2404.04293v1

# Reason from Fallacy: Enhancing Large Language Models’ Logical Reasoning through Logical Fallacy Understanding Abstract Large Language Models (LLMs) have demonstrated good performance in many reasoning tasks, but they still struggle with some complicated reasoning tasks including logical reasoning. One non-negligible reason for LLMs’ suboptimal performance on logical reasoning is their overlooking of understanding logical fallacies correctly. To evaluate LLMs’ capability of logical fallacy understanding (LFU), we propose five concrete tasks from three cognitive dimensions of WHAT, WHY, and HOW in this paper. Towards these LFU tasks, we have successfully constructed a new dataset LFUD based on GPT-4 accompanied by a little human effort. Our extensive experiments justify that our LFUD can be used not only to evaluate LLMs’ LFU capability, but also to fine-tune LLMs to obtain significantly enhanced performance on logical reasoning. Reason from Fallacy: Enhancing Large Language Models’ Logical Reasoning through Logical Fallacy Understanding Yanda Li ${}^{\dagger}$ , Dixuan Wang ${}^{\dagger}$ , Jiaqing Liang ${}^{{\dagger}{\ddagger}\textrm{\Letter}}$ , Guochao Jiang ${}^{\dagger}$ , Qianyu He ${}^{\dagger}$ , Yanghua Xiao ${}^{{\dagger}{\ddagger}}$ , Deqing Yang ${}^{{\dagger}{\ddagger}\textrm{\Letter}}$ ${}^{\dagger}$ School of Data Science, Fudan University, Shanghai, China ${}^{\ddagger}$ Shanghai Key Laboratory of Data Science, Shanghai, China ${}^{\dagger}$ {ydli22, dxwang23, gcjiang22, qyhe21}@m.fudan.edu.cn ${}^{\ddagger}$ {liangjiaqing, shawyh, yangdeqing}@fudan.edu.cn 1 Introduction As a cognitive process, logical reasoning plays an important role in many intellectual activities, such as problem solving, decision making and planning Huang and Chang (2022). Up to now, a lot of efforts have been dedicated to logical reasoning based on language models Cresswell (1973); Kowalski (1974); Iwańska (1993); Liu et al. (2020). More recently, the popularity of large language models (LLMs) such as ChatGPT Ouyang et al. (2022) and GPT-4 OpenAI (2023) stimulates the growth of research on LLM-based logical reasoning. Compared to traditional small language models, LLMs have demonstrated better performance in many reasoning tasks. <details> <summary>x1.png Details</summary>  ### Visual Description ## Diagram: Fallacy Detection by LLM ### Overview The diagram illustrates how a Large Language Model (LLM) can identify a fallacy in reasoning. It shows the transformation of a premise into a hypothesis and the LLM's role in detecting a faulty generalization. The diagram is divided into "Before" and "After" states, highlighting the LLM's intervention. ### Components/Axes * **Top:** * **Premise:** "My French colleague is very romantic." (Contained in a light blue rounded rectangle) * **Arrow:** A blue arrow with a question mark above it, pointing from the premise to the hypothesis. * **Hypothesis:** "I think all French people are romantic." (Contained in a light blue rounded rectangle) * **Bottom-Left ("Before"):** * **Label:** "Before" (Bold text) * **LLM (Robot):** A cartoon robot labeled "LLM" * **Entailment:** A light pink rounded rectangle containing the word "Entailment." * **Red X:** A red "X" mark above the "Entailment" box. * **Red Dashed Border:** A red dashed line surrounds the "Before" section. * **Center:** * **Fallacy Knowledge:** A light yellow rounded rectangle labeled "Fallacy Knowledge" with a book and lightbulb icon. * **Fallacy Rules:** * "A has B -> C has B" * "A in C" * "D in E -> F in D" * "E in F" * "......" * **Bottom-Right ("After"):** * **Label:** "After" (Bold text) * **LLM (Robot):** A cartoon robot labeled "LLM" with a magnifying glass. * **Contradiction! This is Faulty Generalization.:** A light green rounded rectangle containing the text "Contradiction! This is Faulty Generalization." * **Green Checkmark:** A green checkmark above the "Contradiction!" box. * **Green Dashed Border:** A green dashed line surrounds the "After" section. * **Arrows:** * A red arrow points from the "Fallacy Knowledge" box to the "LLM" in the "After" section. * Grey dashed lines connect the "Before" and "After" sections to the premise and hypothesis. ### Detailed Analysis * **Premise to Hypothesis:** The premise "My French colleague is very romantic" is transformed into the hypothesis "I think all French people are romantic." This transformation is indicated by a blue arrow with a question mark, suggesting a potential logical leap or inference. * **Before State:** Initially, the LLM incorrectly identifies the premise as entailing the hypothesis, indicated by the "Entailment" label and the red "X" mark. * **Fallacy Knowledge:** The "Fallacy Knowledge" box contains general rules or patterns of fallacious reasoning. The rules are represented as "A has B -> C has B", "A in C", "D in E -> F in D", and "E in F". The "......" suggests that there are more rules not explicitly listed. * **After State:** After applying its "Fallacy Knowledge," the LLM correctly identifies the hypothesis as a "Contradiction!" and a "Faulty Generalization," indicated by the green checkmark. The LLM in the "After" state has a magnifying glass, suggesting it is analyzing the information. ### Key Observations * The diagram highlights the LLM's ability to evolve its understanding of a statement from an initial incorrect assessment ("Entailment") to a correct identification of a fallacy ("Contradiction! This is Faulty Generalization."). * The "Fallacy Knowledge" box is crucial, as it provides the LLM with the necessary rules to detect logical fallacies. * The use of visual cues (red "X" and green checkmark) clearly indicates the LLM's initial error and subsequent correction. ### Interpretation The diagram demonstrates how an LLM can be used to identify and correct faulty reasoning. The LLM initially makes an incorrect assessment, but by applying its "Fallacy Knowledge," it can identify the logical fallacy and correct its assessment. This suggests that LLMs can be valuable tools for improving the quality of reasoning and decision-making. The diagram illustrates the importance of equipping LLMs with knowledge of common fallacies to improve their reasoning capabilities. The transformation from "Entailment" to "Contradiction!" shows the LLM's ability to learn and adapt its understanding based on new information. </details> Figure 1: LLMs have deficiencies in logical reasoning. Once they understand logical fallacies, they know how to avoid logical fallacies, and thus improve their performance in various logical reasoning tasks. However, LLMs still struggle with some more complex reasoning tasks including logical reasoning. One non-negligible reason for LLMs’ suboptimal performance on logical reasoning is their overlooking of understanding logical fallacies correctly. As early as 350 BC, Aristotle first proposed the concept of logical fallacy in his work Sophistical Refutations Aristotle (2006). Since then, logical fallacies have gradually become an important issue that should be noticed in our lives. “ Thou shalt not commit logical fallacies! ” has even become a worldwide popular idiom to remind us not to commit logical fallacies. By definition, logical fallacies refer to the errors in reasoning Tindale (2007), and they usually happen when the premises are not relevant or sufficient to draw the conclusions. Many previous works Liu et al. (2020); Yu et al. (2020); Joshi et al. (2020); Han et al. (2022) have focused on evaluating LLM logical reasoning capabilities from the perspective of deductive reasoning, natural language inference, reading comprehension, etc. However, few works focus on logical fallacies, which is in fact the major reason causing logical inconsistency in the sentences. Chen et al. have observed that, LLMs often commit logical fallacies in logical reasoning, such as "Either protect the environment or develop the economy." (false dilemma) and "Some roses are not red because not all roses are red." (circular reasoning). It has been found that language models could avoid mistakes only when they understand what mistakes are Chen et al. (2023a); An et al. (2023), which justifies the ancient Greek philosopher Epicurus’s saying “ The mistake is the first step to save yourself. ” Based on our empirical studies, we have also found that the logical reasoning capability of LLMs is closely related to their understanding of logical fallacies. The previous studies related to logical fallacy Jin et al. (2022); Sourati et al. (2023); bench authors (2023) only focus on logical fallacy detection, i.e., the identification and classification of logical fallacies, rather than systematically evaluating LLMs’ capability of logical fallacy understanding (LFU), not to mention improving LLMs’ LFU capability. Moreover, they have not explored the relationships between LFU and logical reasoning, which is crucial to improve LLMs’ capability of logical reasoning through enhancing their LFU capability. To address this problem, we focus on evaluating and enhancing LLMs’ LFU capability in this paper, so as to enhance their capability of logical reasoning. Nonetheless, our work has to face several challenges as follows. First, we need to formalize the concrete tasks for LFU, since no previous studies focus on this problem. Second, we need a new dataset specific to LFU, as the previous datasets of logical fallacies Jin et al. (2022) only contain the logical fallacy types presenting in the sentences. To this end, we should propose a framework of constructing the LFU dataset towards the concrete LFU tasks, and then truthfully evaluating LLMs’ LFU capability with the dataset. To overcome these challenges, we primarily focus on constructing a dataset for LFU in this paper, of which the samples are generated to evaluate models’ achievement on the following five LFU tasks corresponding to three cognitive dimensions of WHAT, WHY, and HOW Swanborn (2010). 1. WHAT -Identification (Task 1) and Classification (Task 2): identifying whether the given sentence contains a logical fallacy and which type of logical fallacy it is. 1. WHY -Deduction (Task 3) and Backward Deduction (Task 4): capturing the reasons causing the logical fallacy in the sentence. 1. HOW -Modification (Task 5): correcting the logical fallacy in the sentence. Our proposed LFU tasks simulate the human understanding process of logical fallacies. Towards these tasks, we design a pipeline framework to automatically generate and synthesize a high-quality dataset, namely Logical Fallacy Understanding Dataset (LFUD), based on GPT-4 accompanied by a little human effort. Specifically, we first collect some sentences as the propositions (statements) which are the basic logic units and used to generate the sentences containing logical fallacies. Then, with the help of GPT-4, we generate sentences based on the propositions with twelve typical logical fallacy types Jin et al. (2022). And for each LFU task we propose, the instances of each fallacy type are synthesized. Then, we use our LFUD to evaluate the LFU capability of some representative LLMs. For the ultimate objective of our work, i.e., enhancing LLMs’ capability of logical reasoning, we further fine-tune these LLMs with the instances in LFUD. Our extensive experiments reveal that fine-tuning LLMs with LFUD can significantly enhance their logical reasoning capability. In summary, our main contributions in this paper include: 1. Inspired by the three cognitive dimensions of WHAT, WHY, and HOW, we propose five concrete tasks which can truthfully evaluate LLMs’ performance on LFU. 2. Towards our proposed five LFU tasks, we devise a new framework for constructing a high-quality dataset, namely LFUD, to evaluate LLMs’ LFU capability, so as to enhance LLMs’ performance on logical reasoning. 3. The LFUD we constructed includes 4,020 instances involving 12 logical fallacy types. Our extensive experiments have demonstrated that our LFUD can not only evaluate LLMs’ LFU capability, but also improve LLMs’ capability of logical reasoning through fine-tuning LLMs with LFUD samples in terms of the LFU tasks. 2 Related Work <details> <summary>x2.png Details</summary>  ### Visual Description ## Diagram: Logical Fallacy Understanding Dataset (LFUD) Creation and Application ### Overview The image is a diagram illustrating the process of creating a Logical Fallacy Understanding Dataset (LFUD) and its application in enhancing Large Language Models (LLMs) for logical reasoning. It outlines the data collection, synthesis, and fine-tuning stages, along with performance evaluation and selected datasets. ### Components/Axes * **Propositions:** Starting point for generating sentences. * **Corpus:** Collection of text data. * Methods for Collection: * Books on Logic and Philosophy * Wikipedia, Philosophy Encyclopedia * GPT-4 * Criteria for Filtering: * Quantity of Subjects * Polarity of Propositions * **Logical Fallacy Sentences:** Sentences containing logical fallacies. * **Logical Fallacy Understanding Dataset (LFUD):** Dataset created for training LLMs. * Dimensions: * WHAT: * Task 1: Identification - Identify whether the given sentence has logical fallacy. * Task 2: Classification - Select the sentence belonging to a certain type of logical fallacy. * WHY: * Task 3: Deduction - Derive the conclusion from the premise according to a certain type of logical fallacy. * Task 4: Backward Deduction - Infer the premise from the conclusion according to a certain type of logical fallacy. * HOW: * Task 5: Modification - Correct the logical fallacy in the given sentence. * **LLMs Enhancement in Logical Reasoning:** Application of LFUD to improve LLMs. * **Selected Datasets:** Datasets used for evaluation. * First-order Logic Reasoning: FOLIO * Natural Language Inference: TaxiNLI * Reading Comprehension: LogiQA, Reclor * **12 Types of Logical Fallacies:** * Faulty Generalization * False Causality * Circular Reasoning * Ad Populum * Ad Hominem * Deductive Fallacy * Appeal to Emotion * False Dilemma * Fallacy of Extension * Fallacy of Relevance * Fallacy of Credibility * Intentional Fallacy ### Detailed Analysis or ### Content Details 1. **Data Collection:** * Propositions are used to generate sentences with GPT-4. * A corpus is collected and filtered. The corpus consists of books on logic and philosophy, Wikipedia, philosophy encyclopedia, and GPT-4 generated text. * Filtering criteria include the quantity of subjects and the polarity of propositions. 2. **Logical Fallacy Sentence Generation:** * Logical fallacy sentences are synthesized based on templates. 3. **LFUD Creation:** * The LFUD is structured around three dimensions: WHAT, WHY, and HOW. * WHAT: Focuses on identifying and classifying logical fallacies. * WHY: Focuses on deduction and backward deduction related to logical fallacies. * HOW: Focuses on modifying sentences to correct logical fallacies. 4. **LLM Fine-tuning and Evaluation:** * The LFUD is used to fine-tune LLMs. * The performance of LLMs in logical reasoning tasks is evaluated. * The diagram shows a comparison of performance "Fine-tuned without LFUD" vs "Fine-tuned with LFUD", with the latter showing improved performance. * Selected datasets for evaluation include FOLIO, TaxiNLI, LogiQA, and Reclor. 5. **Performances in logical reasoning tasks:** * The diagram shows performance bars for LLMs fine-tuned without LFUD and with LFUD. * The performance bars for "Fine-tuned with LFUD" are longer than those for "Fine-tuned without LFUD", indicating improved performance. ### Key Observations * The diagram provides a clear overview of the LFUD creation and application process. * The use of GPT-4 in generating sentences and the structured approach to LFUD creation are notable. * The performance comparison highlights the effectiveness of LFUD in enhancing LLMs for logical reasoning. ### Interpretation The diagram illustrates a systematic approach to improving LLMs' logical reasoning capabilities. By creating a dedicated dataset (LFUD) focused on logical fallacies, the fine-tuned LLMs demonstrate enhanced performance in logical reasoning tasks. The process involves data collection from diverse sources, synthesis of logical fallacy sentences, and a structured approach to training the LLMs. The performance comparison between LLMs fine-tuned with and without LFUD underscores the value of this approach. The diagram suggests that targeted datasets, like LFUD, can significantly improve the performance of LLMs in specific domains. The presence of "自動車" is not relevant to the diagram and appears to be an OCR error. </details> Figure 2: Our framework of constructing LFUD and fine-tuning LLMs with LFUD to enhance logical reasoning. At first, we collected some propositions, based on which the sentences with the logical fallacies of 12 types were generated by GPT-4. Then, for the five LFU tasks we proposed, the QA instances were synthesized based on the previous generated sentences. Finally, we fine-tuned LLMs with LFUD, revealing that fine-tuning LLMs with LFUD can significantly enhance their logical reasoning capability. Logical Reasoning Up to now, a lot of efforts have been dedicated to logical reasoning based on language models Cresswell (1973); Kowalski (1974); Iwańska (1993); Liu et al. (2020). In particular, how to evaluate the models’ logical reasoning capability has attracted increasing attention, including deductive reasoning Ontanon et al. (2022); Han et al. (2022), natural language inference (NLI) Yanaka et al. (2019); Joshi et al. (2020); Liu et al. (2021) and multi-choice reading comprehension (MRC) Liu et al. (2020); Yu et al. (2020); Wang et al. (2022). Recently, the power of LLMs has stimulated the research on logical reasoning with LLMs, including LLMs evaluation Yu et al. (2023); Blair-Stanek et al. (2023); Teng et al. (2023), and LLMs enhancement Zhang et al. (2023); Chen et al. (2023b). Despite these works’ achievements, enhancing LLMs’ logical reasoning capability remains a non-negligible challenge. The major reason for logical inconsistencies in many sentences is the misunderstanding of logical fallacies, which is still under-explored in the research field of logic. Logical Fallacy Logical fallacy is the main reason for the logical inconsistencies presenting in our life. As early as 350 BC, Aristotle first proposed the concept of logical fallacy in his work Sophistical Refutations Aristotle (2006). Since then, logical fallacies have gradually gained attention in human society. In recent years, the studies related to logical fallacies mainly focused on dataset construction Habernal et al. (2018); Martino et al. (2020); Jin et al. (2022) and fallacy classification Stab and Gurevych (2017); Goffredo et al. (2022); Jin et al. (2022); Payandeh et al. (2023). For instance, Jin et al. first proposed the task of Logical Fallacy Detection, presenting a framework of 13 logical fallacy types, and evaluated all sentence samples on a classification task. Sourati et al. proposed a Case-Based Reasoning method that classifies new cases of logical fallacy by language-modeling-driven retrieval and the adaptation of historical cases. However, there is no work to systematically evaluate LLMs’ capability of logical fallacy understanding (LFU). For the first time, our work in this paper proposes a new dataset specific to LFU represented by five concrete tasks corresponding to three cognitive dimensions of WHAT, WHY, and HOW. Learning from Synthetic Data Synthesizing data for model training has gradually gained popularity along with the advancements of language models. This approach is particularly beneficial for tasks that are difficult to be constructed or those with scarce data resources Møller et al. (2023). Currently, synthetic data has been applied in various tasks such as relation extraction Papanikolaou and Pierleoni (2020), text classification Chung et al. (2023), irony detection Abaskohi et al. (2022), translation Sennrich et al. (2015), and sentiment analysis Maqsud (2015). For example, Josifoski et al. proposed a strategy to design an effective synthetic data generation pipeline and applied it to closed information extraction. In addition, Li et al. conducted a series of experiments to evaluate the effectiveness of LLMs in generating synthetic data to support model training for different text classification tasks. Beyond these fundamental tasks, Eldan and Li proposed to use LLMs with synthetic data to generate short stories typically for 3 to 4-year-old only containing words. But they did not focus on logical fallacy. We are the first to focus on the data augmentation strategies in LFU. 3 Methodology of Dataset Construction In this section, we present the pipeline of constructing our LFUD, of which the overall framework is depicted in Figure 2. Starting from the propositions, we detail the steps of synthesizing the samples towards five LFU tasks and the twelve representative logical fallacy types. | Singular Proposition | 54 | | --- | --- | | Particular Proposition | 5 | | Universal Proposition | 8 | | Affirmative Proposition | 56 | | Negative Proposition | 11 | | Propositions without Pronouns | 58 | | Propositions with Pronouns | 9 | | Propositions with Human Subjects | 52 | | Propositions with Non-Human Subjects | 15 | Table 1: Some statistics of the 67 propositions in LFUD. 3.1 Acquiring Propositions At the first step of constructing our LFUD, we collected some propositions which were subsequently used for generating the sentences presenting various logical fallacies. According to Hurley (2000), a proposition is one sentence that is either true or false. We considered several sources of proposition collection, including some authoritative books of logic and philosophy Hurley (2000); Hausman (2012), open websites such as Wikipedia and Stanford Encyclopedia of Philosophy. In addition, LLMs can be utilized to generate some propositions for enriching proposition diversity. To seek the satisfactory LLM for generating propositions, we tested some representative LLMs’ identification performance on 200 instances from the Big-Bench bench authors (2023), consisting of correct and incorrect (logical fallacy) sentences. The results showed that GPT-4 can correctly identify in over 90% of the sentences whether they have logical fallacies, despite the limited capability in directly generating complex tasks. Thus, we leveraged GPT-4 to generate more propositions and subsequent sentences presenting logical fallacies. The considerable propositions should be simple and intuitive, but diverse. Finally, we filtered out 67 propositions and the relevant statistics are listed in Table 1. The following sentences are the proposition examples: 1. Everyone in my family has never been to Europe. 2. X accepted Y’s suggestion. 3. Michael had dinner at an Italian restaurant. | /* Generation Instruction */ As a logician, when presented with a proposition, your objective is to simulate the way of human thinking, generating a sentence with specific type of logical fallacy. The generation should follow these instructions: 1. Generate the sentence with Faulty Generalization. Faulty Generalization occurs when … (Detailed description) 2. The sentence should have complete premise and conclusion, but try not to make it too long. /* Three demonstration examples */ Proposition 1: Neither of the classes I took at UF were interesting. Result 1: A college is not a good college if none of its classes are interesting. Neither of the classes I took at UF were interesting, so UF is not a good college. … /* Input the proposition */ Proposition: Peter visited China last year. /* GPT-4’s output */ Result: Peter visited China last year. Peter is a European. Therefore, all Europeans have been to China. | | --- | Table 2: A prompt case for GPT-4 to generate a sentence with the given logical fallacy type. 3.2 Generating Sentences with GPT-4 Given GPT-4’s capability of natural language generation and logical fallacy identification, we directly used GPT-4 to generate the sentences presenting various logical fallacies in this step. To take into account the logical fallacies existing in our life as many as possible, we refered to the thirteen typical types of logical fallacies (as listed in Table 7 and Appendix B) proposed by Jin et al. (2022). | Dimension | Task name | Task definition | | --- | --- | --- | | WHAT | Task1: Identification | Identify whether the given sentence has logical fallacy. | | Task2: Classification | Select the sentence belonging to a certain type of logical fallacy. | | | WHY | Task3: Deduction | Derive the conclusion from the premise according to a certain type of logical fallacy. | | Task4: Backward Deduction | Infer the premise from the conclusion according to a certain type of logical fallacy. | | | HOW | Task5: Modification | Correct the logical fallacy in the given sentence. | Table 3: Five LFU tasks corresponding to three cognitive dimensions. Given a proposition and a certain logical fallacy type, we asked GPT-4 to generate a sentence of this logical fallacy type with a prompt, which contains the generation instruction and a demonstration example of the given logical fallacy type. Table 2 illustrates the prompt for GPT-4 about the type of Faulty Generalization. Specifically, due to the rather vague definition of Equivocation provided by Jin et al. (2022), and the scarcity of such fallacy instances in real life, GPT-4 can hardly understand Equivocation and generate corresponding sentences correctly. To ensure the quality of the sentences generated by GPT-4, we neglected Equivocation fallacy type and generated the sentences for the rest twelve logical fallacy types. To ensure that the generated sentences meet the requirements, we further manually proofread the sentences with logical fallacies generated by GPT-4. Each generated sentence was proofread with two main areas of concern: structural integrity and validity of fallacies, as described in Appendix C, to ensure that the sentences made sense and met the requirements of specific fallacy type. For each of the 67 propositions, we generated 12 sentences with GPT-4, each of which presents one logical fallacy type. Thus, we generated 804 sentences with logical fallacies in total. These sentences are used to synthesize the samples for concrete LFU tasks as follows. 3.3 Proposing LFU Tasks and Synthesizing Task Instances To evaluate LLMs’ capability of LFU, we need to design concrete evaluation tasks. According to the principles of cognitive science Swanborn (2010), humans generally understand objects from three dimensions: WHAT it is, WHY it is, and HOW it operates, which are interconnected and progressive cognition levels. Inspired by these dimensions, we propose five concrete tasks which are used to verify models’ capability of LFU. Table 3 lists the definitions of the five tasks. Wherein, Task 1 and Task 2 belong to WHAT dimension, which identify whether the given sentence has the logical fallacy (of a certain type). Task 3 and Task 4 belong to WHY dimension, which verify whether the model captures the reason causing the logical fallacy in the sentence. The last Task 5 belongs to HOW dimension, which requires correcting the logical fallacy of the given type in the sentence. Specifically, we synthesized multiple-choice questions for the first four tasks, and sentence generation questions for Task 5. We further provided one toy example for each task in Appendix A. In fact, previous studies Jin et al. (2022); bench authors (2023) have focused on the two tasks of WHAT dimension, i.e., understanding what the logical fallacy in the sentence is. To the best of our knowledge, there are no studies concerning the tasks of WHY and HOW dimensions by now. But notably, the ultimate goal of LFU is to avoid logical fallacies, which requires us to understand the reasons causing logical fallacies and correct logical fallacies. Therefore, we paid more attention to the tasks of WHY and HOW dimension in this paper. For each sentence with one of the twelve logical fallacy types generated in the previous step, we synthesized one QA instance for every LFU task with the question templates. For each LFU task, the question stems (without question options) of all instances are generated according to some templates, as shown in Appendix A. Particularly, for Task 3 and Task 4, we need to identify the premise and conclusion for the given sentence, and further provide question options. Thus, we directly asked GPT-4 to generate the results as we needed. To minimize the impact of instruction design when asking LLMs to achieve these tasks, we first designed some candidate question templates to constitute a template pool in fact, and then randomly chose one template from the pool to generate the question for a certain LFU task. In addtion, we also shuffled the orders of question options. Finally, our LFUD contains 4,020 (QA) instances in total, involving 5 LFU tasks and 12 logical fallacy types, which stem from the 67 propositions and 804 sentences with logical fallacies. LFUD is provided at https://github.com/YandaGo/LFUD 4 Evaluation | LogiQA2.0 | Origin | 45.55 | - | 42.30 | - | 52.74 | - | 47.71 | - | 54.39 | - | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Origin+LOGIC | 44.66 | -1.95 | 35.62 | -15.79 | 53.37 | 1.19 | 45.10 | -5.47 | 52.93 | -2.68 | | | Origin+LFUD | 47.90 | 5.16 | 43.13 | 1.96 | 55.85 | 5.90 | 47.84 | 0.27 | 56.55 | 3.97 | | | Reclor | Origin | 47.20 | - | 40.40 | - | 54.40 | - | 49.20 | - | 55.80 | - | | Origin+LOGIC | 46.20 | -2.12 | 42.20 | 4.46 | 54.00 | -0.74 | 47.80 | -2.85 | 55.80 | 0.00 | | | Origin+LFUD | 50.20 | 6.36 | 46.40 | 14.85 | 57.00 | 4.78 | 51.80 | 5.28 | 58.20 | 4.30 | | | TaxiNLI | Origin | 68.54 | - | 62.68 | - | 78.91 | - | 77.47 | - | 82.33 | - | | Origin+LOGIC | 40.60 | -40.76 | 58.80 | -6.19 | 77.92 | -1.25 | 76.18 | -1.67 | 82.18 | -0.18 | | | Origin+LFUD | 73.70 | 7.53 | 67.26 | 7.31 | 79.76 | 1.08 | 77.77 | 0.39 | 84.02 | 2.05 | | | FOLIO | Origin | 61.76 | - | 50.98 | - | 36.76 | - | 50.49 | - | 72.55 | - | | Origin+LOGIC | 62.25 | 0.79 | 52.45 | 2.88 | 36.28 | -1.31 | 45.10 | -10.68 | 73.53 | 1.35 | | | Origin+LFUD | 66.18 | 7.16 | 59.31 | 16.34 | 44.61 | 21.35 | 56.37 | 11.65 | 76.47 | 5.40 | | Table 4: LLMs’ accuracy(%) on the four logical reasoning tasks (datasets) after being fine-tuned with different data. Origin represents fine-tuning the LLMs with the original training data in the logical reasoning datasets. $\Delta\%$ is accuracy improvement relative to Origin. The best accuracy scores are bolded and the second best scores are underlined. 4.1 Experiment Setup Datasets To evaluate LLMs’ performance on logical reasoning, we used four representative datasets including FOLIO Han et al. (2022), TaxiNLI Joshi et al. (2020), LogiQA Liu et al. (2020), and Reclor Yu et al. (2020) in our experiments. FOLIO focuses on first-order logic reasoning (FOL) that is a classical deductive reasoning task. TaxiNLI is specific to natural language inference (NLI) that tests the logical relationship between a premise and a hypothesis. LogiQA and Reclor are the multi-choice reading comprehension (MRC) datasets, which choose the most suitable answer corresponding to the given text, could better reflect comprehensive logical reasoning abilities. The instances of the four datasets are shown in Appendix D. In addition to the training data in above four datasets and our LFUD, we also used the logical fallacy data LOGIC Jin et al. (2022) to fine-tune LLMs. LOGIC (including LOGIC-CLIMATE) contains thirteen types of logical fallacy sentences, as shown in Appendix B. LLMs We selected five popular LLMs in our experiments, including LLaMA2-7B, LLaMA2-13B Touvron et al. (2023), Vicuna-7B, Vicuna-13B Chiang et al. (2023) and Orca2-7B Mitra et al. (2023). When fine-tuning these LLMs, we set the learning rate to 2.5e-5 and the batch size to 8. To ensure the robustness of our results, we repeated all experiments for three times and reported the average performance (accuracy) scores. Dataset Split For the 4,020 synthesized instances in our LFUD, we randomly selected 3,000 instances (corresponding to 600 sentences with logical fallacies) as the training set and the remaining 1,020 instances (corresponding to 204 sentences with logical fallacies) as the test set. Given the instances of Task 1–4 (choice questions) have fixed answers, we only used the training samples (2,500 instances) of Task 1–4 to fine-tune the five LLMs. And we directly used some test samples of Task 5 to evaluate LLMs’ cross-task learning capability on LFU, as presented in Subsection 4.3. To balance the labels of logical right and fallacy in Task 1 instances, we appended 500 logically correct sentences of Big-Bench bench authors (2023), and thus collected 2,900 training samples in our LFUD in total. 4.2 Effectiveness on Enhancing LLMs’ Logical Reasoning 4.2.1 Overall Performance To justify the value of our LFUD instances on enhancing LLMs’ logical reasoning capability, we merged LFUD training samples with the original training samples in the four logical reasoning datasets, denoted by Origin, to fine-tune LLMs. We compared such a fine-tuning method with the method of fine-tuning LLMs only with Origin. In addition, we also compared the method of fine-tuning LLMs with Origin and some samples in LOGIC Jin et al. (2022), which have the same number as the training samples in LFUD. Table 4 lists the accuracy(%) scores of all five LLMs on the four logical reasoning tasks (datasets) which were fine-tuned with Origin, Origin+LOGIC and Origin+LFUD, respectively. And the performance improvements of Origin+LOGIC and Origin+LFUD relative to Orign are also listed. Based on the results in this table, we have the following observations and analysis. 1. Appending the training samples in our LFUD to Origin when fine-tuning LLMs significantly enhances their performance on all logical reasoning tasks. It shows that learning the LFU tasks we proposed is indeed helpful to improve LLMs’ capability of various logical reasoning. 2. Although the samples in LOGIC are also the sentences with various logical fallacies, Origin+LOGIC cannot obtain the significant performance improvements of logical reasoning. Even worse, it degrades LLMs’ logical reasoning performance, compared with Origin in some cases. It implies that, unlike our LFU tasks from WHAT, WHY and HOW, only identifying the logical fallacy presented by the sentences in LOGIC cannot result in LLMs’ really capability of LFU. In addition, The samples in LOGIC are raw and unclean, with some examples consisting of even fallacy questions and fallacy definitions. <details> <summary>x3.png Details</summary>  ### Visual Description ## Line Chart: Accuracy vs. Percentage ### Overview The image is a line chart comparing the accuracy percentages of four different models (LogiQA2.0, TaxiNLI, Reclor, and FOLIO) across varying percentage points (0%, 25%, 50%, 75%, and 100%). The chart displays how the accuracy of each model changes as the percentage increases. ### Components/Axes * **X-axis:** Percentage, with markers at 0%, 25%, 50%, 75%, and 100%. * **Y-axis:** Accuracy (%), ranging from 40% to 80% with tick marks every 5%. * **Legend:** Located in the top-left corner, identifying each model with a specific color and marker: * LogiQA2.0 (light blue, 'x' marker) * TaxiNLI (red, star marker) * Reclor (yellow, '+' marker) * FOLIO (green, circle marker) ### Detailed Analysis * **LogiQA2.0 (light blue):** The line is relatively flat, showing a slight upward trend. * 0%: 45.55% * 25%: 47.20% * 50%: 47.77% * 75%: 47.71% * 100%: 47.90% * **TaxiNLI (red):** The line shows an upward trend, starting high and increasing slightly. * 0%: 68.54% * 25%: 72.21% * 50%: 72.51% * 75%: 72.61% * 100%: 73.70% * **Reclor (yellow):** The line shows a slight upward trend. * 0%: 47.20% * 25%: 48.20% * 50%: 49.00% * 75%: 49.80% * 100%: 50.20% * **FOLIO (green):** The line shows an upward trend. * 0%: 61.76% * 25%: 63.24% * 50%: 63.73% * 75%: 64.22% * 100%: 66.18% ### Key Observations * TaxiNLI consistently has the highest accuracy across all percentage points. * LogiQA2.0 consistently has the lowest accuracy across all percentage points. * Reclor and LogiQA2.0 have similar accuracy values. * FOLIO shows a moderate increase in accuracy as the percentage increases. ### Interpretation The chart compares the performance of four different models (LogiQA2.0, TaxiNLI, Reclor, and FOLIO) at different percentage points. TaxiNLI outperforms the other models in terms of accuracy, while LogiQA2.0 performs the worst. FOLIO shows a steady improvement in accuracy as the percentage increases. Reclor's performance is similar to LogiQA2.0. The data suggests that TaxiNLI is the most effective model among the four, based on the accuracy metric. The percentage points on the x-axis likely represent the amount of data used for training or some other relevant parameter. </details> Figure 3: LLaMA2-13B’s performance on the four logical reasoning tasks with different scales of LFUD training samples. | LLaMA2-7B | 46.84 | 47.86 | 24.75 | 29.35 | 40.00 | | --- | --- | --- | --- | --- | --- | | LLaMA2-13B | 55.76 | 53.61 | 52.36 | 54.48 | 50.00 | | Vicuna-7B | 32.96 | 57.71 | 60.70 | 56.59 | 46.00 | | Vicuna-13B | 50.76 | 58.46 | 58.33 | 61.32 | 56.00 | | ChatGPT | 54.66 | 73.88 | 62.94 | 70.65 | 60.00 | | GPT-4 | 86.35 | 86.19 | 78.61 | 85.70 | 88.00 | Table 5: Six representative LLMs’ performance on our proposed five LFU tasks. To evaluate Task 5, we manually assessed LLMs’ outputs for 50 randomly selected samples. 4.2.2 Impacts of Different Factors in LFUD To further validate LFUD’s effectiveness on enhancing LLMs’ logical reasoning capability, we also investigated the impacts of different factors in LFUD, including the scale of training data, LFU tasks and logical fallacy types. Due to space limitation, we only display the results of LLaMA2-13B. Training Data Scale To verify the impacts of training data scale, we respectively extracted 25%, 50%, and 75% of the LFUD training data accompanied with Origin to fine-tune LLaMA2-13B, and then tested its performance on the four logical reasoning tasks. From Figure 3 we can see that, LLaMA2-13B’s performance improvement becomes more apparent as the training data scale increases, showing that even only a small part of LFUD samples is also valuable. LFU Task We fine-tuned LLaMA2-13B again with the training data excluding the instances of Task 1, Task 2, Task 3 and Task4, respectively. As shown in Table 6, excluding any task’s instances would lead to the performance decline of LLaMA2-13B. | No Tasks w/o Task1 w/o Task2 | 45.55 46.69 45.74 | 47.20 49.80 48.00 | 68.54 69.53 69.88 | 61.76 63.73 65.20 | | --- | --- | --- | --- | --- | | w/o Task3 | 47.46 | 49.00 | 72.01 | 64.22 | | w/o Task4 | 46.44 | 48.80 | 69.28 | 65.20 | | All Tasks | 47.90 | 50.20 | 73.70 | 66.18 | Table 6: LLaMA2-13B’s performance on the four logical reasoning tasks when excluding different LFU task’s training instances. Logical Fallacy Type Similarly, we respectively excluded the instances of each logical fallacy type from LFUD training data, and then tested LLaMA2-13B’s performance. The results in Table 7 indicate that every logical fallacy type contributes positively to LLM’s logical reasoning capability. | No Fallacy Data w/o Faulty Generalization w/o False Causality | 45.55 46.56 46.69 | 47.20 49.80 47.60 | 68.54 71.91 72.56 | 61.76 64.71 62.75 | | --- | --- | --- | --- | --- | | w/o Circular Reasoning | 46.12 | 49.80 | 72.95 | 64.22 | | w/o Ad Populum | 46.25 | 47.60 | 72.85 | 64.22 | | w/o Ad hominem | 46.95 | 48.60 | 69.53 | 65.20 | | w/o Deductive Fallacy | 45.87 | 49.40 | 73.78 | 62.75 | | w/o Appeal to Emotion | 47.65 | 49.80 | 69.93 | 63.73 | | w/o False Dilemma | 46.12 | 50.00 | 73.10 | 63.24 | | w/o Fallacy of Extension | 45.93 | 49.40 | 72.51 | 64.71 | | w/o Fallacy of Relevance | 47.65 | 50.20 | 70.92 | 61.27 | | w/o Fallacy of Credibility | 47.58 | 48.60 | 72.06 | 62.75 | | w/o Intentional Fallacy | 46.88 | 49.80 | 69.48 | 65.69 | | All Fallacy Types | 47.90 | 50.20 | 73.70 | 66.18 | Table 7: LLaMA2-13B’s performance on the four logical reasoning tasks when excluding different logical fallacy type’s training instances. 4.3 LFU Performance of LLMs Next, we validate LLMs’ capability of LFU through evaluating their performance on the LFU tasks. We want to investigate LLMs’ inherent capability on LFU, thus we directly used all instances of each LFU task in LFUD as the test samples without fine-tuning them with the training data. Performance on Each LFU Task Besides the previous four LLMs, we additionally considered ChatGPT Ouyang et al. (2022) and the latest GPT-4 OpenAI (2023) (using OpenAI API with temperature 0.7) in LFU performance evaluation. To balance the labels of Task 1, we added all 654 correct sentences in Big-Bench into Task 1’s test data. Thus, we have a total of 1,458 instances for Task 1’s evaluation. In addition, as Task 5 is to generate a new sentence rather than a fixed answer, we randomly selected 50 samples from its instances and manually assessed LLMs’ outputs. All tested LLMs’ performance is listed in Table 5, showing that different LLMs’ performance varies significantly on the five LFU tasks. Among the LLMs, GPT-4 has much better performance than others on all tasks, justifying its strong capability of LFU. By contrast, LLaMA2-7B has the worst performance that is even worse than random selection. | LLaMA-2-7B LLaMA-2-13B Vicuna-7B | 0.92 (6/654) 1.99 (13/654) 7.95 (52/654) | | --- | --- | | Vicuna-13B | 26.61 (174/654) | | ChatGPT | 37.92 (248/654) | | GPT-4 | 95.57 (625/654) | Table 8: LLMs’ Performance on identifying 654 logically correct sentences of Task 1. | Faulty Generalization False Causality Circular Reasoning | 76.12 61.19 34.33 | 89.55 70.15 52.24 | 59.70 67.16 55.22 | 50.75 65.67 62.69 | | --- | --- | --- | --- | --- | | Ad Populum | 65.67 | 80.60 | 79.10 | 79.10 | | Ad hominem | 77.61 | 89.55 | 59.70 | 59.70 | | Deductive Fallacy | 40.30 | 49.25 | 62.69 | 77.61 | | Appeal to Emotion | 16.42 | 77.61 | 64.18 | 77.61 | | False Dilemma | 29.85 | 44.78 | 62.69 | 50.75 | | Fallacy of Extension | 53.73 | 25.37 | 41.79 | 38.81 | | Fallacy of Relevance | 25.37 | 37.31 | 11.94 | 44.78 | | Fallacy of Credibility | 40.30 | 53.73 | 61.19 | 64.18 | | Intentional Fallacy | 68.66 | 31.34 | 47.76 | 64.18 | Table 9: Vicuna-13B’s performance on Task 1–4 specific to each type of logical fallacies. The best accuracy scores are bolded and the second best scores are underlined. Identifying Logical Correctness To further investigate whether LLMs really understand logical fallacies, we also asked LLMs to achieve Task 1 for the 654 sentences from Big-Bench that are logically correct (without logical fallacies). Their accuracy scores are listed in Table 8, showing that only GPT-4 has the satisfactory performance for this task. In fact, the rest LLMs tended to recognize the sentences as having logical fallacies for catering to Task 1’s question. In addition, we also found these LLMs except for GPT-4 are easily influenced by the order of question options when achieving Task 1–4, indicating that they cannot well understand logical fallacies. In Terms of Logical Fallacy Type Besides, we evaluated LLMs’ LFU performance on Task 1–4 in terms of a specific logical fallacy type. The results listed in Table 9 show that, LLMs exhibited better performance on the tasks of Faulty Generalization, False Causality, Ad populum and Ad Hominem. These four types of logical fallacies are more distinctive and more frequently present in our life, resulting in that LLMs have encountered more sentences with these logical fallacy types during their pre-training. <details> <summary>x4.png Details</summary>  ### Visual Description ## Bar Chart: Model Accuracy Comparison ### Overview The image is a bar chart comparing the accuracy of different language models, both in their original state and after fine-tuning. The chart displays the accuracy (in percentage) on the y-axis and the model names on the x-axis. Two bars are shown for each model: one representing the original accuracy (dark blue) and the other representing the fine-tuned accuracy (light blue). ### Components/Axes * **Y-axis:** "Accuracy(%)", ranging from 0 to 100, with gridlines at intervals of 20. * **X-axis:** Categorical axis representing the language models: LLaMA2-7B, LLaMA2-13B, Vicuna-7B, and Vicuna-13B. * **Legend:** Located at the top-left of the chart. * Dark blue bar: "Original" * Light blue bar: "Fine-tuned" ### Detailed Analysis The chart presents accuracy data for four language models, comparing their original and fine-tuned performance. * **LLaMA2-7B:** * Original accuracy: 40% * Fine-tuned accuracy: 48% * **LLaMA2-13B:** * Original accuracy: 50% * Fine-tuned accuracy: 62% * **Vicuna-7B:** * Original accuracy: 46% * Fine-tuned accuracy: 50% * **Vicuna-13B:** * Original accuracy: 56% * Fine-tuned accuracy: 80% ### Key Observations * Fine-tuning consistently improves the accuracy of all models. * The Vicuna-13B model shows the most significant improvement after fine-tuning, increasing from 56% to 80%. * The LLaMA2-7B model shows the smallest improvement after fine-tuning, increasing from 40% to 48%. ### Interpretation The bar chart demonstrates the impact of fine-tuning on the accuracy of different language models. The data suggests that fine-tuning is an effective technique for improving model performance. The extent of improvement varies across models, with Vicuna-13B showing the most substantial gain. This could be due to the model's architecture, the fine-tuning dataset, or other factors. The consistent improvement across all models indicates that fine-tuning is a generally beneficial strategy. </details> Figure 4: LLMs’ Performance on Task 5 without fine-tuning (denoted as Original) or after being fine-tuned with training data of Task 1–4. Cross-task Learning Performance Compared with Task 1–4, Task 5 belongs to the higher cognition dimension HOW, and is more difficult for LLMs since it requires to generate a sentence satisfying the demand. An interesting research question is that, whether LLMs can well achieve Task 5 after learning the previous four tasks? To answer this question, for each of Task 1–4 we sampled 60 instances from its training data, and mixed them with the equal amount (240) of general conversation instances from lmsys-chat-1m to fine-tune LLMs, which was used to guarantee LLMs’ generative ability. Then, we evaluated the fine-tuned LLMs’ performance on Task 5, of which the performance is depicted in Figure 4. As well, LLMs’ performance without fine-tuning, denoted as Original, is also displayed in the figure. The results indicate that, all the tested LLMs indeed enhanced their LFU performance through learning Task 1–4, also justifying their good cross-task learning capability of LFU tasks. 5 Conclusion To evaluate LLMs’ LFU performance, we propose five concrete tasks from three cognition dimensions WHAT, WHY, and HOW. Towards these tasks, we constructed a high quality dataset LFUD, which has been proven helpful by our extensive experiments to enhance LLMs’ capability of logical reasoning. We hope our work in this paper is instructive and our LFUD becomes a valuable resource for further research on LFU. Limitations Although we argue that enhancing LLMs’ logical reasoning capability through enabling LLMs to understand logical fallacies is language-independent, we should still acknowledge that the data and experiments of our work were only in English. As we know, LLMs might have different performance on many tasks including logical reasoning, across different languages. Therefore, the effectiveness of our solution proposed in this paper may vary when applied to other languages. Ethical Considerations At first, all authors of this work abide by the provided Code of Ethics. The quality of manual proofreading for logical fallacy sentences is ensured through a double-check strategy outlined in Appendix C. We ensure that the privacy rights of all members for proofreading are respected in the process. Besides, synthetic data generated by LLMs may involve potential ethical risks regarding fairness and bias Bommasani et al. (2021); Blodgett et al. (2020), which results in further consideration when they are employed in downstream tasks. Although our dataset LFUD was built for better understanding logical fallacies, which is not intended for safety-critical applications, we still asked our members for proofreading to refine the offensive and harmful data generated by GPT-4. Despite these considerations, there may still be some unsatisfactory data that goes unnoticed in our final dataset. Acknowledgements This work was supported by Chinese NSF Major Research Plan (No. 92270121), Youth Fund (No. 62102095), Shanghai Science and Technology Innovation Action Plan (No. 21511100401). The computations in this research were performed using the CFFF platform of Fudan University. References - Abaskohi et al. (2022) Amirhossein Abaskohi, Arash Rasouli, Tanin Zeraati, and Behnam Bahrak. 2022. 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False causality occurs when an argument jumps to a conclusion implying a causal relationship without supporting evidence. Circular reasoning occurs when an argument uses the claim it is trying to prove as proof that the claim is true. | Kevin, who is a teenager, enjoys playing chess. Therefore, all teenagers must enjoy playing chess. Whenever David goes hiking in the mountains, it’s a sunny day. Clearly, David’s hiking trips cause sunny weather. Some students are not serious about their studies because they do not focus on their studies. | | --- | --- | --- | | Ad Populum | Ad populum occurs when an argument is based on affirming that something is real or better because the majority thinks so. | It’s widely believed that Nancy relocated to another city, so it must be true. | | Ad Hominem | Ad hominem is an irrelevant attack towards the person or some aspect of the person who is making the argument, instead of addressing the argument or position directly. | John claims that all people should obey the rules of the road. But John has received several speeding tickets in the past. Therefore, it’s not necessary to obey the rules of the road. | | Deductive Fallacy | Deductive fallacy occurs when there is a logical flaw in the reasoning behind the argument, such as Affirming the consequent, Denying the antecedent, Affirming a disjunct and so on. | Should Lucy feel alone, she will surely adopt a puppy. It’s evident Lucy has adopted a puppy. Therefore, it must be that Lucy is feeling lonely. | | Appeal to Emotion | Appeal to emotion is when emotion is used in place of reason to support an argument in place of reason, such as pity, fear, anger, etc. | Jack had his wallet stolen at the concert, think about how desperate and helpless Jack is now, how can we not help him? | | False Dilemma | False dilemma occurs when incorrect limitations are made on the possible options in a scenario when there could be other options. | Most museums will be closed on Mondays either due to low visitor turnout, or due to their disregard for public interest. | | Equivocation | Equivocation is an argument which uses a key term or phrase in an ambiguous way, with one meaning in one portion of the argument and then another meaning in another portion of the argument. | All stars are exploding balls of gas. Miley Cyrus is a star. Therefore, Miley Cyrus is an exploding ball of gas. | | Fallacy of Extension | Fallacy of extension is an argument that attacks an exaggerated or caricatured version of your opponent’s position. | Alex: All flowers don’t stay open forever. Jamie: So you’re saying that all flowers die instantly after they bloom? | | Fallacy of Relevance | Fallacy of relevance, which is also known as Red Herring, occurs when the speaker attempts to divert attention from the primary argument by offering a point that does not suffice as counterpoint/supporting evidence (even if it is true). | A portion of the inhabitants of this city have a fever, but have you considered the high unemployment rate? | | Fallacy of Credibility | Fallacy of credibility is when an appeal is made to some form of ethics, authority, or credibility. | Sharon, an acclaimed pianist with years of experience, claims that practicing every day will increase your piano skills by 50%. She’s an expert, therefore we should believe her. | | Intentional Fallacy | Intentional fallacy is a custom category for when an argument has some element that shows the intent of a speaker to win an argument without actual supporting evidence. | Since no one can prove that Peter didn’t come to China last year, he must have. | Table 10: Descriptions and examples of 13 logical fallacy types Appendix A Details of Five LFU Tasks We list the definitions and examples of our five tasks below. Dimension: WHAT - Task1: Identification - Definition: Identify whether the given sentence has logical fallacy. - Example: Sentence: Many people believe most museums will be closed on Mondays, therefore it’s a fact. Identify if there is any logical fallacy in the sentence. A) Yes, there is a logical fallacy. B) No, there is no logical fallacy. - Task2: Classification - Definition: Select the sentence belonging to a certain type of logical fallacy. - Example: Circular reasoning occurs when an argument uses the claim it is trying to prove as proof that the claim is true. Select which among the following options demonstrates the logical fallacy of circular reasoning. A) Most people believe that Rebecca doesn’t like spicy food, therefore it must be true. B) Rebecca, a renowned food critic, does not like spicy food. Hence, spicy food is not good. C) Rebecca either refrains from spicy food due to discomfort it causes her, or she lacks well-developed taste buds. D) Rebecca doesn’t like spicy food because she dislikes spicy food. Dimension: WHY - Task3: Deduction - Definition: Derive the conclusion from the premise according to a certain type of logical fallacy. - Example: Faulty generalization occurs when a conclusion about all or many instances of a phenomenon is drawn from one or a few instances of that phenomenon. The premise is known: Bob painted his house green and he is a homeowner. With which of the two conclusions can the premise be coupled to create logical fallacy of faulty generalization? A) Green is the most popular house color. B) All homeowners paint their houses green. - Task4: Backward Deduction - Definition: Infer the premise from the conclusion according to a certain type of logical fallacy. - Example: Ad populum occurs when an argument is based on affirming that something is real or better because the majority thinks so. The conclusion is known: Cynthia’s painting must be a masterpiece. With which of the two premises can the conclusion be coupled to create the logical fallacy of ad populum? A) People widely agree that Cynthia made a beautiful painting. B) A famous art critic praised Cynthia’s painting. Dimension: HOW - Task5: Modification - Definition: Correct the logical fallacy in the given sentence. - Example: Original sentence: Person A: The garden needs watering. Person B: So you’re saying we should neglect everything else and just focus on the garden? Correct the logical fallacy in the original sentence and output the modified sentence without any logical fallacy. Appendix B Details of Logic Fallacy Types In Table 10, we showcase the description and examples of 13 logical fallacy types. Appendix C Details of Manual Proofreading The evaluation standard is strictly classified into two main categories: structural integrity and validity of fallacies. Structural integrity focuses on the correctness of grammar, the accuracy of punctuation, and the proper use of syntax. On the other hand, the validity of fallacies ensures that, under specific contexts or themes, the sentences satisfy the need for specific type of logical fallacy. Besides, any offensive and harmful data will be refined during the proofreading. In this process, we assembled an expert team proficient in linguistics and logic. This team comprises four members, including one logician and three graduate students, who are engaged in linguistics, logic, and computer science respectively. They each have the ability to understand and classify various types of logical fallacies. To enhance the efficiency of this process, each sentence was initially processed through Grammarly, eliminating basic grammatical and lexical errors. Subsequently, our expert team manually reviewed the content. Each sentence was assigned to two team members for review. A consensus confirmed the sentence met the requirements, but in case of disagreement, the third team member would be consulted. If three members cannot achieve consensus, the logician will make the final decision. Appendix D Examples of Logical Reasoning Datasets We illustrate data examples of four logical reasoning datasets selected in our experiments, including FOLIO, TaxiNLI, LogiQA, and Reclor. FOLIO Premise: Beasts of Prey is either a fantasy novel or a science fiction novel. Science fiction novels are not about mythological creatures. Beasts of Prey Is about a creature known as the Shetani. Shetanis are mythological. Conclusion: Beasts of prey isn’t a science fiction novel. Answer: True TaxiNLI Premise: Even if auditors do not follow such other standards and methodologies, they may still serve as a useful source of guidance to auditors in planning their work under GAGAS. Hypothesis: Auditors should ignore them when they follow other standards and methodologies. Label: Contradiction LogiQA2.0 Passage: For a television program about astrology, investigators went into the street and found twenty volunteers born under the sign of Gemini who were willing to be interviewed on the program and to take a personality test. The test confirmed the investigators’ personal impressions that each of the volunteers was more sociable and extroverted than people are on average. This modest investigation thus supports the claim that one’s astrological birth sign influences one’s personality. Question: Which one of the following, if true, indicates the most serious flaw in the method used by the investigators? A. People born under astrological signs other than Gemini have been judged by astrologers to be much less sociable than those born under Gemini. B. There is not likely to be a greater proportion of people born under the sign of Gemini on the street than in the population as a whole. C. People who are not sociable and extroverted are not likely to agree to participate in such an investigation. D. The personal impressions the investigators first formed of other people have tended to be confirmed by the investigators’ later experience of those people. Answer: C Reclor Context: Geologist: A new method for forecasting earthquakes has reliably predicted several earthquakes. Unfortunately, this method can predict only that an earthquake will fall somewhere within a range of two and a half points on the Richter scale. Thus, since a difference of two and a half points can be the difference between a marginally perceptible shaking and a quake that causes considerable damage, the new method is unlikely to be useful. Question: Which one of the following, if assumed, enables the geologist’s conclusion to be properly inferred? A. An earthquake-forecasting method is unlikely to be useful unless its predictions always differentiate earthquakes that are barely noticeable from ones that result in substantial destruction. B. Several well-established methods for forecasting earthquakes can predict within much narrower ranges than two and a half points on the Richter scale. C. Even if an earthquake-forecasting method makes predictions within a very narrow range on the Richter scale, this method is not likely to be useful unless its predictions are reliable. D. An earthquake-forecasting method has not been shown to be useful until it has been used to reliably predict a large number of earthquakes. Answer: A