## Heatmap: Syllogism Validity Prediction
### Overview
The image is a heatmap visualizing the number of predicted valid syllogisms for different syllogism formats across four conditions: 'zh+', 'zh-', 'en+', and 'en-'. The color intensity represents the number of predicted valid syllogisms, ranging from 65 (dark purple) to 100 (light yellow). A red horizontal line is present between "EIO-4" and "AAI-1".
### Components/Axes
* **Y-axis:** Syllogism Format. The syllogism formats are listed vertically.
* AAA-1
* EAE-1
* AII-1
* EIO-1
* EAE-2
* AEE-2
* EIO-2
* AOO-2
* AII-3
* IAI-3
* OAO-3
* EIO-3
* AEE-4
* IAI-4
* EIO-4
* AAI-1
* EAO-1
* AEO-2
* EAO-2
* AAI-3
* EAO-3
* AAI-4
* AEO-4
* EAO-4
* **X-axis:** Conditions. The conditions are 'zh+', 'zh-', 'en+', and 'en-'.
* **Color Scale (Legend):** The color scale on the right represents the number of predicted valid syllogisms.
* Light Yellow: 100
* Yellow-Orange: 95
* Orange: 90
* Light Red-Orange: 85
* Red-Orange: 80
* Red: 75
* Purple-Red: 70
* Dark Purple: 65
### Detailed Analysis
The heatmap displays the predicted validity counts for each syllogism format under each condition. The color of each cell corresponds to the number of predicted valid syllogisms, as indicated by the color scale.
* **AAA-1:** All conditions are light yellow, indicating a value of approximately 100.
* **EAE-1:** All conditions are light yellow, indicating a value of approximately 100.
* **AII-1:** All conditions are light yellow, indicating a value of approximately 100.
* **EIO-1:** All conditions are light yellow, indicating a value of approximately 100.
* **EAE-2:** All conditions are light yellow, indicating a value of approximately 100.
* **AEE-2:** All conditions are light yellow, indicating a value of approximately 100.
* **EIO-2:** 'zh+' and 'en+' are light yellow (approximately 100), while 'zh-' and 'en-' are orange (approximately 90).
* **AOO-2:** 'zh+' and 'en+' are light yellow (approximately 100), while 'zh-' and 'en-' are orange (approximately 90).
* **AII-3:** All conditions are light yellow, indicating a value of approximately 100.
* **IAI-3:** All conditions are light yellow, indicating a value of approximately 100.
* **OAO-3:** All conditions are light yellow, indicating a value of approximately 100.
* **EIO-3:** All conditions are light yellow, indicating a value of approximately 100.
* **AEE-4:** 'zh+', 'zh-', and 'en+' are light yellow (approximately 100), while 'en-' is orange (approximately 90).
* **IAI-4:** 'zh+', 'zh-', and 'en+' are light yellow (approximately 100), while 'en-' is orange (approximately 90).
* **EIO-4:** 'zh+', 'zh-', and 'en+' are light yellow (approximately 100), while 'en-' is orange (approximately 90).
* **AAI-1:** 'zh+' and 'zh-' are orange (approximately 90), while 'en+' is red-orange (approximately 80), and 'en-' is light yellow (approximately 100).
* **EAO-1:** 'zh+' and 'en+' are light yellow (approximately 100), while 'zh-' and 'en-' are orange (approximately 90).
* **AEO-2:** All conditions are light yellow, indicating a value of approximately 100.
* **EAO-2:** 'zh+' and 'en+' are light yellow (approximately 100), while 'zh-' and 'en-' are orange (approximately 90).
* **AAI-3:** 'zh+' and 'en-' are orange (approximately 90), 'zh-' is light yellow (approximately 100), and 'en+' is dark purple (approximately 65).
* **EAO-3:** All conditions are light yellow, indicating a value of approximately 100.
* **AAI-4:** 'zh+' and 'zh-' are dark purple (approximately 65), 'en+' is red-orange (approximately 80), and 'en-' is orange (approximately 90).
* **AEO-4:** 'zh+' and 'zh-' are dark purple (approximately 65), 'en+' is purple-red (approximately 70), and 'en-' is red-orange (approximately 80).
* **EAO-4:** 'zh+' is red (approximately 75), 'zh-' is red-orange (approximately 80), 'en+' is dark purple (approximately 65), and 'en-' is orange (approximately 90).
### Key Observations
* Syllogism formats AAA-1, EAE-1, AII-1, EIO-1, EAE-2, AEE-2, AII-3, IAI-3, OAO-3, EIO-3, and EAO-3 consistently show high predicted validity (approximately 100) across all conditions.
* Syllogism formats AAI-4 and AEO-4 show very low predicted validity (approximately 65-80) for 'zh+' and 'zh-' conditions.
* The 'en+' condition often shows lower predicted validity compared to other conditions, especially for AAI-3, AAI-4, AEO-4, and EAO-4.
* The 'en-' condition often shows higher predicted validity compared to other conditions, especially for AAI-1.
### Interpretation
The heatmap suggests that the predicted validity of syllogisms varies significantly depending on the syllogism format and the condition ('zh+', 'zh-', 'en+', 'en-'). The 'zh' and 'en' likely refer to different languages (possibly Chinese and English), and the '+' and '-' likely refer to some manipulation or feature of the text. Some syllogism formats are consistently predicted as valid across all conditions, while others show significant variation. The lower predicted validity for certain syllogism formats under the 'en+' condition may indicate a bias or limitation in the prediction model related to the English language or the specific feature represented by '+'. The dark purple cells indicate syllogisms that are rarely predicted as valid under those conditions, suggesting a potential issue with their logical structure or the model's ability to recognize their validity. The red line does not appear to have any significance.
