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 5 inhabitants: Riley, Aria, Harper, Grace, and Matthew. Riley told you that Matthew is a knight. Aria expressed that If Aria is a knight then Riley is a knave. Harper remarked, "Grace is not a knave". As Grace put it, "Aria is a knave or Matthew is a knave". As Matthew put it, "Harper is a knave and Riley is a knight". 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 Riley is a knight.  No contradiction is found in their claim that Matthew is a knight.
 Assume Matthew is a knight.  No contradiction is found in their claim that Harper is a knave and Riley is a knight.
 Harper cannot be a knight, because this would contradict the claim of Matthew that Harper is a knave and Riley is a knight.
 Assume Harper is a knave.  No contradiction is found in their false claim that Grace is not a knave.
 Grace cannot be a knight, because this would contradict the false claim of Harper that Grace is not a knave.
 Assume Grace is a knave.  No contradiction is found in their false claim that Aria is a knave or Matthew is a knave.
 Aria cannot be a knight, because this would contradict the claim of their own that If Aria is a knight then Riley is a knave.
 Aria cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Riley is a knave.
 We have exhausted all possibilities for Aria, Grace, and Harper, so let us go back and reconsider Matthew.
 Matthew cannot be a knave, because this would contradict the claim of Riley that Matthew is a knight.
 We have exhausted all possibilities for Matthew, so let us go back and reconsider Riley.
 Assume Riley is a knave.  No contradiction is found in their false claim that Matthew is a knight.
 Matthew cannot be a knight, because this would contradict the false claim of Riley that Matthew is a knight.
 Assume Matthew is a knave.  No contradiction is found in their false claim that Harper is a knave and Riley is a knight.
 Assume Harper is a knight.  No contradiction is found in their claim that Grace is not a knave.
 Assume Grace is a knight.  No contradiction is found in their claim that Aria is a knave or Matthew is a knave.
 Assume Aria is a knight.  No contradiction is found in their claim that If Aria is a knight then Riley is a knave.
 Therefore, (1) Riley is a knave
 (2) Aria is a knight
 (3) Harper is a knight
 (4) Grace is a knight
 (5) Matthew 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 5 inhabitants: Riley, Aria, Harper, Grace, and Matthew. Riley told you that Matthew is a knight. Aria expressed that If Aria is a knight then Riley is a knave. Harper remarked, "Grace is not a knave". As Grace put it, "Aria is a knave or Matthew is a knave". As Matthew put it, "Harper is a knave and Riley is a knight". 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 Riley is a knight. No contradiction is found in their claim that Matthew is a knight.
Assume Matthew is a knight. No contradiction is found in their claim that Harper is a knave and Riley is a knight.
Harper cannot be a knight, because this would contradict the claim of Matthew that Harper is a knave and Riley is a knight.
Assume Harper is a knave. No contradiction is found in their false claim that Grace is not a knave.
Grace cannot be a knight, because this would contradict the false claim of Harper that Grace is not a knave.
Assume Grace is a knave. No contradiction is found in their false claim that Aria is a knave or Matthew is a knave.
Aria cannot be a knight, because this would contradict the claim of their own that If Aria is a knight then Riley is a knave.
Aria cannot be a knave, because this would contradict the false claim of their own that If Aria is a knight then Riley is a knave.
We have exhausted all possibilities for Aria, Grace, and Harper, so let us go back and reconsider Matthew.
Matthew cannot be a knave, because this would contradict the claim of Riley that Matthew is a knight.
We have exhausted all possibilities for Matthew, so let us go back and reconsider Riley.
Assume Riley is a knave. No contradiction is found in their false claim that Matthew is a knight.
Matthew cannot be a knight, because this would contradict the false claim of Riley that Matthew is a knight.
Assume Matthew is a knave. No contradiction is found in their false claim that Harper is a knave and Riley is a knight.
Assume Harper is a knight. No contradiction is found in their claim that Grace is not a knave.
Assume Grace is a knight. No contradiction is found in their claim that Aria is a knave or Matthew is a knave.
Assume Aria is a knight. No contradiction is found in their claim that If Aria is a knight then Riley is a knave.
Therefore, (1) Riley is a knave
(2) Aria is a knight
(3) Harper is a knight
(4) Grace is a knight
(5) Matthew is a knave </think>
<answer> (1) Riley is a knave
(2) Aria is a knight
(3) Harper is a knight
(4) Grace is a knight
(5) Matthew is a knave </answer>
Riley Aria Harper Grace Matthew
(1) Riley is a knave
(2) Aria is a knight
(3) Harper is a knight
(4) Grace is a knight
(5) Matthew is a knave
(('telling-truth', 4), ('->', ('telling-truth', 1), ('lying', 0)), ('not', ('lying', 3)), ('or', ('lying', 1), ('lying', 4)), ('and', ('lying', 2), ('telling-truth', 0)))
rule