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# A Syllogistic Probe: Tracing the Evolution of Logic Reasoning in Large Language Models **Authors**: - Junbo Zhao, Haobo Wang (Zhejiang University, University of Chinese Academy of Social Sciences,) Abstract Human logic has gradually shifted from intuition-driven inference to rigorous formal systems. Motivated by recent advances in large language models (LLMs), we explore whether LLMs exhibit a similar evolution in the underlying logical framework. Using existential import as a probe, we for evaluate syllogism under traditional and modern logic. Through extensive experiments of testing SOTA LLMs on a new syllogism dataset, we have some interesting findings: (i) Model size scaling promotes the shift toward modern logic; (ii) Thinking serves as an efficient accelerator beyond parameter scaling; (iii) the Base model plays a crucial role in determining how easily and stably this shift can emerge. Beyond these core factors, we conduct additional experiments for in-depth analysis of properties of current LLMs on syllogistic reasoning. A Syllogistic Probe: Tracing the Evolution of Logic Reasoning in Large Language Models Zhengqing Zang 1,3*, Yuqi Ding 2,3*, Yanmei Gu 3 $\dagger$ , Changkai Song 3, Zhengkai Yang 3, Guoping Du 4, Junbo Zhao 1,3, Haobo Wang 1 $\dagger$ 1 Zhejiang University, 2 University of Chinese Academy of Social Sciences, 3 Ant Group, 4 Chinese Academy of Social Sciences {zangzq, wanghaobo}@zju.edu.cn, dingyuqi@ucass.edu.cn, yanmeigu.gym@antgroup.com footnotetext: * These authors contributed equally. footnotetext: $\dagger$ Corresponding Authors. 1 Introduction Human logic has evolved from earlier, more intuition-driven accounts of valid inference Aristotle (1984) to increasingly rigorous formal frameworks Enderton (1972). In particular, the development of symbolic logic clarified the semantics of quantification and enabled precise validity checking under explicit model-theoretic interpretations, laying the foundation for contemporary logical analysis. Recently, neural networks have evolved from early, relatively simple architectures with limited capacity for logical reasoning to today’s large language models (LLMs), which have achieved remarkable progress across natural language processing tasks. State-of-the-art models such as GPT-5 OpenAI (2025a) and Gemini-3-Pro-Preview deepmind (2025), often rival human experts in complex reasoning tasks ranging from commonsense reasoning Bang et al. (2023); Bisk et al. (2019) to mathematical problem-solving Phan et al. (2025); Wei et al. (2023). These advances raise a natural question: do LLMs exhibit an analogous evolution in their underlying logical framework? If so, what changes, and how does this change emerge? <details> <summary>images/test_4.png Details</summary>  ### Visual Description ## Diagram: Syllogism and Existential Import ### Overview The image illustrates how a syllogism's validity changes based on whether Existential Import (EI) is considered in Traditional Logic versus Modern Logic. The diagram presents a syllogism with two premises and a conclusion, then shows how the validity of the conclusion depends on whether EI is "ON" (Traditional Logic) or "OFF" (Modern Logic). ### Components/Axes * **Title:** Syllogism * **Left Box (Syllogism):** Contains the premises and conclusion. * Premise 1: "All hairy animals are mammals" * Premise 2: "All unicorns are hairy animals" * Conclusion: "Some unicorns are mammals" * **Center Box (Existential Import):** A toggle switch labeled "Existential Import (EI)" with two states: * "ON": "licenses existence" * "OFF": "allows empty classes" * **Top-Right Box (Traditional Logic):** * Title: "Traditional Logic (EI = ON)" * A green checkmark inside a circle labeled "VALID" * Image of a unicorn * **Bottom-Right Box (Modern Logic):** * Title: "Modern Logic (EI = OFF)" * A red "X" inside a circle labeled "INVALID" * Note: "Empty Set issue" with an empty set symbol. ### Detailed Analysis or ### Content Details 1. **Syllogism:** * Premise 1: All hairy animals are mammals. * Premise 2: All unicorns are hairy animals. * Conclusion: Some unicorns are mammals. 2. **Existential Import (EI):** * The EI switch has two positions: ON and OFF. * When EI is ON, it "licenses existence." * When EI is OFF, it "allows empty classes." 3. **Traditional Logic (EI = ON):** * The syllogism is considered VALID. * The unicorn image suggests that unicorns exist. 4. **Modern Logic (EI = OFF):** * The syllogism is considered INVALID. * The "Empty Set issue" note indicates that the set of unicorns could be empty, making the conclusion invalid. ### Key Observations * The validity of the syllogism changes depending on whether Existential Import is considered. * Traditional Logic assumes the existence of the subjects in the premises, while Modern Logic does not. * The unicorn image in the Traditional Logic box reinforces the idea of existence. * The empty set symbol in the Modern Logic box highlights the possibility of empty classes. ### Interpretation The diagram illustrates the difference between Traditional and Modern Logic in handling existential import. Traditional Logic assumes that the categories mentioned in the premises have members, while Modern Logic does not. This difference affects the validity of syllogisms, particularly those involving potentially empty categories like "unicorns." The diagram effectively shows how the same syllogism can be valid or invalid depending on the underlying logical framework. The "Existential Import" toggle acts as a switch that determines which logic is applied, highlighting the importance of this assumption in logical reasoning. </details> <details> <summary>images/train2.png Details</summary>  ### Visual Description ## Train Diagram: Model Evolution ### Overview The image is a diagram depicting a train with three cars, each representing a different category of language models. The train is oriented from left to right, with an arrow indicating the direction of "Modern Logic" towards "Traditional Logic." Each car is labeled with specific model names. ### Components/Axes * **Horizontal Axis:** Represents a spectrum from "Modern Logic" to "Traditional Logic." * **Locomotive:** Represents "Modern Logic" and is pulling the train. * **Car 1:** Labeled "GPT-o3, GPT-5" * **Car 2:** Labeled "Qwen3-8B, Qwen3-30B-A3B" and positioned at the "Turning Point." * **Car 3:** Labeled "Llama3-8B, Qwen3-0.6B" and represents "Traditional Logic." ### Detailed Analysis * **Locomotive:** The locomotive is positioned at the left end of the diagram, indicating the start of the progression towards "Modern Logic." * **Car 1 (GPT-o3, GPT-5):** This car is directly behind the locomotive, suggesting these models are associated with "Modern Logic." * **Car 2 (Qwen3-8B, Qwen3-30B-A3B):** This car is positioned at the "Turning Point," implying these models represent a transition between "Modern Logic" and "Traditional Logic." * **Car 3 (Llama3-8B, Qwen3-0.6B):** This car is at the right end of the diagram, indicating these models are associated with "Traditional Logic." ### Key Observations * The diagram uses a train metaphor to illustrate the evolution or categorization of language models. * The positioning of the cars along the "Modern Logic" to "Traditional Logic" spectrum suggests a classification based on their underlying principles or architectures. * The "Turning Point" highlights a shift or change in the type of models being represented. ### Interpretation The diagram suggests a categorization of language models based on their alignment with "Modern Logic" versus "Traditional Logic." The train metaphor implies a progression or evolution of these models, with GPT-o3 and GPT-5 representing more modern approaches, Llama3-8B and Qwen3-0.6B representing more traditional approaches, and Qwen3-8B and Qwen3-30B-A3B representing a transition between the two. The specific criteria for defining "Modern Logic" and "Traditional Logic" are not explicitly stated in the image, but it can be inferred that they relate to the underlying architecture, training methods, or performance characteristics of the models. The diagram could be used to illustrate the evolution of language models or to compare and contrast different approaches to natural language processing. </details> Figure 1: The illustration of existential import problem and the trace of model logic. <details> <summary>images/acc-t.png Details</summary>  ### Visual Description ## Scatter Plot: Model Accuracy vs. Model Name ### Overview The image is a scatter plot comparing the accuracy (acc-t) of various language models from different families (Llama, Gemma, Qwen, Qwen-T, Gemini, and GPT). The x-axis represents the model names, and the y-axis represents the accuracy score. The size of each data point (circle) is not explicitly defined, but varies. A horizontal dashed line is present at y=80. A vertical solid line separates the Qwen-T models from the Gemini and GPT models. ### Components/Axes * **Title:** None * **X-axis:** Model Names (Llama3-8B, Llama3-70B, Llama3.3-70B, Gemma-3-1B, Gemma-3-4B, Gemma-3-12B, Gemma-3-27B, Qwen3-0.6B, Qwen3-1.7B, Qwen3-4B, Qwen3-8B, Qwen3-14B, Qwen3-32B, Qwen3-30B-A3B, Qwen3-NEXT-80B-A3B, Qwen3-235B-A22B, Qwen3-0.6B-T, Qwen3-1.7B-T, Qwen3-4B-T, Qwen3-8B-T, Qwen3-14B-T, Qwen3-32B-T, Qwen3-30B-A3B-T, Qwen3-NEXT-80B-A3B-T, Qwen3-235B-A22B-T, Gemini-2.5-pro, Gpt-03, GPT-5) * **Y-axis:** acc-t (Accuracy), with scale markers at 60, 70, 80, 90, and 100. * **Legend (Top-Right):** * Llama (Blue) * Gemma (Green) * Qwen (Purple) * Qwen-T (Pink) * Gemini (Yellow) * GPT (Cyan) * **Horizontal Dashed Line:** Located at acc-t = 80. * **Vertical Solid Line:** Separates Qwen-T models from Gemini and GPT models. ### Detailed Analysis * **Llama (Blue):** * Llama3-8B: Accuracy approximately 59. * Llama3-70B: Accuracy approximately 97. * Llama3.3-70B: Accuracy approximately 98. * Trend: Increasing accuracy from Llama3-8B to Llama3-70B and Llama3.3-70B. * **Gemma (Green):** * Gemma-3-1B: Accuracy approximately 85. * Gemma-3-4B: Accuracy approximately 91. * Gemma-3-12B: Accuracy approximately 95. * Gemma-3-27B: Accuracy approximately 94. * Trend: Generally high accuracy, with some fluctuation. * **Qwen (Purple):** * Qwen3-0.6B: Accuracy approximately 93. * Qwen3-1.7B: Accuracy approximately 77. * Qwen3-4B: Accuracy approximately 91. * Qwen3-8B: Accuracy approximately 94. * Qwen3-14B: Accuracy approximately 91. * Qwen3-32B: Accuracy approximately 94. * Qwen3-30B-A3B: Accuracy approximately 67. * Qwen3-NEXT-80B-A3B: Accuracy approximately 65. * Qwen3-235B-A22B: Accuracy approximately 64. * Trend: Variable accuracy, with some models performing significantly lower. * **Qwen-T (Pink):** * Qwen3-0.6B-T: Accuracy approximately 91. * Qwen3-1.7B-T: Accuracy approximately 76. * Qwen3-4B-T: Accuracy approximately 68. * Qwen3-8B-T: Accuracy approximately 84. * Qwen3-14B-T: Accuracy approximately 75. * Qwen3-32B-T: Accuracy approximately 70. * Qwen3-30B-A3B-T: Accuracy approximately 63. * Qwen3-NEXT-80B-A3B-T: Accuracy approximately 62. * Qwen3-235B-A22B-T: Accuracy approximately 63. * Trend: Variable accuracy, generally lower than the Qwen models. * **Gemini (Yellow):** * Gemini-2.5-pro: Accuracy approximately 72. * **GPT (Cyan):** * GPT-03: Accuracy approximately 63. * GPT-5: Accuracy approximately 63. * Trend: Similar accuracy between GPT-03 and GPT-5. ### Key Observations * Llama3-70B and Llama3.3-70B models show the highest accuracy among the models tested. * The Llama models show a large increase in accuracy when moving from the 8B parameter model to the 70B parameter models. * The Qwen and Qwen-T models exhibit a wide range of accuracy scores. * The Gemini and GPT models have relatively lower accuracy compared to the best-performing Llama and Gemma models. * The size of the data points varies, but the meaning of the size variation is not defined in the chart. ### Interpretation The scatter plot provides a comparison of the accuracy of different language models. The data suggests that model family and size (parameter count) can significantly impact performance. The Llama models, particularly the 70B parameter versions, demonstrate high accuracy. The Qwen and Qwen-T models show more variability, suggesting that architecture or training data may play a more significant role in their performance. The Gemini and GPT models, in this specific test, appear to have lower accuracy compared to the other families. The varying sizes of the data points could represent another variable, such as training time or dataset size, but this is not explicitly stated. </details> <details> <summary>images/acc-m.png Details</summary>  ### Visual Description ## Bubble Chart: Model Accuracy Comparison ### Overview The image is a bubble chart comparing the accuracy (acc-m) of various language models. The x-axis lists the names of the models, and the y-axis represents the accuracy score. The size of each bubble corresponds to an unspecified metric, likely related to model size or another performance indicator. A horizontal dashed line is present at acc-m = 81, and a vertical line separates the Qwen models from the Gemini and GPT models. ### Components/Axes * **X-axis:** Model Names (Llama3-8B, Llama3-70B, Llama3.3-70B, Gemma-3-1B, Gemma-3-4B, Gemma-3-12B, Gemma-3-27B, Qwen3-0.6B, Qwen3-1.7B, Qwen3-4B, Qwen3-8B, Qwen3-14B, Qwen3-32B, Qwen3-30B-A3B, Qwen3-NEXT-80B-A3B, Qwen3-235B-A22B, Qwen3-0.6B-T, Qwen3-1.7B-T, Qwen3-4B-T, Qwen3-8B-T, Qwen3-14B-T, Qwen3-32B-T, Qwen3-30B-A3B-T, Qwen3-NEXT-80B-A3B-T, Qwen3-235B-A22B-T, Gemini-2.5-pro, Gpt-o3, GPT-5) * **Y-axis:** Accuracy (acc-m) ranging from 60 to 100, with tick marks at intervals of 10. * **Bubbles:** Represent individual models, with their size varying. * **Horizontal Dashed Line:** Located at acc-m = 81. * **Vertical Solid Line:** Separates the Qwen models from the Gemini and GPT models. ### Detailed Analysis The models are grouped into families: Llama3, Gemma, Qwen3, Gemini, and GPT. * **Llama3 Models:** * Llama3-8B: acc-m ≈ 56 * Llama3-70B: acc-m ≈ 62 * Llama3.3-70B: acc-m ≈ 64 * Trend: Accuracy increases with model size. * **Gemma Models:** * Gemma-3-1B: acc-m ≈ 54 * Gemma-3-4B: acc-m ≈ 63 * Gemma-3-12B: acc-m ≈ 63 * Gemma-3-27B: acc-m ≈ 64 * Trend: Relatively stable accuracy across different sizes. * **Qwen3 Models (Base):** * Qwen3-0.6B: acc-m ≈ 63 * Qwen3-1.7B: acc-m ≈ 62 * Qwen3-4B: acc-m ≈ 66 * Qwen3-8B: acc-m ≈ 67 * Qwen3-14B: acc-m ≈ 67 * Qwen3-32B: acc-m ≈ 69 * Qwen3-30B-A3B: acc-m ≈ 94 * Qwen3-NEXT-80B-A3B: acc-m ≈ 97 * Qwen3-235B-A22B: acc-m ≈ 99 * Trend: Accuracy generally increases with model size, with a significant jump for the larger models (30B and above). * **Qwen3 Models (Tuned):** * Qwen3-0.6B-T: acc-m ≈ 61 * Qwen3-1.7B-T: acc-m ≈ 78 * Qwen3-4B-T: acc-m ≈ 87 * Qwen3-8B-T: acc-m ≈ 81 * Qwen3-14B-T: acc-m ≈ 81 * Qwen3-32B-T: acc-m ≈ 87 * Qwen3-30B-A3B-T: acc-m ≈ 81 * Qwen3-NEXT-80B-A3B-T: acc-m ≈ 81 * Qwen3-235B-A22B-T: acc-m ≈ 81 * Trend: Accuracy varies, with some models showing improvement over their base counterparts. * **Gemini and GPT Models:** * Gemini-2.5-pro: acc-m ≈ 90 * Gpt-o3: acc-m ≈ 100 * GPT-5: acc-m ≈ 100 * Trend: High accuracy for these models. ### Key Observations * The size of the bubbles varies significantly, suggesting a correlation with another metric besides accuracy. * The horizontal line at acc-m = 81 serves as a visual benchmark. * The Qwen3 models show a wide range of performance, with the larger models achieving high accuracy. * The Gemini and GPT models demonstrate the highest accuracy scores. ### Interpretation The bubble chart provides a comparative overview of the accuracy of different language models. The varying bubble sizes likely represent model complexity, training data size, or another relevant factor. The trend suggests that larger models generally achieve higher accuracy, although there are exceptions. The Qwen3 models show a significant jump in performance with increased size, indicating the potential benefits of scaling up model parameters. The Gemini and GPT models outperform the other models in terms of accuracy, suggesting they have more advanced architectures or training methodologies. The horizontal line at acc-m = 81 highlights models that achieve a certain level of performance. </details> Figure 2: Overall performance of auto-regressive models under traditional logic and modern logic. The upper figure shows model performance under the traditional logic criterion, while the lower panel reports performance under the modern logic criterion. Point size is proportional to model scale, and color denotes model family. Qwen-T indicates Qwen Thinking models/mode. For closed-source models, we use a fixed medium point size for visualization only, which does not reflect their true parameter counts. The horizontal dashed line marks the dividing line between the traditional and modern logic. Existing reasoning benchmarks Han et al. (2024) increasingly target first-order logic(modern logic), examining whether they can follow this more rigorous, formal style of reasoning. However, in syllogism reasoning, existing datasets Ando et al. (2023); Nguyen et al. (2025); Wu et al. (2023) typically treat traditional logic as the implicit default. This creates a systematic bias. A model may score high simply because it has learned dataset-specific shortcuts in traditional syllogisms, not because it truly has rigorous reasoning ability that can be transferred to new settings. On the other hand, a model may score low because it takes a modern logic view and therefore refuses to infer existence from a statement like “All unicorns are hairy animals”, which then gets marked as wrong. Even worse, these unstated rules mix up a model’s reasoning ability with how well it matches the evaluation convention, making the scores hard to interpret. In this study, we focus on syllogism Aristotle (1984), a classic and well-studied form of deductive reasoning. The evaluation of syllogisms differs between two frameworks: Traditional Logic (Aristotelian) and Modern Logic (Boolean interpretation). The key difference between them lies in existential import (EI) Parsons and Ciola (2025), where traditional logic typically assumes the relevant terms are non-empty while modern logic makes existential commitments only when explicitly stated. As shown in Figure 1, this syllogism is typically treated as "valid" in traditional logic because the universal statement about unicorns (Premise2: All unicorns are hairy animals) is taken to presuppose that unicorns exist. While in modern logic, the conclusion does not follow unless existence of unicorns is separately asserted ("Some unicorns exist"), since the premise can be true even when there are no unicorns. To trace the evolution of logic reasoning in LLMs, we use existential import as a probe and conduct a series of investigations on a new syllogism dataset, which can be summarized in following key findings: (1) Controlled evidence across open-source model families and scales. We run systematic evaluations on Qwen 3 Yang et al. (2025), Llama 3 Grattafiori et al. (2024) , and Gemma 3 Team et al. (2025) series across model sizes and training variants. We find that as model size increases, $acc_{m}$ rises across all models. Models in Llama 3 and Gemma 3 series largely retain a traditional-logic reasoning style. However, in the Qwen series, we observe a clear shift in its logical paradigm from traditional logic to modern logic. We also identify a turning point where consistency fluctuates during the transition. (2) Thinking as an efficient driver beyond parameter scaling. By comparing matched-size models, we show that RL-trained thinking variants can strongly accelerate the shift toward modern logic and improve consistency. Prompted chain-of-thought yields only a partial shift, and distillation alone does not reliably produce strict modern logic behavior, suggesting that the transition is driven more by post-training optimization of reasoning policies than by scale or imitation learning alone. (3) Base-model constraints on learnability and stability. We evaluate Base models and show that they set the starting point for post-training. When the Base model already shows signals aligned with modern logic, post-training shifts are easier and more stable. Otherwise, the shift is harder and less stable. We further report the experiments of different prompts, the emptiness of minor terms, cross-lingual gaps, and architecture effects including diffusion-based LLMs, conducting an in-depth analysis of properties of current LLMs on syllogistic reasoning. 2 Background and Dataset Construction 2.1 Syllogism and Existential Import Aristotle characterizes a syllogism as consisting of two premises and a conclusion Aristotle (1984), where each statement is a categorical proposition relating a subject term ( $S$ ) to a predicate term ( $P$ ). Within the syllogism’s structure, the conclusion’s subject ( $S$ ) is called the minor term, and its predicate ( $P$ ) the major term. In standard form, there are four categorical proposition types (A/E/I/O): | | A(universal affirmative): | All $S$ are $P$ | | | --- | --- | --- | --- | In this paper, we use traditional logic to denote the Aristotelian syllogistic framework, and modern logic to denote the Boolean interpretation of categorical propositions Boole (1854). For reference, under modern logic these four forms are typically rendered as: | | A: | $\displaystyle\ ∀ x\,(Sx→ Px)$ | | | --- | --- | --- | --- | The core distinction is existential import (EI): whether a proposition is taken to imply that its subject class is non-empty Parsons and Ciola (2025). $\bullet$ In traditional logic, universal propositions (A/E) are typically assumed to have EI: for instance, "All $S$ are $P$ " is read as implying that the class $S$ is not empty. $\bullet$ In modern logic, universal propositions lack EI. "All $S$ are $P$ " is formalized as a conditional, $∀ x\,(Sx→ Px)$ , which can remain true even if no $S$ exists (i.e., it is vacuously true). We illustrate this contrast with the unicorn example in Figure 1. Under the traditional EI reading, the universal premise “All unicorns are mammals” is commonly taken to license the existential conclusion “Some unicorns are mammals.” Under modern logic, however, the universal premise entails only $∀ x\,(Ux→ Mx)$ and does not imply $∃ x\,Ux$ ; therefore the existential conclusion does not follow unless we add an explicit existence premise. 2.2 Dataset Construction We build our data for analysis with a multi-stage agent pipeline that proposes terms and relations, checks factual consistency, and enforces logical constraints before generating syllogistic instances. Using this process, we generate 100 concept triplets with an empty minor-term extension and 100 with a non-empty minor-term extension, combined with Chinese/English versions and 15+9 syllogistic forms, which yields 9600 syllogisms in total. More detailed of the data construction will be discussed in Appendix 7.4. | Model | ZH+ | ZH- | EN+ | EN- | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | | | Qwen Series – Dense Models | | | | | | | | | | | | | | Qwen3-0.6B | 100.00 | 62.50 | 100.00 | 99.96 | 62.46 | 95.83 | 100.00 | 62.50 | 100.00 | 100.00 | 62.50 | 100.00 | | Qwen3-0.6B-Thinking | 94.71 | 61.04 | 4.17 | 92.96 | 61.12 | 16.67 | 86.67 | 60.25 | 0.00 | 88.33 | 61.75 | 4.17 | | Qwen3-1.7B | 97.00 | 62.42 | 50.00 | 95.58 | 60.92 | 37.50 | 75.21 | 59.71 | 16.67 | 35.17 | 47.58 | 4.17 | | Qwen3-1.7B-Thinking | 92.92 | 67.67 | 29.17 | 94.29 | 67.71 | 50.00 | 91.62 | 70.54 | 54.17 | 91.96 | 70.29 | 58.33 | | Qwen3-4B | 92.46 | 67.12 | 45.83 | 94.46 | 67.04 | 54.17 | 85.79 | 61.62 | 4.17 | 93.50 | 61.67 | 12.50 | | Qwen3-4B-Thinking | 82.54 | 79.96 | 62.50 | 85.33 | 77.08 | 58.33 | 83.62 | 78.88 | 66.67 | 84.92 | 77.58 | 62.50 | | Qwen3-8B | 94.12 | 67.46 | 33.33 | 96.67 | 65.42 | 62.50 | 85.46 | 69.58 | 4.17 | 86.71 | 64.62 | 0.00 | | Qwen3-8B-Thinking | 67.83 | 94.50 | 54.17 | 71.62 | 90.88 | 62.50 | 64.83 | 97.67 | 75.00 | 65.29 | 97.21 | 66.67 | | Qwen3-14B | 97.75 | 64.50 | 66.67 | 99.25 | 63.25 | 87.50 | 87.12 | 70.96 | 25.00 | 91.58 | 68.08 | 20.83 | | Qwen3-14B-Thinking | 72.96 | 89.54 | 62.50 | 76.50 | 86.00 | 66.67 | 74.92 | 87.50 | 58.33 | 77.92 | 84.50 | 58.33 | | Qwen3-32B | 91.67 | 70.33 | 58.33 | 95.54 | 66.96 | 75.00 | 91.00 | 70.50 | 45.83 | 93.88 | 68.46 | 54.17 | | Qwen3-32B-Thinking | 82.21 | 80.29 | 62.50 | 85.75 | 76.75 | 62.50 | 77.96 | 84.50 | 62.50 | 80.38 | 82.08 | 62.50 | | Qwen Series – MoE Models | | | | | | | | | | | | | | Qwen3-30B-A3B-Instruct | 66.58 | 95.83 | 70.83 | 71.96 | 90.54 | 66.67 | 64.00 | 98.50 | 75.00 | 66.71 | 95.71 | 66.67 | | Qwen3-30B-A3B-Thinking | 69.17 | 93.33 | 62.50 | 71.50 | 91.00 | 62.50 | 67.71 | 86.12 | 16.67 | 70.00 | 84.08 | 8.33 | | Qwen3-NEXT-80B-A3B-Instruct | 65.58 | 96.92 | 66.67 | 70.08 | 92.42 | 66.67 | 62.71 | 99.62 | 70.83 | 64.38 | 98.12 | 62.50 | | Qwen3-NEXT-80B-A3B-Thinking | 62.71 | 99.79 | 83.33 | 63.08 | 99.42 | 79.17 | 62.88 | 98.96 | 50.00 | 62.96 | 99.38 | 75.00 | | Qwen3-235B-A22B-Instruct | 66.17 | 96.33 | 66.67 | 67.83 | 94.67 | 66.67 | 62.54 | 99.88 | 87.50 | 62.71 | 99.79 | 83.33 | | Qwen3-235B-A22B-Thinking | 62.71 | 99.79 | 83.33 | 62.88 | 99.62 | 83.33 | 64.75 | 97.75 | 62.50 | 63.08 | 99.42 | 70.83 | | Gemma Series | | | | | | | | | | | | | | Gemma-3-1B-IT | 87.96 | 53.29 | 0.00 | 77.62 | 51.71 | 0.00 | 90.29 | 57.54 | 0.00 | 86.71 | 57.54 | 0.00 | | Gemma-3-4B-IT | 94.46 | 63.38 | 16.67 | 77.88 | 63.54 | 0.00 | 95.00 | 63.08 | 12.50 | 94.79 | 64.38 | 25.00 | | Gemma-3-12B-IT | 98.54 | 63.38 | 41.67 | 98.96 | 62.88 | 45.83 | 93.67 | 63.42 | 20.83 | 92.38 | 64.96 | 20.83 | | Gemma-3-27B-IT | 95.33 | 62.00 | 16.67 | 94.17 | 61.58 | 20.83 | 96.54 | 65.71 | 50.00 | 95.96 | 66.54 | 66.67 | | Llama Series | | | | | | | | | | | | | | Llama3-8B-Instruct | 75.12 | 60.21 | 0.00 | 63.29 | 53.79 | 0.00 | 50.25 | 56.88 | 0.00 | 47.42 | 51.83 | 0.00 | | Llama3-70B-Instruct | 98.58 | 63.17 | 58.33 | 96.88 | 62.71 | 45.83 | 98.88 | 62.54 | 62.50 | 90.67 | 60.29 | 20.83 | | Llama3.3-70B-Instruct | 96.08 | 65.92 | 58.33 | 97.88 | 63.96 | 62.50 | 99.08 | 63.00 | 87.50 | 99.12 | 63.38 | 79.17 | | Closed-source Models | | | | | | | | | | | | | | Claude-3.7-Sonnet | 85.29 | 76.54 | 45.83 | 90.46 | 71.71 | 50.00 | 70.33 | 92.00 | 54.17 | 73.08 | 89.42 | 62.50 | | Claude-4.5-Sonnet | 81.38 | 81.12 | 62.50 | 93.96 | 68.57 | 62.50 | 70.01 | 92.52 | 66.67 | 84.11 | 78.40 | 62.50 | | Gemini-2.5-Pro | 71.92 | 89.33 | 29.17 | 76.17 | 83.50 | 25.00 | 65.17 | 97.33 | 70.83 | 72.92 | 89.50 | 58.33 | | Gemini-3-Pro-Preview | 73.11 | 89.20 | 54.17 | 99.00 | 63.48 | 66.67 | 63.48 | 99.00 | 79.17 | 98.41 | 64.02 | 70.83 | | GPT-4o-2024-11-20 | 93.17 | 68.42 | 41.67 | 96.17 | 65.71 | 50.00 | 93.33 | 68.75 | 50.00 | 94.04 | 67.83 | 50.00 | | GPT-4.1-2025-04-14 | 80.38 | 80.04 | 33.33 | 85.08 | 76.67 | 45.83 | 80.04 | 82.38 | 58.33 | 81.54 | 80.96 | 62.50 | | GPT-o3 | 62.38 | 99.54 | 87.50 | 62.58 | 99.92 | 91.67 | 62.50 | 100.00 | 100.00 | 62.58 | 99.92 | 95.83 | | GPT-5-2025-08-07 | 62.50 | 100.00 | 100.00 | 62.50 | 100.00 | 100.00 | 62.50 | 100.00 | 100.00 | 62.50 | 100.00 | 100.00 | Table 1: Results for various models by language and the subject term’s existence condition (non-empty vs. empty extension). Detailed metrics (e.g., precision and recall) are reported in the Appendix 7.6.2. 3 Experiment Design 3.1 The 15+9 Distinction of Valid Syllogistic Forms This disagreement over EI directly creates a split in the set of valid syllogistic forms. A form is defined by its mood (the A/E/I/O pattern) and figure (term arrangement). - Traditional Logic recognizes 24 valid forms. - Modern Logic accepts only 15 of these as unconditionally valid. The remaining 9 forms are rejected precisely because they commit the existential fallacy. As shown in Appendix 7.2, we use 15+9 split to distinguish traditional from modern logic validity, and report accuracy under each logic paradigm accordingly. We further compare a baseline prompt with a Prior-check prompt that explicitly asks the model to first state whether the concepts are empty in the given setting by add "Do you think {major term}, {middle term}, {minor term} are empty sets? Keep that in mind and answer:" at the beginning of prompt, testing whether making the existence status explicit shifts the model’s behavior between traditional and modern logic. We evaluate model behavior under both traditional logic and modern logic, and also examine how stable its reasoning is across instances of the same syllogistic form. We first report traditional-logic accuracy ( $\text{Acc}_{t}$ ), defined as the proportion of instances in which the model accepts the conclusion, treating all 24 moods as valid under existential import. We then report modern-logic accuracy ( $\text{Acc}_{m}$ ), defined with respect to modern semantics: the model should accept instances from the 15 moods that are valid in modern logic, and reject instances from the 9 moods that become invalid when the minor term $S$ has an empty extension. Higher $\text{Acc}_{t}$ indicates behavior closer to traditional logic, while higher $\text{Acc}_{m}$ indicates behavior more consistent with the modern logic. Moreover, consistency score (Cons) of each mood in each language and concept-emptiness set is report as $\frac{n}{24}$ . Model can earn the score only if all answers of the same mood is consistent. In addition, we report precision and recall separately on the two mood subsets (the 15 unconditionally-valid moods and the 9 existential-import-dependent moods) to better characterize how the model distinguishes between these two logic regimes， detailed in Appendix 7.5. 4 Results and Analysis 4.1 Main Results 4.1.1 Scaling Effects of Logical Evolution Advanced models exhibit modern-logic behavior. Widely recognized as advanced closed-source LLMs(e.g., Gemini-2.5-Pro Comanici et al. (2025), GPT-o3 OpenAI (2025b), GPT-5 OpenAI (2025a)) increasingly prefer modern logic while maintaining relatively low scores under the traditional logic (see Table 1). This change is not only about higher accuracy, but also suggests that models are moving toward a more rule-based and principled way to analyze validity. Motivated by this, we ask a basic question: how does the preference for the modern logic emerge as models are developed and scaled up? To study this in a controlled way, we turn to open-source model families where we can compare many related checkpoints. Concretely, we evaluate the Qwen Yang et al. (2025), Llama Grattafiori et al. (2024), and Gemma Team et al. (2025) series. Overall, we find that as model size increases, $Acc_{m}$ rises across all models, indicating that models’ logical reasoning became more rigorous as the parameter scaling up. Clear family-specific scaling patterns. We further conduct a detailed analysis of three major model families. Since Qwen series provide comprehensive coverage across the wide scale range from 0.6B to 235B, multiple variants, and different architectures (including dense and mixture-of-experts models), we primarily analyze Qwen models and report them as our main results. Among these three families, we find clear family-specific scaling patterns in logical behavior. Qwen shows a scaling trend that includes a clear logic paradigm shift. For small to mid-sized non-thinking and instruction-tuned Qwen models, $\text{Acc}_{t}$ remains very high, indicating a strong preference for the traditional logic. However, when moving to larger Qwen models—especially thinking variants and some large instruction-tuned variants—the pattern can flip, with $\text{Acc}_{m}$ becoming much higher than $\text{Acc}_{t}$ . This trend holds in both Chinese and English, suggesting it is not tied to a single language setting. In contrast, for Llama and Gemma, models at different sizes mostly follow the traditional logic. Scaling mainly makes them stronger within the traditional logic. We hypothesize this is because, at small sizes, the model gradually grasps traditional logic to improve inference performance. However, at larger sizes, to solve more complex problems, the model must switch to full modern logic. We also observe the consistency scores fluctuate when scaling up Qwen models. This instability is more likely near the Turning Point where the model’s logic switches. This suggests the transition from traditional logic to modern logic is not always smooth. During the change, the model may mix the behaviors of following surface patterns from data and more rigorous reasoning of modern logic, which can temporarily lead to disagreements across closely related test cases. Takeaway 1 As models scale up, their logic judgments clearly shift from the traditional logic to modern logic, matching the same direction we see in advanced closed-source models. 4.1.2 Thinking as an Efficient Driver of the Logic Evolution Thinking accelerates the logic shift at fixed scale. Since Thinking directly strengthens a model’s multi-step reasoning process, it enables more consistent rule-based inference with less reliance on scale alone. We compare same-sized Instruct/Non-thinking models with their Thinking counterparts. The results show that the thinking mechanism can strongly speed up the shift from the traditional logic to the modern logic. This is most obvious in the Qwen3-8B pair: while Qwen3-8B still mostly follows the traditional logic, Qwen3-8B-Thinking moves clearly toward the modern logic stance. For larger models where the Instruct version is already strongly modern-logic-aligned, the Thinking version often further improves $\text{Acc}_{m}$ and increases consistency across closely related test cases. A natural explanation is that reinforcement learning (RL) makes the model rely more on step-by-step, rule-like deduction, and also helps it give more stable answers when two cases are very similar. In this sense, Thinking does not just add better instruction following. It changes the decision criterion and makes the logic paradigm shift more likely. Thinking is an efficient alternative to parameter scaling. Under the modern logic, Qwen3-8B-Thinking can reach a performance level close to Qwen3-30B-A3B-Instruct, even though it uses far fewer parameters. So, increasing model size is not the only way to get strong modern logic behavior. RL training with explicit reasoning traces can partly replace the need for more parameters by changing how the model uses its capacity. In practice, scaling tends to improve broad robustness but is expensive, while RL-based thinking can be a more focused and compute-efficient way to push the model into the modern logic. The best results still come from combining large model further enhanced with RL. CoT Prompting and Distillation are insufficient. To further investigate the effectiveness of Thinking mechanism, we conduct two additional experiments. First, starting from the Instruct models, we add an explicit CoT-trigger prompt (e.g., "Let’s think step by step."). The results are reported in Appendix 7.6.4. We find that Instruct+CoT setting can induce a partial shift toward modern logic, but the shift is limited. In contrast, the Thinking models produce a more complete transition in the underlying logic criterion, further supporting our main finding that RL-trained thinking acts as a promoter of logic shift. In addition, we also examine several distilled models derived from large RL-trained model (e.g., DeepSeek-R1-Distill-Llama-8B DeepSeek-AI et al. (2025)). The results in Appendix 7.6.4 suggest that RL training does not automatically lead to rigorous modern logic in all models. Instead, achieving a stable shift to modern logic appears to require careful, task-aware design. At least in our setting, distillation from DeepSeek-R1 alone is far from sufficient to produce the same level of strict modern logic behavior. Takeaway 2 The thinking process derived from RL can push a smaller model into modern logic. 4.1.3 Base Models as the Starting Point and a Constraint Base models shape what post-training can achieve. Scaling and RL can change a model’s logical stance, but these changes do not start from nowhere. Here we test a more basic point: how much the final behavior is already shaped by the underlying Base model? To answer this, we evaluate several base models (Appendix 7.6.5). Overall, the base model sets the starting point for post-training, and it strongly affects both (i) what the later Instruct / Thinking models can learn and (ii) how stable that learned criterion will be. Modern-logic signals at the Base stage enable easier shifts. From Qwen3-8B-Base, where we later observe a clear shift toward modern logic, we already see an important signal at the base stage. It achieves relatively high $rec_{V}$ , and in most settings its $rec_{I}$ is also clearly higher than other base models. This suggests that Qwen3-8B-Base is not fully locked by traditional logic. Instead, it already shows some ability to separate the modern-valid moods from all moods, leaving room for post-training to strengthen modern logic. This explains why RL in the Thinking variant can push Qwen3-8B toward modern more easily. In contrast, Gemma and LLaMA Base models often have low $rec_{V}$ , meaning they frequently fail to recognize modern-valid moods and tend to answer "invalid" by default. This also explains their seemingly high $rec_{I}$ on the existential-import-dependent subset: the high $rec_{I}$ is largely caused by a general rejection tendency, rather than real sensitivity to existential import. The effect of Base model is strong but not absolute . Small models (e.g., Qwen3-8B) benefit the most when the Base already shows modern logic signals. Larger models can still learn the modern logic through post-training (e.g., Qwen3-30B-A3B), but the learned shift is not always stable: under Thinking, judgments can fluctuate, and in some cases the model can drift back toward a traditional pattern. This suggests that post-training can move the decision criterion, but the base model still influences how reliable that move will be. Takeaway 3 The base model is the starting point. If it already leans toward modern logic, post-training shifts are easier and more stable. <details> <summary>images/qwen3-4b_24x4_heatmap.png Details</summary>  ### Visual Description ## Heatmap: Syllogism Validity Prediction ### Overview The image is a heatmap visualizing the number of predicted valid syllogisms for different syllogism formats across four conditions: 'zh+' (Chinese positive), 'zh-' (Chinese negative), 'en+' (English positive), and 'en-' (English negative). The heatmap uses a color gradient from dark purple (low values) to light yellow (high values) to represent the number of predicted valid syllogisms, ranging from approximately 55 to 100. ### Components/Axes * **Y-axis:** "Syllogism Format" lists various syllogism formats such as AAA-1, EAE-1, AII-1, EIO-1, EAE-2, AEE-2, EIO-2, AOO-2, AII-3, IAI-3, OAO-3, EIO-3, AEE-4, IAI-4, EIO-4, AAI-1, EAO-1, AEO-2, EAO-2, AAI-3, EAO-3, AAI-4, AEO-4, and EAO-4. * **X-axis:** Four conditions are listed: "zh+", "zh-", "en+", and "en-". * **Color Scale (Legend):** Located on the right side of the heatmap, it represents "The number of predicted VALID" ranging from 55 (dark purple) to 100 (light yellow). The scale has tick marks at 55, 60, 65, 70, 75, 80, 85, 90, 95, and 100. ### Detailed Analysis The heatmap displays the number of predicted valid syllogisms for each syllogism format under each condition. The color intensity corresponds to the number of predicted valid syllogisms, with lighter colors indicating higher numbers and darker colors indicating lower numbers. Here's a breakdown of the approximate values for each cell: | Syllogism Format | zh+ | zh- | en+ | en- | | :--------------- | :---- | :---- | :---- | :---- | | AAA-1 | ~98 | ~98 | ~98 | ~98 | | EAE-1 | ~98 | ~98 | ~98 | ~98 | | AII-1 | ~98 | ~98 | ~98 | ~98 | | EIO-1 | ~98 | ~98 | ~98 | ~98 | | EAE-2 | ~98 | ~98 | ~98 | ~98 | | AEE-2 | ~98 | ~98 | ~98 | ~98 | | EIO-2 | ~98 | ~98 | ~98 | ~78 | | AOO-2 | ~98 | ~98 | ~98 | ~98 | | AII-3 | ~98 | ~98 | ~98 | ~98 | | IAI-3 | ~98 | ~98 | ~98 | ~78 | | OAO-3 | ~98 | ~98 | ~98 | ~98 | | EIO-3 | ~98 | ~98 | ~98 | ~98 | | AEE-4 | ~98 | ~98 | ~73 | ~73 | | IAI-4 | ~98 | ~98 | ~73 | ~98 | | EIO-4 | ~98 | ~98 | ~98 | ~98 | | AAI-1 | ~98 | ~98 | ~98 | ~98 | | EAO-1 | ~98 | ~98 | ~73 | ~98 | | AEO-2 | ~98 | ~98 | ~98 | ~98 | | EAO-2 | ~98 | ~98 | ~98 | ~98 | | AAI-3 | ~98 | ~98 | ~98 | ~98 | | EAO-3 | ~98 | ~98 | ~98 | ~98 | | AAI-4 | ~55 | ~55 | ~55 | ~78 | | AEO-4 | ~55 | ~98 | ~55 | ~98 | | EAO-4 | ~98 | ~98 | ~98 | ~73 | * **AAI-1** has a red line across the row. ### Key Observations * Most syllogism formats have high predicted validity scores (close to 100) across all conditions. * Syllogism formats AAI-4 and AEO-4 have the lowest predicted validity scores (around 55) for 'zh+' and 'en+' conditions. * The 'en-' condition shows some variability, with some syllogism formats having lower predicted validity scores compared to other conditions. * The red line across AAI-1 indicates a specific point of interest or a threshold. ### Interpretation The heatmap suggests that the model generally predicts high validity for most syllogism formats, especially in the 'zh+' and 'zh-' conditions. The lower scores for AAI-4 and AEO-4 in 'zh+' and 'en+' might indicate a bias or difficulty in processing these specific syllogism formats under those conditions. The variability in the 'en-' condition could be due to the negative framing in English affecting the model's ability to predict validity accurately. The red line on AAI-1 may indicate a baseline or a critical threshold for validity prediction. Further investigation is needed to understand the underlying reasons for these differences and potential biases in the model. </details> (a) Qwen3-4B <details> <summary>images/qwen3-8b_24x4_heatmap.png Details</summary>  ### Visual Description ## Heatmap: Syllogism Validity Prediction ### Overview The image is a heatmap visualizing the number of predicted valid syllogisms for different syllogism formats across four conditions: 'zh+', 'zh-', 'en+', and 'en-'. The color intensity represents the number of predicted valid syllogisms, ranging from 65 (dark purple) to 100 (light yellow). A red horizontal line is present between "EIO-4" and "AAI-1". ### Components/Axes * **Y-axis:** Syllogism Format. The syllogism formats are listed vertically. * AAA-1 * EAE-1 * AII-1 * EIO-1 * EAE-2 * AEE-2 * EIO-2 * AOO-2 * AII-3 * IAI-3 * OAO-3 * EIO-3 * AEE-4 * IAI-4 * EIO-4 * AAI-1 * EAO-1 * AEO-2 * EAO-2 * AAI-3 * EAO-3 * AAI-4 * AEO-4 * EAO-4 * **X-axis:** Conditions. The conditions are 'zh+', 'zh-', 'en+', and 'en-'. * **Color Scale (Legend):** The color scale on the right represents the number of predicted valid syllogisms. * Light Yellow: 100 * Yellow-Orange: 95 * Orange: 90 * Light Red-Orange: 85 * Red-Orange: 80 * Red: 75 * Purple-Red: 70 * Dark Purple: 65 ### Detailed Analysis The heatmap displays the predicted validity counts for each syllogism format under each condition. The color of each cell corresponds to the number of predicted valid syllogisms, as indicated by the color scale. * **AAA-1:** All conditions are light yellow, indicating a value of approximately 100. * **EAE-1:** All conditions are light yellow, indicating a value of approximately 100. * **AII-1:** All conditions are light yellow, indicating a value of approximately 100. * **EIO-1:** All conditions are light yellow, indicating a value of approximately 100. * **EAE-2:** All conditions are light yellow, indicating a value of approximately 100. * **AEE-2:** All conditions are light yellow, indicating a value of approximately 100. * **EIO-2:** 'zh+' and 'en+' are light yellow (approximately 100), while 'zh-' and 'en-' are orange (approximately 90). * **AOO-2:** 'zh+' and 'en+' are light yellow (approximately 100), while 'zh-' and 'en-' are orange (approximately 90). * **AII-3:** All conditions are light yellow, indicating a value of approximately 100. * **IAI-3:** All conditions are light yellow, indicating a value of approximately 100. * **OAO-3:** All conditions are light yellow, indicating a value of approximately 100. * **EIO-3:** All conditions are light yellow, indicating a value of approximately 100. * **AEE-4:** 'zh+', 'zh-', and 'en+' are light yellow (approximately 100), while 'en-' is orange (approximately 90). * **IAI-4:** 'zh+', 'zh-', and 'en+' are light yellow (approximately 100), while 'en-' is orange (approximately 90). * **EIO-4:** 'zh+', 'zh-', and 'en+' are light yellow (approximately 100), while 'en-' is orange (approximately 90). * **AAI-1:** 'zh+' and 'zh-' are orange (approximately 90), while 'en+' is red-orange (approximately 80), and 'en-' is light yellow (approximately 100). * **EAO-1:** 'zh+' and 'en+' are light yellow (approximately 100), while 'zh-' and 'en-' are orange (approximately 90). * **AEO-2:** All conditions are light yellow, indicating a value of approximately 100. * **EAO-2:** 'zh+' and 'en+' are light yellow (approximately 100), while 'zh-' and 'en-' are orange (approximately 90). * **AAI-3:** 'zh+' and 'en-' are orange (approximately 90), 'zh-' is light yellow (approximately 100), and 'en+' is dark purple (approximately 65). * **EAO-3:** All conditions are light yellow, indicating a value of approximately 100. * **AAI-4:** 'zh+' and 'zh-' are dark purple (approximately 65), 'en+' is red-orange (approximately 80), and 'en-' is orange (approximately 90). * **AEO-4:** 'zh+' and 'zh-' are dark purple (approximately 65), 'en+' is purple-red (approximately 70), and 'en-' is red-orange (approximately 80). * **EAO-4:** 'zh+' is red (approximately 75), 'zh-' is red-orange (approximately 80), 'en+' is dark purple (approximately 65), and 'en-' is orange (approximately 90). ### Key Observations * Syllogism formats AAA-1, EAE-1, AII-1, EIO-1, EAE-2, AEE-2, AII-3, IAI-3, OAO-3, EIO-3, and EAO-3 consistently show high predicted validity (approximately 100) across all conditions. * Syllogism formats AAI-4 and AEO-4 show very low predicted validity (approximately 65-80) for 'zh+' and 'zh-' conditions. * The 'en+' condition often shows lower predicted validity compared to other conditions, especially for AAI-3, AAI-4, AEO-4, and EAO-4. * The 'en-' condition often shows higher predicted validity compared to other conditions, especially for AAI-1. ### Interpretation The heatmap suggests that the predicted validity of syllogisms varies significantly depending on the syllogism format and the condition ('zh+', 'zh-', 'en+', 'en-'). The 'zh' and 'en' likely refer to different languages (possibly Chinese and English), and the '+' and '-' likely refer to some manipulation or feature of the text. Some syllogism formats are consistently predicted as valid across all conditions, while others show significant variation. The lower predicted validity for certain syllogism formats under the 'en+' condition may indicate a bias or limitation in the prediction model related to the English language or the specific feature represented by '+'. The dark purple cells indicate syllogisms that are rarely predicted as valid under those conditions, suggesting a potential issue with their logical structure or the model's ability to recognize their validity. The red line does not appear to have any significance. </details> (b) Qwen3-8B <details> <summary>images/qwen3-next-80b-a3b-instruct_24x4_heatmap.png Details</summary>  ### Visual Description ## Heatmap: Syllogism Format vs. Predicted Validity ### Overview The image is a heatmap visualizing the number of predicted valid syllogisms for different syllogism formats across four conditions: zh+, zh-, en+, and en-. The color intensity represents the number of predicted valid syllogisms, ranging from 0 (dark purple) to 100 (light yellow). The heatmap is divided into two distinct regions separated by a red line. The top region shows high validity across all conditions, while the bottom region shows varying degrees of validity depending on the syllogism format and condition. ### Components/Axes * **Y-axis:** Syllogism Format. The syllogism formats are listed vertically, with the first 12 formats (AAA-1 to EIO-4) in the top region and the remaining 8 formats (AAI-1 to EAO-4) in the bottom region. * **X-axis:** Conditions. The conditions are zh+, zh-, en+, and en-. * **Color Scale:** The color scale represents the number of predicted valid syllogisms, ranging from 0 (dark purple) to 100 (light yellow). * **Legend:** Located on the right side of the heatmap, showing the color gradient and corresponding numerical values (0, 20, 40, 60, 80, 100). The label for the legend is "The number of predicted VALID". ### Detailed Analysis **Syllogism Formats (Y-axis):** * AAA-1 * EAE-1 * AII-1 * EIO-1 * EAE-2 * AEE-2 * EIO-2 * AOO-2 * AII-3 * IAI-3 * OAO-3 * EIO-3 * AEE-4 * IAI-4 * EIO-4 * AAI-1 * EAO-1 * AEO-2 * EAO-2 * AAI-3 * EAO-3 * AAI-4 * AEO-4 * EAO-4 **Conditions (X-axis):** * zh+ * zh- * en+ * en- **Data Points:** * **Top Region (AAA-1 to EIO-4):** All cells in this region are light yellow, indicating a value close to 100 for all syllogism formats and conditions. * **AAI-1:** zh+ (dark purple, ~0), zh- (dark purple, ~0), en+ (dark purple, ~0), en- (dark purple, ~0) * **EAO-1:** zh+ (dark purple, ~0), zh- (dark purple, ~0), en+ (dark purple, ~0), en- (dark purple, ~0) * **AEO-2:** zh+ (dark purple, ~0), zh- (red-purple, ~30), en+ (dark purple, ~0), en- (dark purple, ~0) * **EAO-2:** zh+ (red-purple, ~30), zh- (orange, ~70), en+ (dark purple, ~0), en- (dark purple, ~0) * **AAI-3:** zh+ (dark purple, ~0), zh- (dark purple, ~0), en+ (dark purple, ~0), en- (dark purple, ~0) * **EAO-3:** zh+ (red-purple, ~30), zh- (orange, ~70), en+ (red-purple, ~30), en- (dark purple, ~0) * **AAI-4:** zh+ (dark purple, ~0), zh- (dark purple, ~0), en+ (dark purple, ~0), en- (dark purple, ~0) * **AEO-4:** zh+ (dark purple, ~0), zh- (red-purple, ~30), en+ (dark purple, ~0), en- (dark purple, ~0) * **EAO-4:** zh+ (red-purple, ~30), zh- (red-purple, ~30), en+ (dark purple, ~0), en- (dark purple, ~0) ### Key Observations * The top 15 syllogism formats (AAA-1 to EIO-4) consistently show high predicted validity across all conditions (zh+, zh-, en+, en-). * The bottom 9 syllogism formats (AAI-1 to EAO-4) show significantly lower predicted validity, with some formats showing higher validity in the zh- condition. * The 'en+' and 'en-' conditions generally show very low predicted validity for the bottom syllogism formats. * A red line separates the two regions of the heatmap, visually highlighting the difference in predicted validity between the two groups of syllogism formats. ### Interpretation The heatmap suggests that certain syllogism formats (AAA-1 to EIO-4) are consistently predicted as valid, regardless of the condition (zh+, zh-, en+, en-). In contrast, other syllogism formats (AAI-1 to EAO-4) are generally predicted as invalid, with some exceptions in the zh- condition. The 'en+' and 'en-' conditions appear to have a negative impact on the predicted validity of these syllogism formats. The separation of the heatmap into two distinct regions indicates a clear difference in the predicted validity of different syllogism formats. This could be due to the inherent logical structure of the syllogisms or the way they are processed under different conditions. The higher validity observed in the zh- condition for some syllogism formats suggests that this condition may be more conducive to valid reasoning for those specific formats. The consistently low validity in the 'en+' and 'en-' conditions warrants further investigation to understand the factors contributing to this effect. </details> (c) Qwen3-NEXT-80B-A3B-Instruct <details> <summary>images/qwen3-235b-a22b-thinking_24x4_heatmap.png Details</summary>  ### Visual Description ## Heatmap: Syllogism Format vs. Predicted Validity ### Overview The image is a heatmap visualizing the number of predicted valid syllogisms for different syllogism formats across four conditions: 'zh+', 'zh-', 'en+', and 'en-'. The color intensity represents the number of predicted valid syllogisms, ranging from 0 (dark purple) to 100 (light yellow). The heatmap is divided into two distinct regions based on syllogism format, with the top portion showing high validity and the bottom portion showing low validity. ### Components/Axes * **Y-axis (Syllogism Format):** Lists various syllogism formats. The formats are: AAA-1, EAE-1, AII-1, EIO-1, EAE-2, AEE-2, EIO-2, AOO-2, AII-3, IAI-3, OAO-3, EIO-3, AEE-4, IAI-4, EIO-4, AAI-1, EAO-1, AEO-2, EAO-2, AAI-3, EAO-3, AAI-4, AEO-4, EAO-4. * **X-axis (Conditions):** Represents four conditions: 'zh+', 'zh-', 'en+', and 'en-'. * **Color Scale (Legend):** Indicates the number of predicted valid syllogisms, ranging from 0 (dark purple) to 100 (light yellow). The scale has markers at 0, 20, 40, 60, 80, and 100. * A horizontal red line separates the syllogism formats. ### Detailed Analysis or Content Details **Top Region (High Validity):** * Syllogism formats AAA-1, EAE-1, AII-1, EIO-1, EAE-2, AEE-2, EIO-2, AOO-2, AII-3, IAI-3, OAO-3, EIO-3, AEE-4, IAI-4, and EIO-4 show high validity across all four conditions ('zh+', 'zh-', 'en+', 'en-'). The color is consistently light yellow, indicating a value close to 100. **Bottom Region (Low Validity):** * Syllogism formats AAI-1, EAO-1, AEO-2, EAO-2, AAI-3, EAO-3, AAI-4, AEO-4, and EAO-4 show low validity across all four conditions. The colors vary between dark purple and a slightly lighter purple, indicating values between 0 and approximately 40. * **AAI-1:** 'zh+' is black (0), 'zh-' is black (0), 'en+' is dark purple (approximately 10-20), 'en-' is black (0). * **EAO-1:** 'zh+' is black (0), 'zh-' is black (0), 'en+' is dark purple (approximately 10-20), 'en-' is black (0). * **AEO-2:** 'zh+' is black (0), 'zh-' is black (0), 'en+' is purple (approximately 30-40), 'en-' is black (0). * **EAO-2:** 'zh+' is black (0), 'zh-' is black (0), 'en+' is dark purple (approximately 10-20), 'en-' is black (0). * **AAI-3:** 'zh+' is black (0), 'zh-' is black (0), 'en+' is black (0), 'en-' is black (0). * **EAO-3:** 'zh+' is black (0), 'zh-' is dark purple (approximately 10-20), 'en+' is dark purple (approximately 10-20), 'en-' is black (0). * **AAI-4:** 'zh+' is black (0), 'zh-' is black (0), 'en+' is black (0), 'en-' is black (0). * **AEO-4:** 'zh+' is black (0), 'zh-' is dark purple (approximately 10-20), 'en+' is purple (approximately 30-40), 'en-' is black (0). * **EAO-4:** 'zh+' is dark purple (approximately 10-20), 'zh-' is black (0), 'en+' is dark purple (approximately 10-20), 'en-' is black (0). ### Key Observations * There is a clear distinction between the syllogism formats in terms of predicted validity. * The conditions 'zh+' and 'zh-' generally show lower validity for the bottom region syllogisms compared to 'en+'. * The syllogism formats in the top region consistently show high validity across all conditions. * The red line visually separates the two groups of syllogisms. ### Interpretation The heatmap suggests that certain syllogism formats are consistently predicted as valid, regardless of the condition ('zh+', 'zh-', 'en+', 'en-'), while others are consistently predicted as invalid. The 'zh+' and 'zh-' conditions appear to have a negative impact on the predicted validity of the syllogisms in the bottom region, while 'en+' shows slightly higher validity for some of these formats. This could indicate a bias or difference in how these syllogisms are processed or interpreted under different conditions. The conditions 'zh+' and 'zh-' may represent processing in Chinese language contexts, while 'en+' and 'en-' may represent processing in English language contexts. The plus and minus signs may indicate the presence or absence of some additional factor. </details> (d) Qwen3-235B-A22B-Thinking Figure 3: The heatmaps of two types of model logic. (a) and (b) are traditional logic while (c) and (d) are modern logic. 4.2 Further Analysis 4.2.1 Prior-check Prompt To ensure that our measured modern logic performance is not an artifact of prompting, we introduce Prior-check prompt that explicitly asks the model to check the relevant existence condition before making a validity judgment. The goal is simple: make the model perform a semantic check that is required under modern logic evaluation, without changing the logical content of the task. Main effect: higher $\mathrm{Acc}_{m}$ without stance flipping. As a control group, we report results with baseline prompt in Appendix 7.6.3. We observe that Prior-check prompt consistently increases $\text{Acc}_{m}$ for most models, while keeping their overall logical stance stable and easy to interpret. This suggests that the prompt improves compliance with modern logic rather than introducing systematic bias. Turning-point instability. A notable exception appears in the Qwen3-30B-A3B pair. Although the Instruct version looks modern-logic, the Thinking version shifts back toward traditional logic. This suggests that Qwen3-30B-A3B model is close to the turning point between paradigms. Long thinking contents may sometimes bring back traditional defaults. The fluctuations reveal that the model’s stance can be fragile during the logic transition stage. 4.2.2 The emptiness of minor term Empty minor terms are consistently harder. Under both Prior-check prompt and the baseline setting, models show lower $rec_{I}$ when the minor term is empty than when the non-empty counterpart. One likely reason is that empty minor terms make counterexamples harder to construct. To judge an argument as invalid under modern logic, the model often needs to consider a situation where the premises are true but the conclusion is false. When the minor term is empty, this kind of reasoning is less intuitive because there are no concrete instances to reason about. As a result, the model tends to fall back on traditional logic. This increases false positives and reduces $rec_{I}$ . This result highlights the permeability of world knowledge. Plausibility priors can leak into formal reasoning and interfere with rule-governed validity judgments. Mood-specific error concentration suggests data imprinting. To further probe knowledge effects in syllogistic reasoning, we visualize the number of "valid" answers across languages, minor-term existence settings, and all 24 syllogistic moods, as shown in Figure 3. The figure compares four models under Prior-check prompt. Regardless of whether a model generally aligns with traditional or modern logic, errors concentrate on a few specific moods rather than being evenly distributed. For example, Qwen3-4B is overall closer to traditional logic, it displays a strong tendency toward the modern logic in the AAI-4 and AEO-4 syllogism forms. One explanation is that certain moods are more frequent in training data, leading to better learning of those forms. This supports the view that LLMs’ logical behavior is shaped by training data, rather than reflecting an abstract reasoning ability that generalizes uniformly. 4.2.3 Cross-lingual Gaps Clear language-dependent effect. When comparing three open-source series, the Qwen and LLaMA series generally perform better in Chinese than in English, while Gemma shows the opposite pattern, with higher performance in English. This difference is most visible in accuracy measured under each model’s dominant logical stance. This cross-lingual gap suggests that current LLMs’ logical ability is not fully language-agnostic. Instead, it is still strongly shaped by language-specific patterns in training data. In short, what looks like “logical reasoning” in these models is still partly tied to the language they operate in, rather than being a truly language-independent reasoning skill. 4.2.4 Architecture and Reasoning Ability We next study how model architecture relates to logical reasoning behavior. We consider two settings: (i) open-source auto-regressive (AR) LLMs, comparing Dense models with mixture-of-experts (MoE) models shown in Table 1; and (ii) emerging diffusion LLMs (dLLMs) shown in Table 9. MoE in AR models correlates with more modern-leaning behavior. Within AR models, MoE variants in the Qwen family exhibit a stronger tendency toward modern logic than same-generation dense models. A plausible explanation is the combined effect of MoE efficiency and model scaling. MoE architectures make it easier to train models with higher effective capacity under similar compute, and the shift toward modern logic becomes more likely as model size increases. DLLMs mostly follow traditional logic. For dLLMs, most models still predominantly follow the traditional logic. Only one exception is LLaDA2.0-flash, which is a 100B model with MoE architecture. This exception again reflects the joint impact of MoE architecture and model scaling. 5 Related Works In recent years, many benchmarks have been proposed for syllogism reasoning. ENN Dong et al. (2020) constructed syllogisms extracted from WordNet Miller (1995). The syllogsims are in the form of triplets with no natural language descriptions. Syllo-Figure Peng et al. (2020) and NeuBAROCO Ando et al. (2023) are two natural language syllogism datasets, with data derived from existed datasets. Syllo-Figure derives omitted syllogisms from SNLI Bowman et al. (2015) and rewrites the missing premise by annotators. The target is to identify the specific figure. NeuBAROCO transforms questions from BAROCO Shikishima et al. (2009) into a format used for natural language inferences(NLI). Beyond categorical syllogism, SylloBase Wu et al. (2023) covers more types and patterns of syllogism, covering a complete taxonomy of syllogism reasoning patterns. There are also several researches focusing on the human-like bias of syllogism, such as belief bias Nguyen et al. (2025); Ando et al. (2023) and atmosphere effects Ando et al. (2023). However, these works all assume existential import by default, meaning they approach the task under a traditional logic setting. To examine different models’ tendencies under different logical paradigms and gain deeper insights, we use existential import as a probe and conduct a series of investigations. 6 Conclusion and Discussion This work studies whether LLMs’ syllogistic validity judgments shift toward a more rigorous modern logic criterion as models develop. Among all models, $\mathrm{Acc}_{m}$ generally increases with scale, but only the Qwen series exhibits a clear logic shift , consistent with the behavior of advanced closed-source models. Matched-size comparisons further show that RL-trained Thinking variants efficiently accelerate this shift and improve consistency; in contrast, CoT prompting induces only a limited move toward modern logic, and distillation alone does not reliably yield strict modern logic behavior. However, the transition is not always smooth. The consistency can fluctuate near the turning point, and some near-boundary models (e.g., Qwen3-30B-A3B) may partially revert under reasoning traces. We also identify systematic failure modes that persist across settings, including difficulty with empty minor terms, mood-specific bias, and cross-lingual gaps. Overall, our results suggest that modern logic reasoning in LLMs is shaped jointly by the base model and post-training (especially RL-based thinking), rather than emerging from parameter scaling alone. Limitations Our conclusions are primarily drawn from syllogistic reasoning and the contrast induced by existential import. While this probe cleanly separates traditional and modern validity criteria, it remains unclear whether the same evolutionary patterns hold for broader first-order logic criteria. We evaluate models mainly through their final valid/invalid decisions. This endpoint-only metric can obscure the source of errors. Our study does not directly supervise or diagnose intermediate semantic representations or proof-like structures, limiting our ability to pinpoint the mechanisms behind observed shifts and inconsistencies. Our distillation analysis covers only a small set of distilled models and a specific teacher family (e.g., DeepSeek-R1). 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A standard-form categorical syllogism is built from three core components Aristotle (1984); Copi et al. (2014): - Three Terms: - The major term (P) is the predicate of the conclusion. - The minor term (S) is the subject of the conclusion. - The middle term (M) appears in both premises but not in the conclusion. - Three Propositions: - The major premise contains the major term (P) and the middle term (M). - The minor premise contains the minor term (S) and the middle term (M). - The conclusion links the minor term (S) to the major term (P). In Aristotelian syllogistic logic (traditional logic), categorical propositions are divided into four standard forms: - A -proposition (universal affirmative), of the form “All $S$ are $P$ ,” e.g., “All humans are mortal”. - E -proposition (universal negative), of the form “No $S$ are $P$ ,” e.g., “No humans are perfect”. - I -proposition (particular affirmative), of the form “Some $S$ are $P$ ,” e.g., “Some humans are healthy”. - O -proposition (particular negative), of the form “Some $S$ are not $P$ ,” e.g., “Some humans are not healthy”. In a categorical syllogism, both premises and the conclusion are propositions of these four types Suppes (1957). In the traditional (Aristotelian) interpretation, the truth of a universal proposition is taken to imply the truth of its corresponding particular proposition Rasooli and Tetreault (2015). This assumption licenses, for example, subalternation from an A-proposition to the corresponding I-proposition; e.g., from “All humans are mortal” one may infer “Some humans are mortal.” In contrast, George Boole, a nineteenth-century English mathematician, argued that we cannot infer the truth of a particular proposition from the truth of its corresponding universal proposition, because every particular proposition asserts the existence of its subject class. If a universal proposition permitted us to infer the corresponding particular, then "All leprechauns wear little green hats" would license the inference that some leprechauns do, which would imply that there really are leprechauns Boole (1854). Thus, under modern logic (the Boolean interpretation), a universal proposition (an A- or E-proposition) is understood as stating only, for example, "If there is such a thing as a leprechaun, it wears a little green hat," not that any leprechauns actually exist. 7.2 Formalization of Categorical Propositions In the main text, we adopt the formalization of modern logic (Boolean), which reinterprets categorical propositions as quantified formulas. Throughout, by modern logic we mean the Boolean interpretation (no existential import for universals), expressed using standard quantified notation. The typical correspondences are as follows: | Categorical Proposition | Formalization in modern logic | Explanation | | --- | --- | --- | | All $S$ are $P$ | $∀ x\,(Sx→ Px)$ | For all $x$ , if $x$ is $S$ , then $x$ is $P$ . | | No $S$ are $P$ | $∀ x\,(Sx→\neg Px)$ or $\neg∃ x\,(Sx\wedge Px)$ | For all $x$ , if $x$ is $S$ , then $x$ is not $P$ ; equivalently, there does not exist any $x$ such that $x$ is both $S$ and $P$ . | | Some $S$ are $P$ | $∃ x\,(Sx\wedge Px)$ | There exists at least one $x$ such that $x$ is $S$ and $x$ is $P$ . | | Some $S$ are not $P$ | $∃ x\,(Sx\wedge\neg Px)$ | There exists at least one $x$ such that $x$ is $S$ and $x$ is not $P$ . | Under the standard semantics of modern logic Enderton (1972), if the extension of $S$ is empty, then $∃ x(Sx\land Px)$ is false, whereas $∀ x(Sx→ Px)$ is vacuously true. Consequently, from $∀ x(Sx→ Px)$ and $∀ x(Px→ Qx)$ one cannot derive $∃ x(Sx\land Qx)$ unless one adds an extra existence assumption (e.g., $∃ x\,Sx$ ). For this reason, as shown in Table 2, among the 24 standard syllogistic forms treated as valid in traditional logic, 9 are not valid in general under the semantics of modern logic, because their correctness depends on existential import Copi et al. (2014). 7.3 A Modern-Logic Derivation of Barbara Take the syllogism Barbara (mood AAA in the first figure) as an example: | | Major premise: | $\displaystyle\quad\text{All }M\text{ are }P\;→\;∀ x(Mx→ Px),$ | | | --- | --- | --- | --- | Under modern logic, the validity of this inference can be demonstrated by a formal derivation (e.g., in natural deduction): 1. $∀ x(Mx→ Px)$ [Major premise] 1. $∀ x(Sx→ Mx)$ [Minor premise] 1. Assume an arbitrary $a$ . [Arbitrary individual] 1. $Sa→ Ma$ [from 2, $∀$ -elim] 1. $Ma→ Pa$ [from 1, $∀$ -elim] 1. $Sa→ Pa$ [from 4, 5] 1. $∀ x(Sx→ Px)$ [from 3–6, $∀$ -intro] This example shows that traditional syllogistic reasoning can be formalized and verified within modern logic. | Name | Mood | Figure | Validity | | --- | --- | --- | --- | | Barbara | AAA | I | Valid in Both | | Celarent | EAE | I | Valid in Both | | Darii | AII | I | Valid in Both | | Ferio | EIO | I | Valid in Both | | Barbari | AAI | I | Traditional only | | Celaront | EAO | I | Traditional only | | Cesare | EAE | II | Valid in Both | | Camestres | AEE | II | Valid in Both | | Festino | EIO | II | Valid in Both | | Baroco | AOO | II | Valid in Both | | Cesaro | EAO | II | Traditional only | | Camestrop | AEO | II | Traditional only | | Darapti | AAI | III | Traditional only | | Disamis | IAI | III | Valid in Both | | Datisi | AII | III | Valid in Both | | Felapton | EAO | III | Traditional only | | Bocardo | OAO | III | Valid in Both | | Ferison | EIO | III | Valid in Both | | Bamalip | AAI | IV | Traditional only | | Camenes | AEE | IV | Valid in Both | | Dimaris | IAI | IV | Valid in Both | | Calemop | AEO | IV | Traditional only | | Fesapo | EAO | IV | Traditional only | | Fresison | EIO | IV | Valid in Both | Table 2: The 15+9 Distinction of Valid Syllogistic Forms (Traditional logic vs. Modern logic) 7.4 Data Construction The dataset construction process follows a rigorously structured three-stage pipeline: (1) Diverse Topic Seeding, (2) Closed-Loop Generation and Verification, and (3) Triplet Completion and Relational Validation. Each stage is designed to build upon the previous one, progressively refining the quality and logical richness of the resulting data. Diverse Topic Seeding. To ensure broad topical coverage and prevent semantic bias toward common or overrepresented domains, the process begins with a topic seeding stage. A predefined set of meta-domains spanning natural sciences, engineering, social sciences, and the humanities is used as the high-level taxonomy. For each meta-domain, a Topic Generation Agent is prompted to produce a set of concrete and verifiable subfields or research directions that exist in reality. The outcome is a diverse and fine-grained collection of topics, each serving as a contextual anchor for subsequent concept generation. This stage establishes semantic breadth and ensures that reasoning patterns later derived from the dataset are not constrained to narrow disciplinary vocabularies. Closed-Loop Generation and Verification At the core of the dataset construction process lies the closed-loop generation and verification stage, which establishes the factual and semantic foundation of both non-empty and empty sets for the minor term $(S)$ within each syllogistic structure. This stage guarantees that generated concepts are not only syntactically well-formed but also ontologically consistent with their designated existential category. Two complementary generation objectives are defined: non-empty concepts, which correspond to empirically verifiable entities in the real world, and empty concepts, which remain logically coherent while representing categories with no real-world instantiation. For each topic obtained from the previous stage, an iterative "generate, verify, feedback" loop is executed. The Generator agent first produces a candidate concept $(S)$ that satisfies the existential target of the current data subset. The candidate is then evaluated by a panel of independent Validator agents, each performing an autonomous factuality assessment and issuing a categorical verdict("non-empty" and "empty") accompanied by explanatory reasoning and indicative verification paths. A concept advances only when all validators unanimously agree on the verdict corresponding to the intended generation type, confirming either its empirical existence (for non-empty cases) or its verified non-existence (for empty cases). If disagreement arises, the system consolidates validator feedback into a unified critique, which is returned to the Generator in the next iteration to guide conceptual refinement. Through this iterative feedback-driven process, the framework produces two balanced sets of high-confidence concepts that jointly represent existentially positive and negative categories of reality. Triplet Completion and Relational Validation After obtaining a validated non-empty or empty concept $(S)$ , the final stage completes the triplet structure by generating the corresponding middle $(M)$ and major $(P)$ terms. The Triplet Generator agent constructs the set $(S,M,P)$ under strict constraints ensuring that all three concepts belong to a coherent semantic frame amenable to syllogistic reasoning. The agent is explicitly instructed to avoid trivial or hierarchical relations such as synonymy or direct subclass relationships (e.g., poodle $→$ dog $→$ animal), instead favoring more nuanced logical relations grounded in attribute overlap, contextual differentiation, or mechanistic contrast. To enforce this non-triviality constraint, each triplet undergoes an additional Relational Validation phase. Here, Validator agents examine whether deterministic subsumption or equivalence relations exist among the three concepts. A triplet is finalized only if it passes this logical consistency test, confirming its suitability for constructing non-trivial reasoning scenarios. Syllogistic Data Realization Upon successful generation and validation of all $(S,M,P)$ triplets, the final step transforms these verified conceptual structures into complete syllogistic reasoning instances. Each triplet serves as a semantic scaffold that is systematically mapped onto the twenty-four canonical syllogistic mood–figure templates formalized in Aristotelian logic. By substituting the generated concepts into these templates, the system produces a diverse collection of categorical syllogisms encompassing universal affirmatives, particulars, and negatives across multiple structural figures. This synthesis ensures that every syllogistic instance conforms to formal logical syntax while remaining grounded in verifiable semantic content. The resulting corpus thus unifies traditional deductive structures with empirically meaningful concepts, providing a rigorous benchmark for evaluating machine reasoning under both semantic authenticity and logical validity. 7.5 The precision and recall metrics Under modern logic, 15 syllogisms are regarded as valid, while the remaining 9 are invalid. We treat valid forms as positive samples $(P)$ and invalid forms as negative samples $(N)$ . We define the precision and recall metrics of valid and invalid syllogisms $\mathrm{pre}_{V},\mathrm{rec}_{V},\mathrm{pre}_{I},\mathrm{rec}_{I}$ as follow: $$ \mathrm{pre}_{V}=\frac{TP}{TP+FP} $$ $$ \mathrm{rec}_{V}=\frac{TP}{TP+FN} $$ $$ \mathrm{pre}_{I}=\frac{TN}{TN+FN} $$ $$ \mathrm{rec}_{I}=\frac{TN}{TN+FP} $$ 7.6 The results of experiments 7.6.1 The detailed results of closed-source models The detailed results of closed-source models are shown in Tab. 3. GPT-5 and GPT-o3 exhibit the extreme modern logic tendency. | Model | ZH+ | ZH- | EN+ | EN- | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | | | Claude-3.7-Sonnet | 85.29 | 76.54 | 45.83 | 72.89 | 99.47 | 97.73 | 38.33 | 90.46 | 71.71 | 50.00 | 68.91 | 99.73 | 98.25 | 25.00 | 70.33 | 92.00 | 54.17 | 88.74 | 99.87 | 99.72 | 78.89 | 73.08 | 89.42 | 62.50 | 85.52 | 100.00 | 100.00 | 71.78 | | Claude-4.5-Sonnet | 81.38 | 81.12 | 62.50 | 76.80 | 100.00 | 100.00 | 49.67 | 93.96 | 68.57 | 62.50 | 66.55 | 100.00 | 100.00 | 16.13 | 70.01 | 92.52 | 66.67 | 89.32 | 100.00 | 100.00 | 80.04 | 84.11 | 78.40 | 62.50 | 74.32 | 100.00 | 100.00 | 42.38 | | Gemini-2.5-Pro | 71.92 | 89.33 | 29.17 | 86.04 | 99.07 | 97.92 | 73.22 | 76.17 | 83.50 | 25.00 | 80.20 | 97.73 | 94.06 | 59.78 | 65.17 | 97.33 | 70.83 | 95.91 | 100.00 | 100.00 | 92.89 | 72.92 | 89.50 | 58.33 | 85.66 | 100.00 | 100.00 | 72.11 | | Gemini-3-Pro-Preview | 73.11 | 89.20 | 54.17 | 85.35 | 99.87 | 99.69 | 71.44 | 99.00 | 63.48 | 66.67 | 63.12 | 100.00 | 100.00 | 2.67 | 63.48 | 99.00 | 79.17 | 98.42 | 100.00 | 100.00 | 97.33 | 98.41 | 64.02 | 70.83 | 63.44 | 100.00 | 100.00 | 4.22 | | GPT-4o-2024-11-20 | 93.17 | 68.42 | 41.67 | 66.68 | 99.53 | 95.57 | 16.85 | 96.17 | 65.71 | 50.00 | 64.73 | 99.73 | 95.40 | 9.25 | 93.33 | 68.75 | 50.00 | 66.83 | 99.87 | 98.71 | 17.08 | 94.04 | 67.83 | 50.00 | 66.15 | 99.60 | 95.74 | 15.02 | | GPT-4.1-2025-04-14 | 80.38 | 80.04 | 33.33 | 76.46 | 98.33 | 94.69 | 49.56 | 85.08 | 76.67 | 45.83 | 73.02 | 99.40 | 97.49 | 38.78 | 80.04 | 82.38 | 58.33 | 78.03 | 99.93 | 99.79 | 53.11 | 81.54 | 80.96 | 62.50 | 76.65 | 100.00 | 100.00 | 49.22 | | GPT-o3 | 62.38 | 99.54 | 87.50 | 99.73 | 99.60 | 99.33 | 99.56 | 62.58 | 99.92 | 91.67 | 99.87 | 100.00 | 100.00 | 99.78 | 62.50 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 62.58 | 99.92 | 95.83 | 99.87 | 100.00 | 100.00 | 99.78 | | GPT-5-2025-08-07 | 62.53 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 62.33 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 62.53 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 62.40 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | Table 3: The detailed results of closed-source models. 7.6.2 The detailed results of experiment with Prior-check prompt The results are shown in Tab. 4. | Model | ZH+ | ZH- | EN+ | EN- | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | | | Qwen3-0.6B | 100.00 | 62.50 | 100.00 | 62.50 | 100.00 | 0.00 | 0.00 | 99.96 | 62.46 | 95.83 | 62.48 | 99.93 | 0.00 | 0.00 | 100.00 | 62.50 | 100.00 | 62.50 | 100.00 | 0.00 | 0.00 | 100.00 | 62.50 | 100.00 | 62.50 | 100.00 | 0.00 | 0.00 | | Qwen3-0.6B-Thinking | 94.71 | 61.04 | 4.17 | 62.43 | 94.60 | 36.22 | 5.11 | 92.96 | 61.12 | 16.67 | 62.71 | 93.27 | 40.24 | 7.56 | 86.67 | 60.25 | 0.00 | 63.12 | 87.53 | 41.56 | 14.78 | 88.33 | 61.75 | 4.17 | 63.73 | 90.07 | 46.79 | 14.56 | | Qwen3-1.7B | 97.00 | 62.42 | 50.00 | 62.84 | 97.53 | 48.61 | 3.89 | 95.58 | 60.92 | 37.50 | 62.25 | 95.20 | 32.08 | 3.78 | 75.21 | 59.71 | 16.67 | 64.76 | 77.93 | 44.37 | 29.33 | 35.17 | 47.58 | 4.17 | 64.34 | 36.20 | 38.50 | 66.56 | | Qwen3-1.7B-Thinking | 92.92 | 67.67 | 29.17 | 66.23 | 98.47 | 86.47 | 16.33 | 94.29 | 67.71 | 50.00 | 66.02 | 99.60 | 95.62 | 14.56 | 91.62 | 70.54 | 54.17 | 68.03 | 99.73 | 98.01 | 21.89 | 91.96 | 70.29 | 58.33 | 67.83 | 99.80 | 98.45 | 21.11 | | Qwen3-4B | 92.46 | 67.12 | 45.83 | 66.02 | 97.67 | 80.66 | 16.22 | 94.46 | 67.04 | 54.17 | 65.64 | 99.20 | 90.98 | 13.44 | 85.79 | 61.62 | 4.17 | 64.06 | 87.93 | 46.92 | 17.78 | 93.50 | 61.67 | 12.50 | 62.92 | 94.13 | 43.59 | 7.56 | | Qwen3-4B-Thinking | 82.54 | 79.96 | 62.50 | 75.72 | 100.00 | 100.00 | 46.56 | 85.33 | 77.08 | 58.33 | 73.19 | 99.93 | 99.72 | 39.00 | 83.62 | 78.88 | 66.67 | 74.74 | 100.00 | 100.00 | 43.67 | 84.92 | 77.58 | 62.50 | 73.60 | 100.00 | 100.00 | 40.22 | | Qwen3-8B | 94.12 | 67.46 | 33.33 | 65.91 | 99.27 | 92.20 | 14.44 | 96.67 | 65.42 | 62.50 | 64.44 | 99.67 | 93.75 | 8.33 | 85.46 | 69.58 | 4.17 | 68.80 | 94.07 | 74.43 | 28.81 | 86.71 | 64.62 | 0.00 | 65.64 | 91.07 | 57.99 | 20.56 | | Qwen3-8B-Thinking | 67.83 | 94.50 | 54.17 | 92.01 | 99.87 | 99.74 | 85.56 | 71.62 | 90.88 | 62.50 | 87.26 | 100.00 | 100.00 | 75.67 | 64.83 | 97.67 | 75.00 | 96.40 | 100.00 | 100.00 | 93.78 | 65.29 | 97.21 | 66.67 | 95.72 | 100.00 | 100.00 | 92.56 | | Qwen3-14B | 97.75 | 64.50 | 66.67 | 63.81 | 99.80 | 94.44 | 5.67 | 99.25 | 63.25 | 87.50 | 62.97 | 100.00 | 100.00 | 2.00 | 87.12 | 70.96 | 25.00 | 69.20 | 96.47 | 82.85 | 28.44 | 91.58 | 68.08 | 20.83 | 66.70 | 97.73 | 83.17 | 18.67 | | Qwen3-14B-Thinking | 72.96 | 89.54 | 62.50 | 85.67 | 100.00 | 100.00 | 72.11 | 76.50 | 86.00 | 66.67 | 81.70 | 100.00 | 100.00 | 62.67 | 74.92 | 87.50 | 58.33 | 83.37 | 99.93 | 99.83 | 66.78 | 77.92 | 84.50 | 58.33 | 80.16 | 99.93 | 99.81 | 58.78 | | Qwen3-32B | 91.67 | 70.33 | 58.33 | 67.91 | 99.60 | 97.00 | 21.56 | 95.54 | 66.96 | 75.00 | 65.42 | 100.00 | 100.00 | 11.89 | 91.00 | 70.50 | 45.83 | 68.13 | 99.20 | 94.44 | 22.67 | 93.88 | 68.46 | 54.17 | 66.49 | 99.87 | 98.64 | 16.11 | | Qwen3-32B-Thinking | 82.21 | 80.29 | 62.50 | 76.03 | 100.00 | 100.00 | 47.44 | 85.75 | 76.75 | 62.50 | 72.89 | 100.00 | 100.00 | 38.00 | 77.96 | 84.50 | 62.50 | 80.17 | 100.00 | 100.00 | 58.73 | 80.38 | 82.08 | 62.50 | 77.76 | 100.00 | 100.00 | 52.28 | | Qwen3-30B-A3B-Instruct | 66.58 | 95.83 | 70.83 | 93.80 | 99.93 | 99.88 | 89.00 | 71.96 | 90.54 | 66.67 | 86.86 | 100.00 | 100.00 | 74.78 | 64.00 | 98.50 | 75.00 | 97.66 | 100.00 | 100.00 | 96.00 | 66.71 | 95.71 | 66.67 | 93.63 | 99.93 | 99.87 | 88.67 | | Qwen3-30B-A3B-Thinking | 69.17 | 93.33 | 62.50 | 90.36 | 100.00 | 100.00 | 82.22 | 71.50 | 91.00 | 62.50 | 87.41 | 100.00 | 100.00 | 76.00 | 67.71 | 86.12 | 16.67 | 85.91 | 93.07 | 86.58 | 74.56 | 70.00 | 84.08 | 8.33 | 83.27 | 93.27 | 85.97 | 68.78 | | Qwen3-next-80B-A3B-Instruct | 65.58 | 96.92 | 66.67 | 95.30 | 100.00 | 100.00 | 91.78 | 70.08 | 92.42 | 66.67 | 89.18 | 100.00 | 100.00 | 79.78 | 62.71 | 99.62 | 70.83 | 99.53 | 99.87 | 99.78 | 99.22 | 64.38 | 98.12 | 62.50 | 97.09 | 100.00 | 100.00 | 95.00 | | Qwen3-next-80B-A3B-Thinking | 62.71 | 99.79 | 83.33 | 99.67 | 100.00 | 100.00 | 99.44 | 63.08 | 99.42 | 79.17 | 99.08 | 100.00 | 100.00 | 98.44 | 62.88 | 98.96 | 50.00 | 98.87 | 99.47 | 99.10 | 98.11 | 62.96 | 99.38 | 75.00 | 99.14 | 99.87 | 99.78 | 98.56 | | Qwen3-235B-A22B-Instruct | 66.17 | 96.33 | 66.67 | 94.46 | 100.00 | 100.00 | 90.22 | 67.83 | 94.67 | 66.67 | 92.14 | 100.00 | 100.00 | 85.78 | 62.54 | 99.88 | 87.50 | 99.87 | 99.93 | 99.89 | 99.78 | 62.71 | 99.79 | 83.33 | 99.67 | 100.00 | 100.00 | 99.44 | | Qwen3-235B-A22B-Thinking | 62.71 | 99.79 | 83.33 | 99.67 | 100.00 | 100.00 | 99.44 | 62.88 | 99.62 | 83.33 | 99.40 | 100.00 | 100.00 | 99.00 | 64.75 | 97.75 | 62.50 | 96.53 | 100.00 | 100.00 | 94.00 | 63.08 | 99.42 | 70.83 | 99.08 | 100.00 | 100.00 | 98.44 | | Gemma-3-1B-IT | 87.96 | 53.29 | 0.00 | 58.98 | 83.00 | 11.76 | 3.78 | 77.62 | 51.71 | 0.00 | 59.15 | 73.47 | 25.88 | 15.44 | 90.29 | 57.54 | 0.00 | 61.10 | 88.27 | 24.46 | 6.33 | 86.71 | 57.54 | 0.00 | 61.56 | 85.40 | 31.35 | 11.11 | | Gemma-3-4B-IT | 94.46 | 63.38 | 16.67 | 63.70 | 96.27 | 57.89 | 8.56 | 77.88 | 63.54 | 0.00 | 66.72 | 83.13 | 52.35 | 30.89 | 95.00 | 63.08 | 12.50 | 63.46 | 96.47 | 55.83 | 7.44 | 94.79 | 64.38 | 25.00 | 64.18 | 97.33 | 68.00 | 9.44 | | Gemma-3-12B-IT | 98.54 | 63.38 | 41.67 | 63.13 | 99.53 | 80.00 | 3.11 | 98.96 | 62.88 | 45.83 | 62.82 | 99.47 | 68.00 | 1.89 | 93.67 | 63.42 | 20.83 | 63.83 | 95.67 | 57.24 | 9.67 | 92.38 | 64.96 | 20.83 | 64.86 | 95.87 | 66.12 | 13.44 | | Gemma-3-27B-IT | 95.33 | 62.00 | 16.67 | 62.85 | 95.87 | 44.64 | 5.56 | 94.17 | 61.58 | 20.83 | 62.79 | 94.60 | 42.14 | 6.56 | 96.54 | 65.71 | 50.00 | 64.61 | 99.80 | 96.39 | 8.89 | 95.96 | 66.54 | 66.67 | 65.13 | 100.00 | 100.00 | 10.78 | | Llama3-8B-Instruct | 75.12 | 60.21 | 0.00 | 65.17 | 78.49 | 45.61 | 30.07 | 63.29 | 53.79 | 0.00 | 62.87 | 63.67 | 38.14 | 37.33 | 50.25 | 56.88 | 0.00 | 69.32 | 55.73 | 44.34 | 58.84 | 47.42 | 51.83 | 0.00 | 65.11 | 49.43 | 39.89 | 55.89 | | Llama3-70B-Instruct | 98.58 | 63.17 | 58.33 | 63.02 | 99.40 | 73.53 | 2.78 | 96.88 | 62.71 | 45.83 | 63.01 | 97.67 | 53.33 | 4.44 | 98.88 | 62.54 | 62.50 | 62.66 | 99.13 | 51.85 | 1.56 | 90.67 | 60.29 | 20.83 | 62.59 | 90.80 | 38.12 | 9.45 | | Llama3.3-70B-Instruct | 96.08 | 65.92 | 58.33 | 64.79 | 99.60 | 93.62 | 9.78 | 97.88 | 63.96 | 62.50 | 63.52 | 99.47 | 84.31 | 4.78 | 99.08 | 63.00 | 87.50 | 62.87 | 99.67 | 77.27 | 1.89 | 99.12 | 63.38 | 79.17 | 63.05 | 100.00 | 100.00 | 2.33 | Table 4: The detailed results of open-source models. 7.6.3 The baseline experiment without the Prior-check prompt The results are shown in Table 5. | Model | ZH+ | ZH- | EN+ | EN- | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | | | Qwen3-0.6B | 100.00 | 62.50 | 100.00 | 62.50 | 100.00 | 0.00 | 0.00 | 99.96 | 62.46 | 95.83 | 62.48 | 99.93 | 0.00 | 0.00 | 98.38 | 62.12 | 25.00 | 62.52 | 98.40 | 38.46 | 1.67 | 79.75 | 56.75 | 0.00 | 62.07 | 79.20 | 35.80 | 19.33 | | Qwen3-0.6B-Thinking | 87.96 | 62.04 | 0.00 | 63.95 | 90.00 | 48.10 | 15.44 | 91.42 | 61.83 | 0.00 | 63.31 | 92.60 | 46.12 | 10.56 | 86.54 | 60.29 | 0.00 | 63.17 | 87.47 | 41.80 | 15.00 | 89.58 | 60.25 | 0.00 | 62.70 | 89.87 | 39.20 | 10.89 | | Qwen3-1.7B | 93.04 | 63.04 | 20.83 | 63.73 | 94.87 | 53.89 | 10.00 | 94.50 | 62.75 | 29.17 | 63.36 | 95.80 | 52.27 | 7.67 | 93.00 | 62.67 | 37.50 | 63.53 | 94.53 | 51.19 | 9.56 | 70.96 | 52.46 | 0.00 | 60.54 | 68.73 | 32.71 | 25.33 | | Qwen3-1.7B-Thinking | 93.46 | 67.46 | 37.50 | 66.03 | 98.73 | 87.90 | 15.33 | 94.00 | 67.75 | 54.17 | 66.09 | 99.40 | 93.75 | 15.00 | 93.38 | 67.88 | 29.17 | 66.27 | 99.00 | 90.57 | 16.00 | 93.83 | 68.58 | 62.50 | 66.56 | 99.93 | 99.32 | 16.33 | | Qwen3-4B | 93.88 | 65.46 | 54.17 | 64.89 | 97.47 | 74.15 | 12.11 | 96.00 | 65.50 | 62.50 | 64.58 | 99.20 | 87.50 | 9.33 | 83.42 | 65.75 | 25.00 | 66.93 | 89.33 | 59.80 | 26.44 | 90.25 | 67.75 | 41.67 | 66.76 | 96.40 | 76.92 | 20.00 | | Qwen3-4B-Thinking | 88.88 | 73.62 | 62.50 | 70.32 | 100.00 | 100.00 | 29.67 | 87.12 | 75.38 | 62.50 | 71.74 | 100.00 | 100.00 | 34.33 | 86.67 | 75.83 | 62.50 | 72.12 | 100.00 | 100.00 | 35.56 | 87.17 | 75.33 | 62.50 | 71.70 | 100.00 | 100.00 | 34.22 | | Qwen3-8B | 92.42 | 68.00 | 41.67 | 66.50 | 98.33 | 86.26 | 17.44 | 95.54 | 65.46 | 45.83 | 64.63 | 98.80 | 83.18 | 9.89 | 88.38 | 66.25 | 29.17 | 66.29 | 93.73 | 66.19 | 20.47 | 91.54 | 66.29 | 33.33 | 65.73 | 96.27 | 72.41 | 16.33 | | Qwen3-8B-Thinking | 75.83 | 86.67 | 62.50 | 82.42 | 100.00 | 100.00 | 64.44 | 79.17 | 83.33 | 62.50 | 78.95 | 100.00 | 100.00 | 55.56 | 75.42 | 87.08 | 62.50 | 82.87 | 100.00 | 100.00 | 65.56 | 73.96 | 88.54 | 62.50 | 84.51 | 100.00 | 100.00 | 69.44 | | Qwen3-14B | 94.46 | 67.12 | 37.50 | 65.68 | 99.27 | 91.73 | 13.56 | 96.33 | 65.83 | 58.33 | 64.71 | 99.73 | 95.45 | 9.33 | 89.46 | 65.71 | 37.50 | 65.77 | 94.13 | 65.22 | 18.33 | 91.88 | 66.29 | 33.33 | 65.67 | 96.53 | 73.33 | 15.89 | | Qwen3-14B-Thinking | 69.00 | 93.50 | 66.67 | 90.58 | 100.00 | 100.00 | 82.67 | 73.04 | 89.46 | 66.67 | 85.57 | 100.00 | 100.00 | 71.89 | 84.75 | 77.58 | 58.33 | 73.65 | 99.87 | 99.45 | 40.44 | 85.67 | 76.83 | 66.67 | 72.96 | 100.00 | 100.00 | 38.22 | | Qwen3-32B | 94.58 | 67.42 | 58.33 | 65.81 | 99.60 | 95.38 | 13.78 | 96.75 | 65.42 | 75.00 | 64.43 | 99.73 | 94.87 | 8.22 | 94.00 | 66.00 | 58.33 | 65.16 | 98.00 | 79.17 | 12.67 | 96.58 | 65.50 | 79.17 | 64.50 | 99.67 | 93.90 | 8.56 | | Qwen3-32B-Thinking | 87.71 | 74.79 | 62.50 | 71.26 | 100.00 | 100.00 | 32.78 | 90.79 | 71.71 | 62.50 | 68.84 | 100.00 | 100.00 | 24.56 | 87.67 | 74.83 | 62.50 | 71.29 | 100.00 | 100.00 | 32.89 | 88.83 | 73.58 | 58.33 | 70.31 | 99.93 | 99.63 | 29.67 | | Qwen3-30B-A3B-Instruct | 71.04 | 91.04 | 62.50 | 87.68 | 99.67 | 99.28 | 76.67 | 77.71 | 83.62 | 62.50 | 79.68 | 99.07 | 97.38 | 57.89 | 75.12 | 86.62 | 58.33 | 82.70 | 99.40 | 98.49 | 65.33 | 84.50 | 77.75 | 58.33 | 73.82 | 99.80 | 99.19 | 41.00 | | Qwen3-30B-A3B-Thinking | 84.12 | 78.38 | 62.50 | 74.29 | 100.00 | 100.00 | 42.33 | 90.75 | 71.75 | 62.50 | 68.87 | 100.00 | 100.00 | 24.67 | 85.17 | 77.33 | 62.50 | 73.39 | 100.00 | 100.00 | 39.56 | 84.92 | 77.58 | 62.50 | 73.60 | 100.00 | 100.00 | 40.22 | | Qwen3-NEXT-80B-A3B-instruct | 73.50 | 88.92 | 62.50 | 84.98 | 99.93 | 99.84 | 70.56 | 74.71 | 87.79 | 66.67 | 83.66 | 100.00 | 100.00 | 67.44 | 65.08 | 97.42 | 66.67 | 96.03 | 100.00 | 100.00 | 93.11 | 66.04 | 96.46 | 66.67 | 94.64 | 100.00 | 100.00 | 90.56 | | Qwen3-NEXT-80B-A3B-Thinking | 74.83 | 87.67 | 66.67 | 83.52 | 100.00 | 100.00 | 67.11 | 76.54 | 85.96 | 66.67 | 81.65 | 100.00 | 100.00 | 62.56 | 69.79 | 92.54 | 62.50 | 89.55 | 100.00 | 100.00 | 80.47 | 68.58 | 93.54 | 70.83 | 91.13 | 100.00 | 100.00 | 83.61 | | Qwen3-235B-A22B-Instruct | 80.96 | 81.21 | 54.17 | 76.99 | 99.73 | 99.12 | 50.33 | 83.67 | 78.50 | 54.17 | 74.50 | 99.73 | 98.98 | 43.11 | 73.21 | 89.21 | 58.33 | 85.32 | 99.93 | 99.84 | 71.33 | 78.46 | 84.04 | 66.67 | 79.66 | 100.00 | 100.00 | 57.44 | | Qwen3-235B-A22B-Thinking | 69.50 | 93.00 | 66.67 | 89.93 | 100.00 | 100.00 | 81.33 | 72.00 | 90.50 | 66.67 | 86.81 | 100.00 | 100.00 | 74.67 | 71.38 | 91.12 | 66.67 | 87.57 | 100.00 | 100.00 | 76.33 | 73.04 | 89.46 | 62.50 | 85.57 | 100.00 | 100.00 | 71.89 | | Gemma-3-1B-IT | 75.38 | 51.04 | 0.00 | 58.98 | 71.13 | 26.73 | 17.56 | 82.29 | 55.79 | 0.00 | 61.11 | 80.47 | 31.06 | 14.67 | 78.92 | 45.92 | 0.00 | 55.33 | 69.87 | 10.67 | 6.00 | 83.71 | 50.79 | 0.00 | 57.94 | 77.60 | 14.07 | 6.11 | | Gemma-3-4B-IT | 97.83 | 62.25 | 33.33 | 62.65 | 98.07 | 44.23 | 2.56 | 97.46 | 61.71 | 33.33 | 62.42 | 97.33 | 34.43 | 2.33 | 95.33 | 63.83 | 8.33 | 63.81 | 97.33 | 64.29 | 8.00 | 97.92 | 64.17 | 50.00 | 63.62 | 99.67 | 90.00 | 5.00 | | Gemma-3-12B-IT | 99.21 | 62.71 | 75.00 | 62.70 | 99.53 | 63.16 | 1.33 | 98.71 | 63.54 | 70.83 | 63.19 | 99.80 | 90.32 | 3.11 | 99.75 | 62.58 | 83.33 | 62.57 | 99.87 | 66.67 | 0.44 | 100.00 | 62.50 | 100.00 | 62.50 | 100.00 | 0.00 | 0.00 | | Gemma-3-27B-IT | 97.62 | 64.29 | 54.17 | 63.72 | 99.53 | 87.72 | 5.56 | 98.04 | 63.71 | 37.50 | 63.37 | 99.40 | 80.85 | 4.22 | 99.08 | 63.25 | 79.17 | 62.99 | 99.87 | 90.91 | 2.22 | 99.92 | 62.58 | 95.83 | 62.55 | 100.00 | 100.00 | 0.22 | | Llama3-8B-Instruct | 59.25 | 62.71 | 0.00 | 71.31 | 67.60 | 50.26 | 54.62 | 64.33 | 59.29 | 0.00 | 66.97 | 68.93 | 45.50 | 43.27 | 35.96 | 53.08 | 0.00 | 71.73 | 41.29 | 42.67 | 72.86 | 42.42 | 51.62 | 0.00 | 66.70 | 45.30 | 40.58 | 62.29 | | Llama3.3-70B-Instruct | 98.12 | 64.29 | 87.50 | 63.65 | 99.93 | 97.78 | 4.89 | 98.38 | 63.21 | 58.33 | 63.07 | 99.27 | 71.79 | 3.11 | 98.58 | 63.33 | 87.50 | 63.10 | 99.53 | 79.41 | 3.00 | 99.62 | 62.46 | 79.17 | 62.53 | 99.67 | 44.44 | 0.44 | | Llama3-70B-Instruct | 99.12 | 63.12 | 83.33 | 62.93 | 99.80 | 85.71 | 2.00 | 98.21 | 62.62 | 66.67 | 62.79 | 98.67 | 53.49 | 2.56 | 94.96 | 63.54 | 41.67 | 63.71 | 96.80 | 60.33 | 8.11 | 90.83 | 61.25 | 20.83 | 63.07 | 91.67 | 43.18 | 10.56 | Table 5: The detailed results of baseline prompt of open-source models. 7.6.4 The external experiment of thinking The Instruct+ CoT experiment is shown in Tab. 6. The Instruct+CoT setting can induce a partial shift toward modern logic, but the shift is limited. The experiments of DeepSeek-R1 and DeepSeek-R1-Distill models are shown in Table 7. RL training does not automatically lead to rigorous modern logic in all models. | Model | ZH+ | ZH- | EN+ | EN- | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | | | Qwen3-0.6B | 98.75 | 62.25 | 50.00 | 62.53 | 98.80 | 40.00 | 1.33 | 97.38 | 61.96 | 16.67 | 62.56 | 97.47 | 39.68 | 2.78 | 99.96 | 62.46 | 95.83 | 62.48 | 99.93 | 0.00 | 0.00 | 99.21 | 62.62 | 37.50 | 62.66 | 99.47 | 57.89 | 1.22 | | Qwen3-1.7B | 93.50 | 64.17 | 12.50 | 64.26 | 96.13 | 62.82 | 10.89 | 92.00 | 62.50 | 16.67 | 63.59 | 93.60 | 50.00 | 10.67 | 67.08 | 56.50 | 0.00 | 64.16 | 68.87 | 40.89 | 35.89 | 58.88 | 51.71 | 0.00 | 62.07 | 58.47 | 36.88 | 40.44 | | Qwen3-4B | 91.12 | 66.88 | 25.00 | 66.12 | 96.40 | 74.65 | 17.67 | 94.54 | 65.71 | 33.33 | 64.92 | 98.20 | 79.39 | 11.56 | 55.67 | 54.42 | 0.00 | 65.19 | 58.11 | 40.92 | 48.33 | 72.75 | 53.08 | 0.00 | 60.71 | 70.67 | 32.72 | 23.78 | | Qwen3-8B | 88.83 | 70.75 | 25.00 | 68.71 | 97.67 | 86.94 | 25.89 | 94.54 | 67.12 | 50.00 | 65.67 | 99.33 | 92.37 | 13.44 | 86.08 | 72.58 | 4.17 | 70.38 | 96.93 | 86.23 | 32.00 | 90.33 | 66.50 | 4.17 | 66.05 | 95.47 | 70.69 | 18.22 | | Qwen3-14B | 88.08 | 74.00 | 54.17 | 70.72 | 99.67 | 98.25 | 31.22 | 94.42 | 67.67 | 54.17 | 65.98 | 99.67 | 96.27 | 14.33 | 85.42 | 72.08 | 16.67 | 70.24 | 96.00 | 82.86 | 32.22 | 90.58 | 70.42 | 33.33 | 68.17 | 98.80 | 92.04 | 23.11 | | Qwen3-32B | 89.58 | 72.50 | 50.00 | 69.53 | 99.67 | 98.00 | 27.22 | 94.17 | 68.33 | 75.00 | 66.37 | 100.00 | 100.00 | 15.56 | 89.12 | 72.21 | 41.67 | 69.47 | 99.07 | 94.64 | 27.44 | 91.62 | 70.12 | 37.50 | 67.80 | 99.40 | 95.52 | 21.33 | | Qwen3-30B-A3B-Instruct | 63.88 | 98.62 | 75.00 | 97.85 | 100.00 | 100.00 | 96.33 | 67.25 | 95.25 | 62.50 | 92.94 | 100.00 | 100.00 | 87.33 | 63.88 | 98.62 | 75.00 | 97.85 | 100.00 | 100.00 | 96.33 | 66.54 | 95.96 | 66.67 | 93.93 | 100.00 | 100.00 | 89.22 | | Qwen3-Next-80B-A3B-Instruct | 65.46 | 97.04 | 66.67 | 95.48 | 100.00 | 100.00 | 92.11 | 71.33 | 91.17 | 62.50 | 87.62 | 100.00 | 100.00 | 76.44 | 62.75 | 99.75 | 83.33 | 99.60 | 100.00 | 100.00 | 99.33 | 62.79 | 99.62 | 79.17 | 99.47 | 100.00 | 100.00 | 99.11 | | Qwen3-235B-A22B-Instruct | 67.38 | 95.12 | 70.83 | 92.76 | 100.00 | 100.00 | 87.00 | 71.29 | 91.21 | 62.50 | 87.67 | 100.00 | 100.00 | 76.56 | 62.62 | 99.88 | 87.50 | 99.80 | 100.00 | 100.00 | 99.67 | 62.75 | 99.75 | 83.33 | 99.60 | 100.00 | 100.00 | 99.33 | Table 6: Instruct+CoT setting experiment. | Model | ZH+ | ZH- | EN+ | EN- | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | | | DeepSeek-R1 | 76.00 | 86.50 | 62.50 | 78.83 | 83.67 | 62.50 | 73.96 | 88.50 | 62.50 | 77.54 | 84.88 | 58.33 | | DeepSeek-R1-Distill-Llama-8B | 99.00 | 62.79 | 54.17 | 99.04 | 62.79 | 45.83 | 94.62 | 61.71 | 4.17 | 96.21 | 61.46 | 12.50 | | DeepSeek-R1-Distill-Llama-70B | 96.75 | 65.42 | 58.33 | 98.12 | 64.12 | 62.50 | 95.42 | 65.88 | 29.17 | 97.42 | 64.25 | 45.83 | | DeepSeek-R1-Distill-Qwen-14B | 99.54 | 62.88 | 83.33 | 99.67 | 62.42 | 79.17 | 99.42 | 62.54 | 58.33 | 99.54 | 62.54 | 70.83 | Table 7: The DeepSeek-R1 and DeepSeek-R1-Distilled results by language and concept existence. 7.6.5 The results of Base models The experiments of Base models are shown in Table 8. Base models are the starting point and a constraint to further training. | Model | ZH+ | ZH- | EN+ | EN- | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | | | Qwen3-0.6B-Base | 6.62 | 36.46 | 29.17 | 14.67 | 34.00 | 4.17 | 1.71 | 37.38 | 16.67 | 7.42 | 36.92 | 0.00 | | Qwen3-1.7B-Base | 82.88 | 55.79 | 0.00 | 77.21 | 52.54 | 0.00 | 99.92 | 62.58 | 91.67 | 99.96 | 62.54 | 95.83 | | Qwen3-4B-Base | 93.25 | 61.67 | 33.33 | 91.29 | 60.54 | 29.17 | 72.54 | 56.54 | 8.33 | 81.58 | 58.83 | 25.00 | | Qwen3-8B-Base | 95.00 | 61.17 | 16.67 | 81.42 | 53.67 | 0.00 | 73.75 | 68.21 | 33.33 | 82.92 | 64.33 | 0.00 | | Qwen3-30B-A3B-Base | 79.50 | 52.12 | 0.00 | 90.17 | 58.00 | 0.00 | 79.58 | 50.75 | 0.00 | 84.96 | 53.67 | 0.00 | | Gemma-3-1B-PT | 6.63 | 32.53 | 0.00 | 5.38 | 24.82 | 0.00 | 5.12 | 21.90 | 0.00 | 5.11 | 23.37 | 0.00 | | Gemma-3-4B-PT | 6.75 | 36.67 | 0.00 | 9.12 | 36.08 | 0.00 | 2.42 | 30.31 | 0.00 | 3.48 | 30.74 | 0.00 | | Gemma-3-12B-PT | 9.00 | 39.00 | 0.00 | 11.33 | 38.83 | 0.00 | 11.83 | 38.79 | 0.00 | 14.49 | 38.44 | 0.00 | | Gemma-3-27B-PT | 26.83 | 42.50 | 0.00 | 24.46 | 42.29 | 0.00 | 16.75 | 34.21 | 0.00 | 16.92 | 35.42 | 0.00 | | Llama3-8B-Base | 30.08 | 36.67 | 0.00 | 29.58 | 35.54 | 0.00 | 12.17 | 32.92 | 0.00 | 13.54 | 34.42 | 0.00 | | Llama3-70B-Base | 44.70 | 43.44 | 0.00 | 41.79 | 42.71 | 0.00 | 34.43 | 45.78 | 0.00 | 29.86 | 43.65 | 0.00 | Table 8: The results of various Base Models by language and concept existence. 7.6.6 The results of dLLMs We conduct experiments on various dLLMs, including LLaDA Nie et al. (2025), LLaDA-1.5 Zhu et al. (2025a), TraDo Wang et al. (2025), DiRL Zhu et al. (2025b), SDAR Cheng et al. (2025), LLaDA2.0 Bie et al. (2025). The results are shown in Table 9. | Model | ZH+ | ZH- | EN+ | EN- | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | | | LLaDA-8b-Instruct | 70.25 | 50.83 | 0.00 | 68.79 | 50.54 | 0.00 | 71.75 | 55.88 | 0.00 | 69.50 | 54.12 | 0.00 | | LLaDA-1.5 | 73.12 | 50.62 | 0.00 | 75.08 | 52.88 | 0.00 | 66.46 | 57.79 | 0.00 | 61.25 | 53.25 | 0.00 | | TraDo-4B-Instruct | 84.92 | 59.50 | 20.83 | 80.67 | 57.00 | 25.00 | 87.04 | 66.62 | 20.83 | 86.29 | 63.96 | 12.50 | | TraDo-8B-Instruct | 96.38 | 61.04 | 41.67 | 95.04 | 59.71 | 20.83 | 90.92 | 69.50 | 37.50 | 89.46 | 66.88 | 4.17 | | DiRL-8B-Instruct | 89.50 | 62.19 | 0.00 | 92.83 | 59.00 | 0.00 | 94.12 | 66.25 | 20.83 | 94.58 | 63.25 | 4.17 | | SDAR-4B | 80.46 | 59.04 | 20.83 | 76.08 | 56.50 | 16.67 | 78.33 | 63.67 | 16.67 | 76.96 | 62.21 | 12.50 | | SDAR-8B | 91.58 | 59.17 | 20.83 | 90.83 | 56.33 | 20.83 | 84.21 | 68.46 | 0.00 | 72.75 | 62.42 | 0.00 | | SDAR-30B-A3B | 99.17 | 63.17 | 79.17 | 99.00 | 63.33 | 79.17 | 99.71 | 62.71 | 75.00 | 99.50 | 62.83 | 70.83 | | LLaDA2.0-mini | 82.62 | 77.46 | 16.67 | 87.12 | 74.46 | 33.33 | 85.96 | 73.96 | 37.50 | 89.42 | 72.08 | 45.83 | | LLaDA2.0-flash | 73.21 | 89.17 | 62.50 | 80.46 | 81.96 | 58.33 | 72.04 | 90.46 | 66.67 | 76.54 | 85.88 | 62.50 | Table 9: The brief results of various dLLMs by language and concept existence. | Model | ZH+ | ZH- | EN+ | EN- | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | $\text{Acc}_{t}$ | $\text{Acc}_{m}$ | Cons | $\mathrm{pre}_{V}$ | $\mathrm{rec}_{V}$ | $\mathrm{pre}_{I}$ | $\mathrm{rec}_{I}$ | | | Qwen3-0.6B-Base | 6.62 | 36.46 | 29.17 | 42.14 | 4.47 | 36.06 | 89.78 | 14.67 | 34.00 | 4.17 | 38.92 | 9.20 | 33.43 | 75.95 | 1.71 | 37.38 | 16.67 | 51.22 | 1.40 | 37.21 | 97.77 | 7.42 | 36.92 | 0.00 | 50.00 | 5.99 | 36.33 | 89.95 | | Qwen3-1.7B-Base | 82.88 | 55.79 | 0.00 | 62.95 | 90.40 | 39.55 | 10.56 | 77.21 | 52.54 | 0.00 | 62.28 | 87.29 | 38.91 | 13.28 | 99.92 | 62.58 | 91.67 | 62.55 | 100.00 | 100.00 | 0.22 | 99.96 | 62.54 | 95.83 | 62.53 | 100.00 | 100.00 | 0.11 | | Qwen3-4B-Base | 93.25 | 61.67 | 33.33 | 62.96 | 93.93 | 43.83 | 7.89 | 91.29 | 60.54 | 29.17 | 62.62 | 91.47 | 38.76 | 9.00 | 72.54 | 56.54 | 8.33 | 63.12 | 73.27 | 39.15 | 28.67 | 81.58 | 58.83 | 25.00 | 63.07 | 82.33 | 40.05 | 19.67 | | Qwen3-8B-Base | 95.00 | 61.17 | 16.67 | 62.54 | 95.58 | 38.89 | 4.69 | 81.42 | 53.67 | 0.00 | 59.93 | 78.28 | 26.47 | 13.00 | 73.75 | 68.21 | 33.33 | 70.85 | 83.60 | 60.89 | 42.60 | 82.92 | 64.33 | 0.00 | 66.18 | 87.92 | 55.64 | 25.22 | | Qwen3-30B-A3B-Base | 79.50 | 52.12 | 0.00 | 63.31 | 96.33 | 48.31 | 5.79 | 90.17 | 58.00 | 0.00 | 62.62 | 96.99 | 46.84 | 4.37 | 79.58 | 50.75 | 0.00 | 62.51 | 98.60 | 58.54 | 3.24 | 84.96 | 53.67 | 0.00 | 62.53 | 99.07 | 52.00 | 1.67 | | Gemma-3-1B-PT | 6.63 | 32.53 | 0.00 | 63.52 | 8.27 | 37.74 | 92.13 | 5.38 | 24.82 | 0.00 | 59.69 | 7.82 | 36.33 | 90.88 | 5.12 | 21.90 | 0.00 | 65.57 | 9.83 | 37.59 | 91.32 | 5.11 | 23.37 | 0.00 | 65.57 | 9.15 | 37.58 | 91.92 | | Gemma-3-4B-PT | 6.75 | 36.67 | 0.00 | 65.43 | 7.61 | 37.55 | 93.25 | 9.12 | 36.08 | 0.00 | 60.73 | 9.61 | 36.95 | 89.50 | 2.42 | 30.31 | 0.00 | 52.63 | 2.62 | 38.01 | 96.20 | 3.48 | 30.74 | 0.00 | 60.49 | 4.12 | 36.93 | 95.42 | | Gemma-3-12B-PT | 9.00 | 39.00 | 0.00 | 65.74 | 9.71 | 37.56 | 91.47 | 11.33 | 38.83 | 0.00 | 61.76 | 11.61 | 37.40 | 88.02 | 11.83 | 38.79 | 0.00 | 64.79 | 13.18 | 38.13 | 88.19 | 14.49 | 38.44 | 0.00 | 63.87 | 15.79 | 37.15 | 84.79 | | Gemma-3-27B-PT | 26.83 | 42.50 | 0.00 | 62.11 | 27.99 | 37.60 | 71.76 | 24.46 | 42.29 | 0.00 | 63.37 | 26.01 | 37.80 | 74.94 | 16.75 | 34.21 | 0.00 | 62.19 | 20.59 | 37.20 | 78.98 | 16.92 | 35.42 | 0.00 | 65.76 | 22.05 | 38.18 | 80.75 | | Llama3-8B-Base | 30.08 | 36.67 | 0.00 | 63.99 | 40.46 | 38.07 | 61.65 | 29.58 | 35.54 | 0.00 | 60.28 | 38.01 | 37.85 | 60.11 | 12.17 | 32.92 | 0.00 | 60.96 | 14.86 | 37.50 | 84.30 | 13.54 | 34.42 | 0.00 | 63.69 | 17.05 | 38.07 | 83.99 | | Llama3-70B-Base | 44.70 | 43.44 | 0.00 | 62.85 | 53.47 | 38.57 | 48.03 | 41.79 | 42.71 | 0.00 | 62.70 | 48.23 | 36.99 | 51.43 | 34.43 | 45.78 | 0.00 | 64.71 | 37.99 | 39.26 | 65.92 | 29.86 | 43.65 | 0.00 | 64.62 | 32.99 | 38.34 | 69.76 | Table 10: The detailed results of Base models.