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 3 inhabitants: Joseph, Aiden, and Jacob. "If Jacob is a knight then Jacob is a knave," Joseph mentioned. "Jacob is not a knave," Aiden declared. According to Jacob, "Joseph is a knave if and only if Aiden 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 Joseph is a knight.  No contradiction is found in their claim that If Jacob is a knight then Jacob is a knave.
 Jacob cannot be a knight, because this would contradict the claim of Joseph that If Jacob is a knight then Jacob is a knave.
 Assume Jacob is a knave.  No contradiction is found in their false claim that Joseph is a knave if and only if Aiden is a knave.
 Aiden cannot be a knight, because this would contradict the claim of their own that Jacob is not a knave.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Jacob is not a knave.
 Therefore, (1) Joseph is a knight
 (2) Aiden is a knave
 (3) Jacob is a knave
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 3 inhabitants: Joseph, Aiden, and Jacob. "If Jacob is a knight then Jacob is a knave," Joseph mentioned. "Jacob is not a knave," Aiden declared. According to Jacob, "Joseph is a knave if and only if Aiden 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 Joseph is a knight. No contradiction is found in their claim that If Jacob is a knight then Jacob is a knave.
Jacob cannot be a knight, because this would contradict the claim of Joseph that If Jacob is a knight then Jacob is a knave.
Assume Jacob is a knave. No contradiction is found in their false claim that Joseph is a knave if and only if Aiden is a knave.
Aiden cannot be a knight, because this would contradict the claim of their own that Jacob is not a knave.
Assume Aiden is a knave. No contradiction is found in their false claim that Jacob is not a knave.
Therefore, (1) Joseph is a knight
(2) Aiden is a knave
(3) Jacob is a knave </think>
<answer> (1) Joseph is a knight
(2) Aiden is a knave
(3) Jacob is a knave </answer>
Joseph Aiden Jacob
(1) Joseph is a knight
(2) Aiden is a knave
(3) Jacob is a knave
(('->', ('telling-truth', 2), ('lying', 2)), ('not', ('lying', 2)), ('<=>', ('lying', 0), ('lying', 1)))
rule