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: Jackson, Aiden, Victoria, Matthew, and Emily. "Victoria is a knight if and only if Aiden is a knight," Jackson declared. Aiden expressed that Matthew is not a knight. Victoria stated, "If Emily is a knave then Jackson is a knave". Matthew commented, "If Jackson is a knight then Aiden is a knight". Emily noted, "Victoria is a knave or Aiden 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 Jackson is a knight.  No contradiction is found in their claim that Victoria is a knight if and only if Aiden is a knight.
 Assume Victoria is a knight.  No contradiction is found in their claim that If Emily is a knave then Jackson is a knave.
 Assume Emily is a knight.  No contradiction is found in their claim that Victoria is a knave or Aiden is a knight.
 Assume Aiden is a knight.  No contradiction is found in their claim that Matthew is not a knight.
 Matthew cannot be a knight, because this would contradict the claim of Aiden that Matthew is not a knight.
 Matthew cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knight then Aiden is a knight.
 We have exhausted all possibilities for Matthew, so let us go back and reconsider Aiden.
 Aiden cannot be a knave, because this would contradict the claim of Jackson that Victoria is a knight if and only if Aiden is a knight.
 We have exhausted all possibilities for Aiden, so let us go back and reconsider Emily.
 Emily cannot be a knave, because this would contradict the claim of Victoria that If Emily is a knave then Jackson is a knave.
 We have exhausted all possibilities for Emily, so let us go back and reconsider Victoria.
 Assume Victoria is a knave.  No contradiction is found in their false claim that If Emily is a knave then Jackson is a knave.
 Emily cannot be a knight, because this would contradict the false claim of Victoria that If Emily is a knave then Jackson is a knave.
 Emily cannot be a knave, because this would contradict the false claim of their own that Victoria is a knave or Aiden is a knight.
 We have exhausted all possibilities for Emily and Victoria, so let us go back and reconsider Jackson.
 Assume Jackson is a knave.  No contradiction is found in their false claim that Victoria is a knight if and only if Aiden is a knight.
 Assume Victoria is a knight.  No contradiction is found in their claim that If Emily is a knave then Jackson is a knave.
 Assume Emily is a knight.  No contradiction is found in their claim that Victoria is a knave or Aiden is a knight.
 Aiden cannot be a knight, because this would contradict the false claim of Jackson that Victoria is a knight if and only if Aiden is a knight.
 Aiden cannot be a knave, because this would contradict the claim of Emily that Victoria is a knave or Aiden is a knight.
 We have exhausted all possibilities for Aiden, so let us go back and reconsider Emily.
 Assume Emily is a knave.  No contradiction is found in their false claim that Victoria is a knave or Aiden is a knight.
 Aiden cannot be a knight, because this would contradict the false claim of Jackson that Victoria is a knight if and only if Aiden is a knight.
 Assume Aiden is a knave.  No contradiction is found in their false claim that Matthew is not a knight.
 Assume Matthew is a knight.  No contradiction is found in their claim that If Jackson is a knight then Aiden is a knight.
 Therefore, (1) Jackson is a knave
 (2) Aiden is a knave
 (3) Victoria is a knight
 (4) Matthew is a knight
 (5) Emily 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: Jackson, Aiden, Victoria, Matthew, and Emily. "Victoria is a knight if and only if Aiden is a knight," Jackson declared. Aiden expressed that Matthew is not a knight. Victoria stated, "If Emily is a knave then Jackson is a knave". Matthew commented, "If Jackson is a knight then Aiden is a knight". Emily noted, "Victoria is a knave or Aiden 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 Jackson is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Aiden is a knight.
Assume Victoria is a knight. No contradiction is found in their claim that If Emily is a knave then Jackson is a knave.
Assume Emily is a knight. No contradiction is found in their claim that Victoria is a knave or Aiden is a knight.
Assume Aiden is a knight. No contradiction is found in their claim that Matthew is not a knight.
Matthew cannot be a knight, because this would contradict the claim of Aiden that Matthew is not a knight.
Matthew cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knight then Aiden is a knight.
We have exhausted all possibilities for Matthew, so let us go back and reconsider Aiden.
Aiden cannot be a knave, because this would contradict the claim of Jackson that Victoria is a knight if and only if Aiden is a knight.
We have exhausted all possibilities for Aiden, so let us go back and reconsider Emily.
Emily cannot be a knave, because this would contradict the claim of Victoria that If Emily is a knave then Jackson is a knave.
We have exhausted all possibilities for Emily, so let us go back and reconsider Victoria.
Assume Victoria is a knave. No contradiction is found in their false claim that If Emily is a knave then Jackson is a knave.
Emily cannot be a knight, because this would contradict the false claim of Victoria that If Emily is a knave then Jackson is a knave.
Emily cannot be a knave, because this would contradict the false claim of their own that Victoria is a knave or Aiden is a knight.
We have exhausted all possibilities for Emily and Victoria, so let us go back and reconsider Jackson.
Assume Jackson is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Aiden is a knight.
Assume Victoria is a knight. No contradiction is found in their claim that If Emily is a knave then Jackson is a knave.
Assume Emily is a knight. No contradiction is found in their claim that Victoria is a knave or Aiden is a knight.
Aiden cannot be a knight, because this would contradict the false claim of Jackson that Victoria is a knight if and only if Aiden is a knight.
Aiden cannot be a knave, because this would contradict the claim of Emily that Victoria is a knave or Aiden is a knight.
We have exhausted all possibilities for Aiden, so let us go back and reconsider Emily.
Assume Emily is a knave. No contradiction is found in their false claim that Victoria is a knave or Aiden is a knight.
Aiden cannot be a knight, because this would contradict the false claim of Jackson that Victoria is a knight if and only if Aiden is a knight.
Assume Aiden is a knave. No contradiction is found in their false claim that Matthew is not a knight.
Assume Matthew is a knight. No contradiction is found in their claim that If Jackson is a knight then Aiden is a knight.
Therefore, (1) Jackson is a knave
(2) Aiden is a knave
(3) Victoria is a knight
(4) Matthew is a knight
(5) Emily is a knave </think>
<answer> (1) Jackson is a knave
(2) Aiden is a knave
(3) Victoria is a knight
(4) Matthew is a knight
(5) Emily is a knave </answer>
Jackson Aiden Victoria Matthew Emily
(1) Jackson is a knave
(2) Aiden is a knave
(3) Victoria is a knight
(4) Matthew is a knight
(5) Emily is a knave
(('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('not', ('telling-truth', 3)), ('->', ('lying', 4), ('lying', 0)), ('->', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('lying', 2), ('telling-truth', 1)))
rule