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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 Logical Frameworks Comparison ### Overview The diagram illustrates a comparison between syllogistic reasoning and two logical frameworks (traditional vs. modern logic) using a unicorn/mammal syllogism example. It highlights how existential import (EI) settings affect validity judgments. ### Components/Axes 1. **Left Panel (Syllogism)**: - **Premise 1**: "All hairy animals are mammals" (hairy animals = orange, mammals = blue) - **Premise 2**: "All unicorns are hairy animals" (unicorns = purple, hairy animals = orange) - **Conclusion**: "Some unicorns are mammals" (unicorns = purple, mammals = blue) - Visual elements: Scroll icons for premises, gavel icon for conclusion 2. **Central Toggle (Existential Import - EI)**: - Switch labeled "licenses existence" with ON (green) and OFF (gray) positions - Text: "allows empty classes" next to OFF position 3. **Right Panel (Logic Frameworks)**: - **Top Box (Traditional Logic)**: - Label: "Traditional Logic (EI = ON)" - Green checkmark with "VALID" - Unicorn head icon (striped mane) - **Bottom Box (Modern Logic)**: - Label: "Modern Logic (EI = OFF)" - Red X with "INVALID" - Note: "Empty Set issue" with circle-slash symbol ### Detailed Analysis - **Color Coding**: - Orange: "hairy animals" (Premise 1) - Blue: "mammals" (Premise 1 & Conclusion) - Purple: "unicorns" (Premise 2 & Conclusion) - Green: Valid (Traditional Logic) - Red: Invalid (Modern Logic) - **Flow**: 1. Syllogism premises → Existential Import toggle → Logic framework validity 2. Arrows: Orange (Premise 2) → Blue/Green (Traditional Logic) → Red (Modern Logic) - **Key Symbols**: - ✅ Green circle: Validity confirmation - ❌ Red circle: Invalidity marker - 🦄 Unicorn: Existential example - ∅ Circle-slash: Empty set prohibition ### Key Observations 1. Traditional Logic (EI ON) validates the syllogism through unicorn existence assumption 2. Modern Logic (EI OFF) invalidates it due to potential empty unicorn set 3. Color progression: Orange → Blue (valid path) vs. Orange → Red (invalid path) 4. Positional contrast: Valid (top) vs. Invalid (bottom) frameworks ### Interpretation The diagram demonstrates how existential import assumptions fundamentally alter logical conclusions: - **Traditional Logic** (EI ON) preserves syllogistic validity by assuming non-empty sets, allowing "Some unicorns are mammals" to hold if unicorns exist. - **Modern Logic** (EI OFF) rejects this assumption, rendering the syllogism invalid when applied to potentially empty categories like unicorns. - The unicorn example serves as a philosophical boundary case, exposing the ontological commitments of different logical systems. The empty set prohibition in modern logic reflects its stricter formal requirements compared to traditional logic's existential flexibility. </details> <details> <summary>images/train2.png Details</summary>  ### Visual Description ## Diagram: AI Model Evolution Framework ### Overview The image depicts a stylized train diagram representing the evolution of AI models across three conceptual phases: "Modern Logic," "Turning Point," and "Traditional Logic." The train engine and three carriages are labeled with specific AI model names, suggesting a progression or transition between eras of AI development. ### Components/Axes - **Axis Labels**: - Horizontal axis: "Modern Logic" (left), "Turning Point" (center), "Traditional Logic" (right). - **Text Embedded in Diagram**: - **Train Engine**: No explicit label, but visually distinct as the locomotive. - **Carriage 1 (Modern Logic)**: "GPT-o3, GPT-5" - **Carriage 2 (Turning Point)**: "Qwen3-8B, Qwen3-30B-A3B" - **Carriage 3 (Traditional Logic)**: "Llama3-8B, Qwen3-0.6B" ### Detailed Analysis - **Model Placement**: - **Modern Logic (Left)**: Dominated by large-scale models (GPT-o3, GPT-5), implying cutting-edge, resource-intensive architectures. - **Turning Point (Center)**: Features mid-sized models (Qwen3-8B, Qwen3-30B-A3B), suggesting a transitional phase balancing capability and efficiency. - **Traditional Logic (Right)**: Smaller models (Llama3-8B, Qwen3-0.6B), indicating a shift toward lightweight, cost-effective solutions. - **Visual Flow**: The train moves left-to-right, symbolizing a chronological or developmental progression. ### Key Observations 1. **Model Size Transition**: - Modern Logic models are the largest (e.g., GPT-o3, GPT-5), while Traditional Logic models are significantly smaller (e.g., Qwen3-0.6B). 2. **Hybrid Architectures**: - The Turning Point includes both 8B and 30B parameter models, hinting at experimental or hybrid approaches. 3. **No Numerical Data**: The diagram lacks quantitative metrics (e.g., performance scores, training costs), relying on categorical labels for interpretation. ### Interpretation The diagram metaphorically illustrates the evolution of AI models from resource-heavy, large-scale systems ("Modern Logic") to more efficient, smaller architectures ("Traditional Logic"). The "Turning Point" phase highlights experimentation with mid-sized models, possibly reflecting industry shifts toward optimizing performance while reducing computational demands. The absence of numerical data limits precise analysis but emphasizes conceptual categorization. This progression aligns with real-world trends where AI development balances capability with sustainability, though the specific model names (e.g., GPT-o3, Qwen3 variants) suggest speculative or future-oriented frameworks. </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 Comparison ### Overview The image is a scatter plot comparing the accuracy (acc-t) of various large language models (LLMs) across different model families. The y-axis represents accuracy (60-100), while the x-axis lists specific model variants. Different colors represent distinct model families, with a legend on the right for reference. ### Components/Axes - **Y-axis**: "acc-t" (accuracy metric), scaled from 60 to 100 in increments of 10. - **X-axis**: Model names (e.g., "Llama3-8B", "Gemma3-27B", "GPT-5"), ordered left-to-right. - **Legend**: Located in the top-right corner, mapping colors to model families: - Blue: Llama - Green: Gemma - Purple: Gwen - Pink: Gwen-T - Yellow: Gemini - Light Blue: GPT ### Detailed Analysis 1. **Llama Family** (Blue): - Llama3-8B: 59 - Llama3-70B: 96 - Llama3-3-70B: 98 - Llama3-3-1B: 85 2. **Gemma Family** (Green): - Gemma3-3-12B: 95 - Gemma3-3-27B: 96 - Gemma3-3-4B: 87 3. **Gwen Family** (Purple): - Gwen3-3-0.6B: 100 - Gwen3-3-1.7B: 77 - Gwen3-3-4B: 92 - Gwen3-3-8B: 93 - Gwen3-3-14B: 94 - Gwen3-3-32B: 67 - Gwen3-3-30B-A3B: 68 - Gwen3-3-NEXT-80B-A3B: 66 - Gwen3-3-235B-A22B: 65 4. **Gwen-T Family** (Pink): - Gwen3-3-0.6B-T: 91 - Gwen3-3-8B-T: 84 - Gwen3-3-14B-T: 77 - Gwen3-3-32B-T: 81 - Gwen3-3-30B-A3B-T: 70 - Gwen3-3-NEXT-80B-A3B-T: 64 - Gwen3-3-235B-A22B-T: 63 - Gwen3-3-235B-A22B-T: 65 5. **Gemini Family** (Yellow): - Gemini-2.5-pro: 71 6. **GPT Family** (Light Blue): - GPT-3: 63 - GPT-5: 63 ### Key Observations - **Highest Accuracy**: Gwen3-3-0.6B (100) and Llama3-3-70B (98) achieve near-perfect scores. - **Lowest Accuracy**: Llama3-8B (59) and GPT-3/GPT-5 (63) perform significantly below the 80% threshold. - **Model Size Correlation**: Larger models (e.g., 70B, 235B) generally show higher accuracy, but exceptions exist (e.g., GPT-5 at 63). - **Threshold Line**: The dashed line at 80% separates high-performing models (above) from lower-performing ones (below). - **Outliers**: Gemini-2.5-pro (71) underperforms relative to its size compared to other families. ### Interpretation The data suggests a strong correlation between model size and accuracy, with larger models (e.g., 70B, 235B) typically achieving higher scores. However, this trend is not universal—GPT-5 and Gemini-2.5-pro underperform relative to their size. The Gwen3-3-0.6B model stands out as an anomaly with perfect accuracy despite its smaller size. The dashed 80% threshold acts as a benchmark, highlighting models that meet or exceed this standard. The Gwen-T family shows a notable drop in accuracy when transitioning to larger variants (e.g., Gwen3-3-235B-A22B-T at 65 vs. Gwen3-3-0.6B-T at 91), suggesting potential architectural or training challenges in scaling. The plot underscores the importance of model architecture and training methodology beyond mere parameter count in determining performance. </details> <details> <summary>images/acc-m.png Details</summary>  ### Visual Description ## Scatter Plot: Model Accuracy Comparison ### Overview The image is a scatter plot comparing the accuracy (acc-m) of various AI language models. The x-axis lists model names (e.g., Llama3-8B, GPT-5), while the y-axis represents accuracy in milli-units (50–100). A dashed horizontal line at 80 marks a performance threshold. Data points are color-coded by model family, with sizes varying (though size encoding is not explicitly labeled). ### Components/Axes - **X-axis**: Model names (e.g., Llama3-8B, Llama3-70B, Gemini-2.5-pro, GPT-5). Labels are spaced unevenly, with larger models (e.g., GPT-5) positioned far right. - **Y-axis**: Accuracy (acc-m), ranging from 50 to 100. A dashed line at 80 is labeled as a benchmark. - **Legend**: Located on the far right, associating colors with model families: - Blue: Llama3 - Green: Gemma3 - Purple: Qwen3 - Pink: Qwen3-NEXT - Yellow: Gemini - Light Blue: GPT ### Detailed Analysis - **Llama3 Models**: - Llama3-8B (blue, ~55 acc-m) - Llama3-70B (blue, ~63 acc-m) - Llama3-3-1B (blue, ~55 acc-m) - Llama3-3-12B (blue, ~64 acc-m) - Llama3-3-27B (blue, ~65 acc-m) - **Gemma3 Models**: - Gemma3-3-4B (green, ~64 acc-m) - Gemma3-3-12B (green, ~64 acc-m) - Gemma3-3-27B (green, ~65 acc-m) - **Qwen3 Models**: - Qwen3-3-0.6B (purple, ~62 acc-m) - Qwen3-3-1.7B (purple, ~59 acc-m) - Qwen3-3-4B (purple, ~65 acc-m) - Qwen3-3-8B (purple, ~67 acc-m) - Qwen3-3-14B (purple, ~67 acc-m) - Qwen3-3-30B-A3B (purple, ~69 acc-m) - Qwen3-3-30B-A3B (purple, ~95 acc-m) - Qwen3-3-30B-A3B (purple, ~97 acc-m) - Qwen3-3-30B-A3B (purple, ~98 acc-m) - **Qwen3-NEXT Models**: - Qwen3-3-0.6B-T (pink, ~61 acc-m) - Qwen3-3-1.7B-T (pink, ~79 acc-m) - Qwen3-3-4B-T (pink, ~79 acc-m) - Qwen3-3-8B-T (pink, ~88 acc-m) - Qwen3-3-14B-T (pink, ~87 acc-m) - Qwen3-3-30B-A3B-T (pink, ~98 acc-m) - Qwen3-3-30B-A3B-T (pink, ~100 acc-m) - **Gemini Models**: - Gemini-2.5-pro (yellow, ~90 acc-m) - **GPT Models**: - GPT-3 (light blue, ~100 acc-m) - GPT-4 (light blue, ~100 acc-m) - GPT-5 (light blue, ~100 acc-m) ### Key Observations 1. **Model Size vs. Accuracy**: Larger models (e.g., Llama3-70B, GPT-5) generally achieve higher accuracy, with GPT-5 and Qwen3-NEXT-A3B-T reaching 100 acc-m. 2. **Threshold Performance**: Only models in the Qwen3-NEXT, Gemini, and GPT families exceed the 80 acc-m benchmark. Qwen3-NEXT-A3B-T and GPT-5 are the highest performers. 3. **Outliers**: - Qwen3-3-0.6B (purple, ~62 acc-m) underperforms relative to its size. - Gemini-2.5-pro (yellow, ~90 acc-m) lags behind GPT-5 despite similar size. ### Interpretation The plot demonstrates a clear trend where larger models (e.g., GPT-5, Qwen3-NEXT-A3B-T) achieve near-perfect accuracy (100 acc-m), while smaller models (e.g., Llama3-8B, Qwen3-3-0.6B) struggle to reach the 80 acc-m threshold. The dashed line at 80 serves as a critical benchmark, separating mid-tier performers (e.g., Qwen3-3-8B-T at 88 acc-m) from top-tier models. Notably, GPT-5 and Qwen3-NEXT-A3B-T dominate the upper-right quadrant, suggesting architectural or training advantages. The absence of size encoding in the legend leaves uncertainty about whether point size correlates with model parameters or another metric. This visualization underscores the importance of model scale and optimization in achieving high accuracy. </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: | $\displaystyle\ \forall x\,(Sx\rightarrow Px)$ | | | --- | --- | --- | --- | 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, $\forall x\,(Sx\rightarrow Px)$ , 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 $\forall x\,(Ux\rightarrow Mx)$ and does not imply $\exists x\,Ux$ ; 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 Format Validity Across Language Combinations ### Overview The image is a heatmap visualizing the number of predicted VALID outcomes for various syllogism formats across four language combinations: zh+ (Chinese positive), zh- (Chinese negative), en+ (English positive), and en- (English negative). The color intensity corresponds to the count of valid predictions, with darker colors indicating lower values (55-60) and lighter colors indicating higher values (90-100). A red horizontal line at "EIO-4" divides the chart. --- ### Components/Axes - **Y-Axis (Rows)**: Syllogism formats (e.g., 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, AAII-1, EAO-1, AEO-2, EAO-2, AAII-3, EAO-3, AAII-4, AEO-4, EAO-4). - **X-Axis (Columns)**: Language combinations: zh+, zh-, en+, en-. - **Color Scale**: Ranges from 55 (dark purple) to 100 (yellow), representing the number of predicted VALID outcomes. - **Legend**: Located on the right, mapping colors to counts. - **Red Line**: Horizontal line at "EIO-4" (row 15), separating the chart into two regions. --- ### Detailed Analysis 1. **Syllogism Formats**: - **High Validity (Light Yellow)**: - Formats like 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, AAII-1, EAO-1, AEO-2, EAO-2, AAII-3, EAO-3, and EAO-4 show consistently high validity (90-100) across most language combinations. - **Moderate Validity (Orange/Red)**: - Formats like AOO-2, EIO-2, and EIO-4 exhibit moderate validity (75-85) in specific language pairs (e.g., en+ and en- for EIO-2). - **Low Validity (Dark Purple/Black)**: - Formats like AAII-4, AEO-4, and EIO-4 show very low validity (55-60) in zh+ and zh- combinations. EIO-4 also has low validity in en+ and en-. 2. **Language Combinations**: - **zh+ and zh-**: - Most formats perform well (90-100), except AAII-4, AEO-4, and EIO-4, which have low validity (55-60). - **en+ and en-**: - Generally high validity (90-100) for most formats, but EIO-2 and EIO-4 show moderate validity (75-85). 3. **Red Line at EIO-4**: - The red line at "EIO-4" (row 15) may indicate a threshold or a critical point where validity drops significantly for certain language pairs (e.g., zh+ and zh-). --- ### Key Observations 1. **Consistent High Performance**: - Formats like AAA-1, EAE-1, and AII-1 maintain high validity (90-100) across all language combinations. 2. **Language-Specific Trends**: - Chinese (zh+) and English (en+) combinations generally show higher validity than their negative counterparts (zh- and en-). - EIO-4 and AAII-4 are outliers with low validity in zh+ and zh-. 3. **Red Line Significance**: - The red line at EIO-4 may highlight a critical format where validity is context-dependent, particularly in Chinese language pairs. --- ### Interpretation The heatmap reveals that syllogism formats with simpler structures (e.g., AAA-1, EAE-1) perform consistently well across languages, suggesting robustness in prediction. Formats like EIO-4 and AAII-4, however, show significant drops in validity for Chinese language pairs, indicating potential challenges in handling negations or complex logical structures in these contexts. The red line at EIO-4 may serve as a visual marker for formats requiring further investigation or optimization. The data underscores the importance of language-specific tuning for syllogism prediction models, particularly for formats sensitive to negation or syntactic complexity. </details> (a) Qwen3-4B <details> <summary>images/qwen3-8b_24x4_heatmap.png Details</summary>  ### Visual Description ## Heatmap: Syllogism Format vs. Predicted VALID Outcomes ### Overview The image is a heatmap visualizing the relationship between syllogism formats (rows) and variables (columns: zh+, zh-, en+, en-). Color intensity represents the number of predicted VALID outcomes, with a color scale from black (65) to yellow (100). A red horizontal line at EIO-4 serves as a reference point. ### Components/Axes - **Y-Axis (Syllogism Format)**: - Categories: 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. - Positioned vertically on the left. - **X-Axis (Variables)**: - Categories: zh+, zh-, en+, en-. - Positioned horizontally at the bottom. - **Legend**: - Color scale from black (65) to yellow (100), labeled "The number of predicted VALID." - Located on the right side. - **Red Line**: - Horizontal line at EIO-4, dividing the heatmap into upper and lower sections. ### Detailed Analysis - **Color Distribution**: - **Upper Section (Above Red Line)**: Predominantly yellow (90–100), indicating high predicted VALID counts. - **Lower Section (Below Red Line)**: Gradual shift to darker colors (red to black), with the lowest values (black) in the bottom-right quadrant (AAI-4, AEO-4, EAO-4 with en+ and en-). - **Notable Exceptions**: - AAI-3 (en+) and AAI-4 (en+) show purple (70–75), lower than surrounding cells. - EAO-4 (en+) is dark purple (65–70), the lowest value in the heatmap. ### Key Observations 1. **High Predicted VALIDs**: Most syllogism formats (e.g., AAA-1, EAE-1) consistently show high values (90–100) across all variables. 2. **Critical Threshold**: The red line at EIO-4 marks a boundary where predicted VALIDs drop significantly below 90. 3. **Lowest Values**: The bottom-right quadrant (AAI-4, AEO-4, EAO-4 with en+ and en-) contains the darkest cells (65–70), suggesting poor performance in these combinations. 4. **Variable Impact**: - `en+` and `en-` variables correlate with lower values in the lower rows. - `zh+` and `zh-` variables maintain higher values even in lower rows. ### Interpretation The heatmap reveals that syllogism formats generally perform well in predicting VALID outcomes, but specific combinations (e.g., AAI-4 with en+ and en-) exhibit significantly lower reliability. The red line at EIO-4 may indicate a critical threshold where performance declines. The dominance of dark colors in the lower rows suggests that certain syllogism formats (e.g., AAI-4, EAO-4) are less robust when paired with `en+` and `en-` variables. This could imply limitations in the model's ability to handle these combinations or the need for further validation of these syllogism structures. The data underscores the importance of contextual factors (variables) in determining the reliability of syllogistic reasoning. </details> (b) Qwen3-8B <details> <summary>images/qwen3-next-80b-a3b-instruct_24x4_heatmap.png Details</summary>  ### Visual Description ## Heatmap: Syllogism Format vs. Language Categories ### Overview The image is a heatmap visualizing the relationship between syllogism formats (y-axis) and language categories (x-axis: zh+, zh-, en+, en-). Color intensity represents the number of predicted VALID outcomes, ranging from 0 (black) to 100 (yellow). A red horizontal line separates the top and bottom halves of the chart. ### Components/Axes - **Y-Axis (Syllogism Format)**: - Categories: 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 (top to bottom). - **X-Axis (Language Categories)**: - Categories: zh+, zh-, en+, en- (left to right). - **Color Legend**: - Scale: 0 (black) to 100 (yellow), labeled "The number of predicted VALID." - Red line at the midpoint (y-axis) separates high and low-value regions. ### Detailed Analysis - **Top Half (Above Red Line)**: - All cells are uniformly yellow (≈100), indicating maximum predicted VALID for all combinations in this region. - **Bottom Half (Below Red Line)**: - **EAO-2**: - zh+: ≈20 (light purple), zh-: ≈60 (orange), en+: ≈0 (black), en-: ≈10 (dark purple). - **EAO-3**: - zh+: ≈20 (light purple), zh-: ≈60 (orange), en+: ≈0 (black), en-: ≈10 (dark purple). - **EAO-4**: - zh+: ≈0 (black), zh-: ≈20 (light purple), en+: ≈0 (black), en-: ≈10 (dark purple). - **Other Bottom Rows**: - Values cluster between 0 (black) and 20 (light purple), with occasional orange (≈60) in zh- categories. ### Key Observations 1. **High-Value Region**: The top half (above the red line) shows perfect prediction (100% VALID) across all syllogism formats and language categories. 2. **Low-Value Region**: The bottom half exhibits sparse VALID predictions, with most cells near 0 (black) or 10-20 (purple/orange). 3. **Red Line Significance**: The red line likely represents a threshold (e.g., 50% VALID), dividing high-confidence and low-confidence predictions. 4. **Language-Specific Trends**: - zh- categories (e.g., EAO-2, EAO-3) show higher VALID predictions (≈60) compared to zh+ (≈20) and en+ (≈0). - en- consistently shows low VALID predictions (≈10) across most syllogism formats. ### Interpretation The heatmap suggests that syllogism formats in the top half (e.g., AAA-1, EAE-1) are universally predicted as VALID, possibly due to structural simplicity or alignment with training data. In contrast, formats in the bottom half (e.g., EAO-2, EAO-4) exhibit language-dependent performance, with zh- categories outperforming others. The red line may indicate a critical cutoff for model confidence, beyond which predictions become unreliable. The stark contrast between high and low regions implies potential biases in the model’s handling of complex syllogisms or non-native language structures. </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. Language Combinations ### Overview The image is a heatmap visualizing the relationship between syllogism formats (y-axis) and language combinations (x-axis), with color intensity representing the number of predicted VALID outcomes. The color scale ranges from black (0) to yellow (100), with a red horizontal line dividing the chart into two distinct regions. ### Components/Axes - **Y-Axis (Syllogism Format)**: - Categories: 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. - Spatial Positioning: Top-to-bottom, with the red line at the midpoint separating "high-value" (top) and "low-value" (bottom) regions. - **X-Axis (Language Combinations)**: - Categories: zh+ (Chinese positive), zh- (Chinese negative), en+ (English positive), en- (English negative). - Spatial Positioning: Left-to-right, with equal spacing between categories. - **Color Legend**: - Scale: Black (0) → Purple (20) → Red (40) → Yellow (100). - Position: Right side of the chart. ### Detailed Analysis 1. **Top Region (Above Red Line)**: - **Dominant Colors**: Yellow (80-100) and light orange (60-80). - **Key Data Points**: - AAA-1: Yellow (95-100) across all x-axis categories. - EAE-1: Yellow (90-95) for zh+ and en+; orange (80-85) for zh- and en-. - AII-1: Yellow (90-95) for zh+ and en+; orange (80-85) for zh- and en-. - EIO-1: Yellow (95-100) for zh+ and en+; orange (80-85) for zh- and en-. - EAE-2: Yellow (90-95) for zh+ and en+; orange (80-85) for zh- and en-. - AEE-2: Yellow (95-100) for zh+ and en+; orange (80-85) for zh- and en-. - EIO-2: Yellow (90-95) for zh+ and en+; orange (80-85) for zh- and en-. - AOO-2: Yellow (95-100) for zh+ and en+; orange (80-85) for zh- and en-. - AII-3: Yellow (90-95) for zh+ and en+; orange (80-85) for zh- and en-. - IAI-3: Yellow (95-100) for zh+ and en+; orange (80-85) for zh- and en-. - OAO-3: Yellow (90-95) for zh+ and en+; orange (80-85) for zh- and en-. - EIO-3: Yellow (95-100) for zh+ and en+; orange (80-85) for zh- and en-. - AEE-4: Yellow (90-95) for zh+ and en+; orange (80-85) for zh- and en-. - IAI-4: Yellow (95-100) for zh+ and en+; orange (80-85) for zh- and en-. - EIO-4: Yellow (95-100) for zh+ and en+; orange (80-85) for zh- and en-. 2. **Bottom Region (Below Red Line)**: - **Dominant Colors**: Black (0-20) and dark purple (20-40). - **Key Data Points**: - AAI-1: Black (0-5) for zh+ and zh-; dark purple (10-20) for en+ and en-. - EAO-1: Black (0-5) for zh+ and zh-; dark purple (10-20) for en+ and en-. - AEO-2: Black (0-5) for zh+ and zh-; dark purple (10-20) for en+ and en-. - EAO-2: Black (0-5) for zh+ and zh-; dark purple (10-20) for en+ and en-. - AAI-3: Black (0-5) for zh+ and zh-; dark purple (10-20) for en+ and en-. - EAO-3: Black (0-5) for zh+ and zh-; dark purple (10-20) for en+ and en-. - AAI-4: Black (0-5) for zh+ and zh-; dark purple (10-20) for en+ and en-. - AEO-4: Black (0-5) for zh+ and zh-; dark purple (10-20) for en+ and en-. - EAO-4: Black (0-5) for zh+ and zh-; dark purple (10-20) for en+ and en-. ### Key Observations 1. **Red Line Division**: The red line at the midpoint creates a clear dichotomy: - **Top Region**: High validity (80-100) for most syllogism formats, especially with zh+ and en+. - **Bottom Region**: Low validity (0-20) for most syllogism formats, with minimal variation across x-axis categories. 2. **Language Impact**: - **zh+ and en+**: Consistently higher validity scores across all syllogism formats. - **zh- and en-**: Lower validity scores, though still higher in the top region. 3. **Format-Specific Trends**: - **Top Region 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, EIO-4 show strong performance. - **Bottom Region Formats**: AAI-1, EAO-1, AEO-2, EAO-2, AAI-3, EAO-3, AAI-4, AEO-4, EAO-4 exhibit poor performance. ### Interpretation The heatmap suggests that syllogism formats in the top region (e.g., AAA-1, EAE-1) are more robust in predicting VALID outcomes, particularly when combined with Chinese positive (zh+) or English positive (en+) language cues. The bottom region formats (e.g., AAI-1, EAO-1) perform poorly, indicating potential limitations in their structure or sensitivity to language polarity. The stark contrast between regions implies that language polarity (positive vs. negative) and syllogism complexity (e.g., AAA-1 vs. AAI-1) are critical factors in prediction validity. The red line may represent a threshold for acceptable performance, with formats above it being deemed "reliable" and those below "unreliable." </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. 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External Links: 2512.22234, Link Cited by: §7.6.6. ## 7 Appendix ### 7.1 Syllogism and Categorical Propositions The core structure of the syllogism was first systematically articulated by the ancient Greek philosopher Aristotle (384–322 BCE) in the Organon. He defines a syllogism as a form of reasoning in which the conclusion follows necessarily from the premises, and it is standardly analyzed as involving a major premise, a minor premise, and a conclusion. 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 $P$ | $\forall x\,(Sx\rightarrow Px)$ | For all $x$ , if $x$ is $S$ , then $x$ is $P$ . | | No $S$ are $P$ | $\forall x\,(Sx\rightarrow\neg Px)$ or $\neg\exists x\,(Sx\wedge Px)$ | 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 $P$ | $\exists x\,(Sx\wedge Px)$ | There exists at least one $x$ such that $x$ is $S$ and $x$ is $P$ . | | Some $S$ are not $P$ | $\exists x\,(Sx\wedge\neg Px)$ | 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 $\exists x(Sx\land Px)$ is false, whereas $\forall x(Sx\rightarrow Px)$ is vacuously true. Consequently, from $\forall x(Sx\rightarrow Px)$ and $\forall x(Px\rightarrow Qx)$ one cannot derive $\exists x(Sx\land Qx)$ unless one adds an extra existence assumption (e.g., $\exists x\,Sx$ ). 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: | $\displaystyle\quad\text{All }M\text{ are }P\;\to\;\forall x(Mx\rightarrow Px),$ | | | --- | --- | --- | --- | Under modern logic, the validity of this inference can be demonstrated by a formal derivation (e.g., in natural deduction): 1. $\forall x(Mx\rightarrow Px)$ [Major premise] 1. $\forall x(Sx\rightarrow Mx)$ [Minor premise] 1. Assume an arbitrary $a$ . [Arbitrary individual] 1. $Sa\rightarrow Ma$ [from 2, $\forall$ -elim] 1. $Ma\rightarrow Pa$ [from 1, $\forall$ -elim] 1. $Sa\rightarrow Pa$ [from 4, 5] 1. $\forall x(Sx\rightarrow Px)$ [from 3–6, $\forall$ -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 $\rightarrow$ dog $\rightarrow$ 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.