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: Harper, Aria, Matthew, and Aiden. Harper told you that Aria is not a knight. Aria said that If Harper is a knight then Matthew is a knave. Matthew told you that Aiden is not a knight. Aiden expressed that Matthew is a knight and Aria 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 Harper is a knight.  No contradiction is found in their claim that Aria is not a knight.
 Aria cannot be a knight, because this would contradict the claim of Harper that Aria is not a knight.
 Assume Aria is a knave.  No contradiction is found in their false claim that If Harper is a knight then Matthew is a knave.
 Assume Matthew is a knight.  No contradiction is found in their claim that Aiden is not a knight.
 Aiden cannot be a knight, because this would contradict the claim of Matthew that Aiden is not a knight.
 Aiden cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight and Aria is a knave.
 We have exhausted all possibilities for Aiden, so let us go back and reconsider Matthew.
 Matthew cannot be a knave, because this would contradict the false claim of Aria that If Harper is a knight then Matthew is a knave.
 We have exhausted all possibilities for Matthew and Aria, so let us go back and reconsider Harper.
 Assume Harper is a knave.  No contradiction is found in their false claim that Aria is not a knight.
 Assume Aria is a knight.  No contradiction is found in their claim that If Harper is a knight then Matthew is a knave.
 Assume Matthew is a knight.  No contradiction is found in their claim that Aiden is not a knight.
 Aiden cannot be a knight, because this would contradict the claim of Matthew that Aiden is not a knight.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Matthew is a knight and Aria is a knave.
 Therefore, (1) Harper is a knave
 (2) Aria is a knight
 (3) Matthew is a knight
 (4) Aiden 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 4 inhabitants: Harper, Aria, Matthew, and Aiden. Harper told you that Aria is not a knight. Aria said that If Harper is a knight then Matthew is a knave. Matthew told you that Aiden is not a knight. Aiden expressed that Matthew is a knight and Aria 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 Harper is a knight. No contradiction is found in their claim that Aria is not a knight.
Aria cannot be a knight, because this would contradict the claim of Harper that Aria is not a knight.
Assume Aria is a knave. No contradiction is found in their false claim that If Harper is a knight then Matthew is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that Aiden is not a knight.
Aiden cannot be a knight, because this would contradict the claim of Matthew that Aiden is not a knight.
Aiden cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight and Aria is a knave.
We have exhausted all possibilities for Aiden, so let us go back and reconsider Matthew.
Matthew cannot be a knave, because this would contradict the false claim of Aria that If Harper is a knight then Matthew is a knave.
We have exhausted all possibilities for Matthew and Aria, so let us go back and reconsider Harper.
Assume Harper is a knave. No contradiction is found in their false claim that Aria is not a knight.
Assume Aria is a knight. No contradiction is found in their claim that If Harper is a knight then Matthew is a knave.
Assume Matthew is a knight. No contradiction is found in their claim that Aiden is not a knight.
Aiden cannot be a knight, because this would contradict the claim of Matthew that Aiden is not a knight.
Assume Aiden is a knave. No contradiction is found in their false claim that Matthew is a knight and Aria is a knave.
Therefore, (1) Harper is a knave
(2) Aria is a knight
(3) Matthew is a knight
(4) Aiden is a knave </think>
<answer> (1) Harper is a knave
(2) Aria is a knight
(3) Matthew is a knight
(4) Aiden is a knave </answer>
Harper Aria Matthew Aiden
(1) Harper is a knave
(2) Aria is a knight
(3) Matthew is a knight
(4) Aiden is a knave
(('not', ('telling-truth', 1)), ('->', ('telling-truth', 0), ('lying', 2)), ('not', ('telling-truth', 3)), ('and', ('telling-truth', 2), ('lying', 1)))
rule