, Figure 14 · p. 17, Figure 15 · p. 17

APPENDIX D PROMPT ENGINEERING

  • The implementation considers both zero-shot and few-shot settings and uses constructed prompts to obtain model outputs.The prompts are shown in Appendix Table 10.Source: Appendix D · p. 17

APPENDIX E NEULR DATASET

Appendix E describes NeuLR’s construction and prompt forms: selected content words are neutralized, and prompts explain the neutral strings used in the reasoning task.

E.1 Construction of NeuLR

  • NeuLR is proposed to benchmark pure logical reasoning by reducing the influence of knowledge bias through neutral content.The data is sourced from,.Source: §E.1 · p. 17
  • Names, species, and properties are replaced by type-specific prefixes followed by six randomly generated characters.Table 9 illustrates the replacement process.Source: §E.1 · p. 17, Table 9 · p. 17

E.2 Prompt Forms

  • NeuLR prompts identify the task as neutral-content abductive reasoning, define the NP, SP, and ADP prefixes, and request a short missing fact.Other parts of the prompts remain the same as in the previous form.Source: §E.2 · p. 17
  • The evaluation includes zero-shot, few-shot, and chain-of-thought settings, with chain-of-thought prompts using dataset-provided explanations.The appendix provides reasoning examples for the settings.Source: §E.2 · pp. 18–19

APPENDIX F SUPPLEMENTARY ANALYSIS

The hop-count analysis finds a cross-task gap: LLMs perform relatively well in deduction but remain far from good in induction and abduction.

Supplementary analysis

  • text-davinci-003’s performance drops as hops increase in induction and abduction, failing all inductive cases above six hops and abductive cases above one hop.In deduction, performance declines overall but shows slight gains above five hops; the authors describe potential for multi-hop reasoning in that setting.Source: Appendix F · p. 19
  • BARD reaches 100% deductive accuracy above five hops without reduced rigor, and its inductive performance stabilizes and gains above six hops.BARD struggles in abduction, where it is inferior to ChatGPT but better than text-davinci-003.Source: Appendix F · p. 19
  • LLMs do relatively well in deductive multi-hop reasoning but remain far from good in inductive and abductive settings.The authors conclude that complex multi-hop reasoning still leaves substantial room for improvement.Source: Appendix F · p. 19

APPENDIX G CASE STUDIES

The case studies show model outputs on reasoning examples alongside annotations of answer and explanation quality, including errors in evidence selection and reasoning.

APPENDIX G CASE STUDIES

  • The case studies display contexts, questions, and outputs from several ChatGPT, Davinci-003, and BARD settings, with annotations for answer and explanation quality and reasoning errors.The annotations include answer correctness, explanation correctness, completeness, redundancy, and five error indicators for false explanations.Source: Appendix G · p. 19
  • For the donut abductive case, ChatGPT lists four possible explanations for the extra donut and says the true hypothesis cannot be known for sure.The case is annotated for answer correctness, explanation correctness, completeness, and redundancy.Source: Appendix G · pp. 30–31
  • In the rule-based case, the generated explanation for “Dave is rough” gives “Dave is sad” and cites facts 9 and 18.Another missing-fact case answers that the bear likes the cat and cites Fact15.Source: Appendix G · pp. 32–33
  • Critical-reasoning examples mark the temperature extrapolation flaw as D, challenge the microwave argument with D, infer D in a ranking question, and label the survey conclusion entailed..Source: Appendix G · pp. 34–37

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