1. **William's statement**: "William is a knight and Chloe is a knight.'- If William is telling the truth (i.e., he is a knighht), then both parts of his statement must be true. Howeve$5,5if William is a knight, the statement "William is a knighht" is true, but the statement "Chloe is a knight" cannotdetermine the truth about Chloe at this point since we haven't analyzed Chloe's statement yet. Therefore, William cannot be a knight becausse it would lead to a contradiction.

2. **Now that we know William is a knave, let's analyze Chloe's staatement**: "Lily is a knight.- Since William is a knave, Chloe's statement can be eitther true or false. If Chloe is a knight, her statement mu- Let's test both possibilities. 

4. **Analyzing Lily's statement**: "William is a knave and Jack is a knight.-Since William is a knave and Lily is a knight, her staterment is true. This means Lily is indeed telling the truth5. *Analyzing Jack's statement**:"William is a knave."-Since William is a knave, Jack's statement is true, so Jaack is a knight**Analyzing Logan's statement**: "Lily is a knave if and onlyif William is a knave."- Since Lily is a knight and William is a knave, this statement is false. Therefore, Logan is a knave.7. *Analyzing Chloe's statement again**: Wee already determined that if Chloe is a knight, her statement "Lilyis aknight" is true, so she is a knight.

Now,we havedetermined:William is a knave.Chloe is a knight.- Lily is a knight.- Jack is a knight.- Logan is a knave.

Let'sverify all statements:VerifyWilliam: "William is a knight and Chloe is a knight" (False, since William is a knave).Chloe: "Lily is a knight"(True).Logan: "Lily is a knave if and only if William is a knave"(False, since Lily is a knight and William is a knave)Jack: "William is a knave"(True).Lily: "William is a knave and Jack is a knight" (True) 

Since both assuming Sofia is aknight and a knave lead to contradictions, we need tore-evaluate our initial assumption. However, the only consistent path is to recheck the inittial assumption that William is a knightLet's assume William is a knight again and proceed with the same logic to ensure no contradictions arise.The consistent path will be威廉不是一个有效的输入,让我继续使用正常的推理方式来解决这个问题,意味着威廉的陈述是正确的。再次从威廉开始:威廉说:"威廉是骑士或者索菲亚是骑士"。假设威廉是骑士,那么他的陈述必须为真,因此"威廉是骑士或者索菲亚是骑士"为真,这接下来检查索菲亚的陈述:"诺亚不是骑士",假设索菲亚是骑士,那么她的陈述必须为真,意味着诺亚确实不是骑士(即诺亚是骗子)。现在检查诺亚的陈述:"佐伊不是骗子"。如果诺亚是骗子,那么这个陈述为假,这意味着"佐伊不是骗子"为假,即佐伊是骗子。如果佐伊是骗子,那么她所做的陈述"如果诺亚是骑士那么梅森是骗子"将为假。因为如果诺亚是骑士,那么如果诺亚是骑士那么梅森是骗子"将为真,但由于佐伊是骗子,她应该说这导致矛盾。因此,索菲亚不能是骑士。既然索菲亚不能是骑士,那么她必须是骗子。因此,她的陈述"诺亚不是骑士"为假,这意味着诺亚是骑士。现在我们检查诺亚的陈述"佐伊不是骗子"。既然诺亚是骑士,这个陈述必须为真,所以佐伊确实不是骗子,佐伊是骑士。接下来检查佐伊的陈述:"如果诺亚是骑士那么梅森是骗子因为诺亚是骑士,该条件为真,而佐伊的陈述为真,因此佐伊是骑士。然后我们检查梅森的陈述:"威廉是骗子或者佐伊是骗子"。威廉是骑士,佐伊是骑士因此梅森的陈述为假,因此梅森是骗子。最后检查威廉的陈述:"威廉是骑士或者索菲亚是骑士"。威廉是骑士,索菲亚是骗子,因此威廉的陈述为真,这与我们的推理一致。综上所述,我们得到了以下结果:1.威廉是骑士2.索菲亚是骗子3.诺亚是骑士4.佐伊是骑士5.梅森是骗子(1) William is a knight,(2)Sofia is a knave Noah is a knight,(4)Zoey is




    
 a knight,(5)Mason is a knave<|im_end|>

python ./examples/data_preprocess/kk.py \    --template_type=qwen-instruct \    --local_dir {processed_data_path} \    --data_path {raw_data_path}

<|im_start|>system\nYou are a helpful assistant. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> think> and<answer> answer> tags, respectively, i.e., <think> reasoning process here think><answer> answer here answer>.  Now the user asks you to solve a logical reasoning problem. After thinking, when you finally reach a conclusion, clearly state the identity of each character within <answer> answer> tags. i.e., <answer> (1) Zoey is a knight\n(2) ... answer>.\n<|im_end|>\n<|im_start|>user\n{quiz}\n<|im_end|>\n<|im_start|>assistant\n<think>

def validate_response_structure(processed_str: str) -> bool:    """Performs comprehensive validation of response structure.
    Args:        processed_str: Processed response string from the model
    Returns:        Boolean indicating whether all formatting requirements are met    """    print("\n[Structure Validation]")    validation_passed = True
    # Check required tags    tags = {        'think_start': ('', 1),        'think_end': ('', 1),        'answer_start': ('', 1),        'answer_end': ('', 1)    }
    positions = {}    for tag_name, (tag_str, expected_count) in tags.items():        count = processed_str.count(tag_str)        positions[tag_name] = pos = processed_str.find(tag_str)
        print(f"  {tag_str}: count={count}, position={pos}")
        if count != expected_count:            print(f"  [Error] {tag_str} appears {count} times (expected {expected_count})")            validation_passed = False
    # Verify tag order    if (positions['think_start'] > positions['think_end'] or        positions['think_end'] > positions['answer_start'] or        positions['answer_start'] > positions['answer_end']):        print("  [Error] Incorrect tag order: Expected ......")        validation_passed = False    else:        print("  Tag sequence validation passed")
    return validation_passed

# Validate response structureformat_correct = validate_response_structure(processed_str)format_score = format_reward if format_correct else-abs(format_reward)

if




    
 format_correct and answer_text:        pred_status = parse_model_answer(answer_text, expected_names)        if pred_status:            print(f"\n[Content Validation]")            print(f"  Expected: {gt_status}")            print(f"  Predicted: {pred_status}")
            if pred_status == gt_status:                answer_score = 2                print("  Content validation: FULL MATCH")            else:                answer_score = -1.5                print("  Content validation: MISMATCH")        else:            answer_score = -2            print( "Fail to parse answer")    else:        print("\n[Content Validation] Skipped due to format errors or missing answer")