{"schema":"dms.institute.fel_lean_english.v1","ok":true,"closed":24,"supported":1,"open":2,"failed":0,"obligations":[{"id":"object.1.prim","kind":"defeq","statement":"object.1 is primitive","status":"closed","lean":"axiom object.1 : Primitive"},{"id":"relation.1.prim","kind":"defeq","statement":"relation.1 is primitive","status":"closed","lean":"axiom relation.1 : Primitive"},{"id":"change.1.prim","kind":"defeq","statement":"change.1 is primitive","status":"closed","lean":"axiom change.1 : Primitive"},{"id":"information.1.prim","kind":"defeq","statement":"information.1 is primitive","status":"closed","lean":"axiom information.1 : Primitive"},{"id":"system.1.defeq","kind":"defeq","statement":"system.1 ≡ a set of objects and the relations among them","status":"closed","lean":"theorem system_1_def : system.1 ≡ a set of objects and the relations among them := by\n  unfold system.1\n  rfl\n-- kernel closed"},{"id":"state.1.defeq","kind":"defeq","statement":"state.1 ≡ condition of a system at a specified time","status":"closed","lean":"theorem state_1_def : state.1 ≡ condition of a system at a specified time := by\n  unfold state.1\n  rfl\n-- kernel closed"},{"id":"state.2.defeq","kind":"defeq","statement":"state.2 ≡ political organization governing a territory","status":"closed","lean":"theorem state_2_def : state.2 ≡ political organization governing a territory := by\n  unfold state.2\n  rfl\n-- kernel closed"},{"id":"state.3.defeq","kind":"defeq","statement":"state.3 ≡ to explicitly express information","status":"closed","lean":"theorem state_3_def : state.3 ≡ to explicitly express information := by\n  unfold state.3\n  rfl\n-- kernel closed"},{"id":"signal.1.defeq","kind":"defeq","statement":"signal.1 ≡ information that a system can detect as a change","status":"closed","lean":"theorem signal_1_def : signal.1 ≡ information that a system can detect as a change := by\n  unfold signal.1\n  rfl\n-- kernel closed"},{"id":"cause.1.defeq","kind":"defeq","statement":"cause.1 ≡ a change in one system that produces a change in another system","status":"closed","lean":"theorem cause_1_def : cause.1 ≡ a change in one system that produces a change in another system := by\n  unfold cause.1\n  rfl\n-- kernel closed"},{"id":"causal_relation.1.defeq","kind":"defeq","statement":"causal_relation.1 ≡ relation in which a change in one system produces a change in another system","status":"closed","lean":"theorem causal_relation_1_def : causal_relation.1 ≡ relation in which a change in one system produces a change in another system := by\n  unfold causal_relation.1\n  rfl\n-- kernel closed"},{"id":"identify.1.defeq","kind":"defeq","statement":"identify.1 ≡ to distinguish a relation from alternatives using information","status":"closed","lean":"theorem identify_1_def : identify.1 ≡ to distinguish a relation from alternatives using information := by\n  unfold identify.1\n  rfl\n-- kernel closed"},{"id":"agent.1.defeq","kind":"defeq","statement":"agent.1 ≡ a system that produces change","status":"closed","lean":"theorem agent_1_def : agent.1 ≡ a system that produces change := by\n  unfold agent.1\n  rfl\n-- kernel closed"},{"id":"goal.1.defeq","kind":"defeq","statement":"goal.1 ≡ a specified state of a system","status":"closed","lean":"theorem goal_1_def : goal.1 ≡ a specified state of a system := by\n  unfold goal.1\n  rfl\n-- kernel closed"},{"id":"action.1.defeq","kind":"defeq","statement":"action.1 ≡ a change an agent produces in a system","status":"closed","lean":"theorem action_1_def : action.1 ≡ a change an agent produces in a system := by\n  unfold action.1\n  rfl\n-- kernel closed"},{"id":"communication.1.defeq","kind":"defeq","statement":"communication.1 ≡ an action that produces a signal for another agent","status":"closed","lean":"theorem communication_1_def : communication.1 ≡ an action that produces a signal for another agent := by\n  unfold communication.1\n  rfl\n-- kernel closed"},{"id":"prediction.1.defeq","kind":"defeq","statement":"prediction.1 ≡ identifying a future state from a causal relation","status":"closed","lean":"theorem prediction_1_def : prediction.1 ≡ identifying a future state from a causal relation := by\n  unfold prediction.1\n  rfl\n-- kernel closed"},{"id":"learning.1.defeq","kind":"defeq","statement":"learning.1 ≡ identifying causal relations","status":"closed","lean":"theorem learning_1_def : learning.1 ≡ identifying causal relations := by\n  unfold learning.1\n  rfl\n-- kernel closed"},{"id":"learning.1.test","kind":"instance","statement":"\"Observing an unexplained correlation alone\" not instanceof learning.1","status":"supported","lean":"theorem learning_1_test : \"Observing an unexplained correlation alone\" not instanceof learning.1 := by\n  instance","note":"case does not contain causal_relation.1, identify.1"},{"id":"learning.1.test","kind":"instance","statement":"\"Identifying that pressing a switch causes a light to turn on\" instanceof learning.1","status":"open","lean":"theorem learning_1_test : \"Identifying that pressing a switch causes a light to turn on\" instanceof learning.1 := by\n  instance","note":"missing causal_relation.1"},{"id":"learning.1.test","kind":"instance","statement":"\"Memorizing a random sequence without identifying any causal relation\" not instanceof learning.1","status":"open","lean":"theorem learning_1_test : \"Memorizing a random sequence without identifying any causal relation\" not instanceof learning.1 := by\n  instance","note":"the case mentions the definitional dependencies and also a negation; the kernel does not interpret English negation"},{"id":"problem.1.defeq","kind":"defeq","statement":"problem.1 ≡ a difference between a current state and a goal","status":"closed","lean":"theorem problem_1_def : problem.1 ≡ a difference between a current state and a goal := by\n  unfold problem.1\n  rfl\n-- kernel closed"},{"id":"problem_solving.1.defeq","kind":"defeq","statement":"problem_solving.1 ≡ an action that changes a current state toward a goal","status":"closed","lean":"theorem problem_solving_1_def : problem_solving.1 ≡ an action that changes a current state toward a goal := by\n  unfold problem_solving.1\n  rfl\n-- kernel closed"},{"id":"knowledge.1.defeq","kind":"defeq","statement":"knowledge.1 ≡ identified causal relations that remain available for prediction","status":"closed","lean":"theorem knowledge_1_def : knowledge.1 ≡ identified causal relations that remain available for prediction := by\n  unfold knowledge.1\n  rfl\n-- kernel closed"},{"id":"intelligence.1.defeq","kind":"defeq","statement":"intelligence.1 ≡ the capacity of an agent for learning and problem solving","status":"closed","lean":"theorem intelligence_1_def : intelligence.1 ≡ the capacity of an agent for learning and problem solving := by\n  unfold intelligence.1\n  rfl\n-- kernel closed"},{"id":"reasoning.1.defeq","kind":"defeq","statement":"reasoning.1 ≡ identifying consequences of relations and states","status":"closed","lean":"theorem reasoning_1_def : reasoning.1 ≡ identifying consequences of relations and states := by\n  unfold reasoning.1\n  rfl\n-- kernel closed"},{"id":"creativity.1.defeq","kind":"defeq","statement":"creativity.1 ≡ identifying a relation that was not previously identified","status":"closed","lean":"theorem creativity_1_def : creativity.1 ≡ identifying a relation that was not previously identified := by\n  unfold creativity.1\n  rfl\n-- kernel closed"}],"lean":"-- FEL Lean-English. Not Lean 4. The kernel checks unfolding; it does not run lean.\nnamespace FEL\n\naxiom object.1 : Primitive\naxiom relation.1 : Primitive\naxiom change.1 : Primitive\naxiom information.1 : Primitive\ntheorem system_1_def : system.1 ≡ a set of objects and the relations among them := by\n  unfold system.1\n  rfl\n-- kernel closed\ntheorem state_1_def : state.1 ≡ condition of a system at a specified time := by\n  unfold state.1\n  rfl\n-- kernel closed\ntheorem state_2_def : state.2 ≡ political organization governing a territory := by\n  unfold state.2\n  rfl\n-- kernel closed\ntheorem state_3_def : state.3 ≡ to explicitly express information := by\n  unfold state.3\n  rfl\n-- kernel closed\ntheorem signal_1_def : signal.1 ≡ information that a system can detect as a change := by\n  unfold signal.1\n  rfl\n-- kernel closed\ntheorem cause_1_def : cause.1 ≡ a change in one system that produces a change in another system := by\n  unfold cause.1\n  rfl\n-- kernel closed\ntheorem causal_relation_1_def : causal_relation.1 ≡ relation in which a change in one system produces a change in another system := by\n  unfold causal_relation.1\n  rfl\n-- kernel closed\ntheorem identify_1_def : identify.1 ≡ to distinguish a relation from alternatives using information := by\n  unfold identify.1\n  rfl\n-- kernel closed\ntheorem agent_1_def : agent.1 ≡ a system that produces change := by\n  unfold agent.1\n  rfl\n-- kernel closed\ntheorem goal_1_def : goal.1 ≡ a specified state of a system := by\n  unfold goal.1\n  rfl\n-- kernel closed\ntheorem action_1_def : action.1 ≡ a change an agent produces in a system := by\n  unfold action.1\n  rfl\n-- kernel closed\ntheorem communication_1_def : communication.1 ≡ an action that produces a signal for another agent := by\n  unfold communication.1\n  rfl\n-- kernel closed\ntheorem prediction_1_def : prediction.1 ≡ identifying a future state from a causal relation := by\n  unfold prediction.1\n  rfl\n-- kernel closed\ntheorem learning_1_def : learning.1 ≡ identifying causal relations := by\n  unfold learning.1\n  rfl\n-- kernel closed\ntheorem learning_1_test : \"Observing an unexplained correlation alone\" not instanceof learning.1 := by\n  instance\ntheorem learning_1_test : \"Identifying that pressing a switch causes a light to turn on\" instanceof learning.1 := by\n  instance\ntheorem learning_1_test : \"Memorizing a random sequence without identifying any causal relation\" not instanceof learning.1 := by\n  instance\ntheorem problem_1_def : problem.1 ≡ a difference between a current state and a goal := by\n  unfold problem.1\n  rfl\n-- kernel closed\ntheorem problem_solving_1_def : problem_solving.1 ≡ an action that changes a current state toward a goal := by\n  unfold problem_solving.1\n  rfl\n-- kernel closed\ntheorem knowledge_1_def : knowledge.1 ≡ identified causal relations that remain available for prediction := by\n  unfold knowledge.1\n  rfl\n-- kernel closed\ntheorem intelligence_1_def : intelligence.1 ≡ the capacity of an agent for learning and problem solving := by\n  unfold intelligence.1\n  rfl\n-- kernel closed\ntheorem reasoning_1_def : reasoning.1 ≡ identifying consequences of relations and states := by\n  unfold reasoning.1\n  rfl\n-- kernel closed\ntheorem creativity_1_def : creativity.1 ≡ identifying a relation that was not previously identified := by\n  unfold creativity.1\n  rfl\n-- kernel closed\n\nend FEL\n","physical_validation":false,"lean4":false,"note":"The LLM proposes. This kernel checks definitional unfolding. sorry does not close. Instance tests are syntactic support. English negation is not in the kernel."}