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 7 inhabitants: Zoey, Daniel, Luke, Logan, Owen, Emma, and Jackson. In a statement by Zoey: "Luke is a knave". In a statement by Daniel: "Daniel is a knight if and only if Owen is a knave". According to Luke, "Daniel is a knight or Luke is a knight". Logan noted, "Jackson is a knave or Daniel is a knave". As Owen put it, "Emma is a knight and Logan is a knight". Emma told you that If Logan is a knight then Jackson is a knave. According to Jackson, "Logan 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 Zoey is a knight.  No contradiction is found in their claim that Luke is a knave.
 Luke cannot be a knight, because this would contradict the claim of Zoey that Luke is a knave.
 Assume Luke is a knave.  No contradiction is found in their false claim that Daniel is a knight or Luke is a knight.
 Daniel cannot be a knight, because this would contradict the false claim of Luke that Daniel is a knight or Luke is a knight.
 Assume Daniel is a knave.  No contradiction is found in their false claim that Daniel is a knight if and only if Owen is a knave.
 Owen cannot be a knight, because this would contradict the false claim of Daniel that Daniel is a knight if and only if Owen is a knave.
 Assume Owen is a knave.  No contradiction is found in their false claim that Emma is a knight and Logan is a knight.
 Assume Emma is a knight.  No contradiction is found in their claim that If Logan is a knight then Jackson is a knave.
 Logan cannot be a knight, because this would contradict the false claim of Owen that Emma is a knight and Logan is a knight.
 Logan cannot be a knave, because this would contradict the false claim of their own that Jackson is a knave or Daniel is a knave.
 We have exhausted all possibilities for Logan, so let us go back and reconsider Emma.
 Assume Emma is a knave.  No contradiction is found in their false claim that If Logan is a knight then Jackson is a knave.
 Assume Logan is a knight.  No contradiction is found in their claim that Jackson is a knave or Daniel is a knave.
 Jackson cannot be a knight, because this would contradict the claim of their own that Logan is a knave.
 Jackson cannot be a knave, because this would contradict the false claim of Emma that If Logan is a knight then Jackson is a knave.
 We have exhausted all possibilities for Jackson, so let us go back and reconsider Logan.
 Logan cannot be a knave, because this would contradict the false claim of their own that Jackson is a knave or Daniel is a knave.
 We have exhausted all possibilities for Logan, Emma, Owen, Daniel, and Luke, so let us go back and reconsider Zoey.
 Assume Zoey is a knave.  No contradiction is found in their false claim that Luke is a knave.
 Assume Luke is a knight.  No contradiction is found in their claim that Daniel is a knight or Luke is a knight.
 Assume Daniel is a knight.  No contradiction is found in their claim that Daniel is a knight if and only if Owen is a knave.
 Owen cannot be a knight, because this would contradict the claim of Daniel that Daniel is a knight if and only if Owen is a knave.
 Assume Owen is a knave.  No contradiction is found in their false claim that Emma is a knight and Logan is a knight.
 Assume Emma is a knight.  No contradiction is found in their claim that If Logan is a knight then Jackson is a knave.
 Logan cannot be a knight, because this would contradict the false claim of Owen that Emma is a knight and Logan is a knight.
 Assume Logan is a knave.  No contradiction is found in their false claim that Jackson is a knave or Daniel is a knave.
 Assume Jackson is a knight.  No contradiction is found in their claim that Logan is a knave.
 Therefore, (1) Zoey is a knave
 (2) Daniel is a knight
 (3) Luke is a knight
 (4) Logan is a knave
 (5) Owen is a knave
 (6) Emma is a knight
 (7) Jackson 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 7 inhabitants: Zoey, Daniel, Luke, Logan, Owen, Emma, and Jackson. In a statement by Zoey: "Luke is a knave". In a statement by Daniel: "Daniel is a knight if and only if Owen is a knave". According to Luke, "Daniel is a knight or Luke is a knight". Logan noted, "Jackson is a knave or Daniel is a knave". As Owen put it, "Emma is a knight and Logan is a knight". Emma told you that If Logan is a knight then Jackson is a knave. According to Jackson, "Logan 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 Zoey is a knight. No contradiction is found in their claim that Luke is a knave.
Luke cannot be a knight, because this would contradict the claim of Zoey that Luke is a knave.
Assume Luke is a knave. No contradiction is found in their false claim that Daniel is a knight or Luke is a knight.
Daniel cannot be a knight, because this would contradict the false claim of Luke that Daniel is a knight or Luke is a knight.
Assume Daniel is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Owen is a knave.
Owen cannot be a knight, because this would contradict the false claim of Daniel that Daniel is a knight if and only if Owen is a knave.
Assume Owen is a knave. No contradiction is found in their false claim that Emma is a knight and Logan is a knight.
Assume Emma is a knight. No contradiction is found in their claim that If Logan is a knight then Jackson is a knave.
Logan cannot be a knight, because this would contradict the false claim of Owen that Emma is a knight and Logan is a knight.
Logan cannot be a knave, because this would contradict the false claim of their own that Jackson is a knave or Daniel is a knave.
We have exhausted all possibilities for Logan, so let us go back and reconsider Emma.
Assume Emma is a knave. No contradiction is found in their false claim that If Logan is a knight then Jackson is a knave.
Assume Logan is a knight. No contradiction is found in their claim that Jackson is a knave or Daniel is a knave.
Jackson cannot be a knight, because this would contradict the claim of their own that Logan is a knave.
Jackson cannot be a knave, because this would contradict the false claim of Emma that If Logan is a knight then Jackson is a knave.
We have exhausted all possibilities for Jackson, so let us go back and reconsider Logan.
Logan cannot be a knave, because this would contradict the false claim of their own that Jackson is a knave or Daniel is a knave.
We have exhausted all possibilities for Logan, Emma, Owen, Daniel, and Luke, so let us go back and reconsider Zoey.
Assume Zoey is a knave. No contradiction is found in their false claim that Luke is a knave.
Assume Luke is a knight. No contradiction is found in their claim that Daniel is a knight or Luke is a knight.
Assume Daniel is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Owen is a knave.
Owen cannot be a knight, because this would contradict the claim of Daniel that Daniel is a knight if and only if Owen is a knave.
Assume Owen is a knave. No contradiction is found in their false claim that Emma is a knight and Logan is a knight.
Assume Emma is a knight. No contradiction is found in their claim that If Logan is a knight then Jackson is a knave.
Logan cannot be a knight, because this would contradict the false claim of Owen that Emma is a knight and Logan is a knight.
Assume Logan is a knave. No contradiction is found in their false claim that Jackson is a knave or Daniel is a knave.
Assume Jackson is a knight. No contradiction is found in their claim that Logan is a knave.
Therefore, (1) Zoey is a knave
(2) Daniel is a knight
(3) Luke is a knight
(4) Logan is a knave
(5) Owen is a knave
(6) Emma is a knight
(7) Jackson is a knight </think>
<answer> (1) Zoey is a knave
(2) Daniel is a knight
(3) Luke is a knight
(4) Logan is a knave
(5) Owen is a knave
(6) Emma is a knight
(7) Jackson is a knight </answer>
Zoey Daniel Luke Logan Owen Emma Jackson
(1) Zoey is a knave
(2) Daniel is a knight
(3) Luke is a knight
(4) Logan is a knave
(5) Owen is a knave
(6) Emma is a knight
(7) Jackson is a knight
(('lying', 2), ('<=>', ('telling-truth', 1), ('lying', 4)), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('lying', 6), ('lying', 1)), ('and', ('telling-truth', 5), ('telling-truth', 3)), ('->', ('telling-truth', 3), ('lying', 6)), ('lying', 3))
rule