A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 4 inhabitants: Amelia, Jackson, Luke, and Emma. Amelia said that Jackson is not a knight. Jackson said that Luke is a knight and Emma is a knight. According to Luke, "Amelia is a knight if and only if Amelia is a knave". Emma said that Amelia is a knight if and only if Jackson is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> 
user
Assume Amelia is a knight.  No contradiction is found in their claim that Jackson is not a knight.
 Jackson cannot be a knight, because this would contradict the claim of Amelia that Jackson is not a knight.
 Assume Jackson is a knave.  No contradiction is found in their false claim that Luke is a knight and Emma is a knight.
 Luke cannot be a knight, because this would contradict the claim of their own that Amelia is a knight if and only if Amelia is a knave.
 Assume Luke is a knave.  No contradiction is found in their false claim that Amelia is a knight if and only if Amelia is a knave.
 Assume Emma is a knight.  No contradiction is found in their claim that Amelia is a knight if and only if Jackson is a knave.
 Therefore, (1) Amelia is a knight
 (2) Jackson is a knave
 (3) Luke is a knave
 (4) Emma is a knight
A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 4 inhabitants: Amelia, Jackson, Luke, and Emma. Amelia said that Jackson is not a knight. Jackson said that Luke is a knight and Emma is a knight. According to Luke, "Amelia is a knight if and only if Amelia is a knave". Emma said that Amelia is a knight if and only if Jackson is a knave. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> 
Assume Amelia is a knight. No contradiction is found in their claim that Jackson is not a knight.
Jackson cannot be a knight, because this would contradict the claim of Amelia that Jackson is not a knight.
Assume Jackson is a knave. No contradiction is found in their false claim that Luke is a knight and Emma is a knight.
Luke cannot be a knight, because this would contradict the claim of their own that Amelia is a knight if and only if Amelia is a knave.
Assume Luke is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Amelia is a knave.
Assume Emma is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Jackson is a knave.
Therefore, (1) Amelia is a knight
(2) Jackson is a knave
(3) Luke is a knave
(4) Emma is a knight </think>
<answer> (1) Amelia is a knight
(2) Jackson is a knave
(3) Luke is a knave
(4) Emma is a knight </answer>
Amelia Jackson Luke Emma
(1) Amelia is a knight
(2) Jackson is a knave
(3) Luke is a knave
(4) Emma is a knight
(('not', ('telling-truth', 1)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('<=>', ('telling-truth', 0), ('lying', 0)), ('<=>', ('telling-truth', 0), ('lying', 1)))
rule