premise
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| hypothesis
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Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
D directly affects E.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=4__node_j=5__causal_relation=parent__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
D influences E through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=4__node_j=5__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E directly affects D.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=4__node_j=5__causal_relation=child__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E influences D through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=4__node_j=5__causal_relation=non-child_descendant__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
D and E together cause some other variable(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=4__node_j=5__causal_relation=has_collider__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both D and E.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=4__node_j=5__causal_relation=has_confounder__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
D directly affects F.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=4__node_j=6__causal_relation=parent__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
D influences F through some mediator(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=4__node_j=6__causal_relation=non-parent_ancestor__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F directly affects D.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=4__node_j=6__causal_relation=child__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F influences D through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=4__node_j=6__causal_relation=non-child_descendant__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
D and F together cause some other variable(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=4__node_j=6__causal_relation=has_collider__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both D and F.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=4__node_j=6__causal_relation=has_confounder__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E directly affects A.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=1__causal_relation=parent__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E influences A through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=1__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
A directly affects E.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=1__causal_relation=child__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
A influences E through some mediator(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=1__causal_relation=non-child_descendant__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E and A together cause some other variable(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=1__causal_relation=has_collider__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both E and A.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=1__causal_relation=has_confounder__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E directly affects B.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=2__causal_relation=parent__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E influences B through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=2__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
B directly affects E.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=2__causal_relation=child__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
B influences E through some mediator(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=2__causal_relation=non-child_descendant__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E and B together cause some other variable(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=2__causal_relation=has_collider__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both E and B.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=2__causal_relation=has_confounder__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E directly affects C.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=3__causal_relation=parent__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E influences C through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=3__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
C directly affects E.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=3__causal_relation=child__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
C influences E through some mediator(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=3__causal_relation=non-child_descendant__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E and C together cause some other variable(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=3__causal_relation=has_collider__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both E and C.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=3__causal_relation=has_confounder__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E directly affects D.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=4__causal_relation=parent__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E influences D through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=4__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
D directly affects E.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=4__causal_relation=child__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
D influences E through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=4__causal_relation=non-child_descendant__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E and D together cause some other variable(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=4__causal_relation=has_collider__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both E and D.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=4__causal_relation=has_confounder__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E directly affects F.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=6__causal_relation=parent__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E influences F through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=6__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F directly affects E.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=6__causal_relation=child__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F influences E through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=6__causal_relation=non-child_descendant__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E and F together cause some other variable(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=5__node_j=6__causal_relation=has_collider__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both E and F.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=5__node_j=6__causal_relation=has_confounder__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F directly affects A.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=1__causal_relation=parent__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F influences A through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=1__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
A directly affects F.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=1__causal_relation=child__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
A influences F through some mediator(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=1__causal_relation=non-child_descendant__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F and A together cause some other variable(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=1__causal_relation=has_collider__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both F and A.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=1__causal_relation=has_confounder__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F directly affects B.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=2__causal_relation=parent__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F influences B through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=2__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
B directly affects F.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=2__causal_relation=child__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
B influences F through some mediator(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=2__causal_relation=non-child_descendant__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F and B together cause some other variable(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=2__causal_relation=has_collider__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both F and B.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=2__causal_relation=has_confounder__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F directly affects C.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=3__causal_relation=parent__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F influences C through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=3__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
C directly affects F.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=3__causal_relation=child__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
C influences F through some mediator(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=3__causal_relation=non-child_descendant__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F and C together cause some other variable(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=3__causal_relation=has_collider__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both F and C.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=3__causal_relation=has_confounder__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F directly affects D.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=4__causal_relation=parent__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F influences D through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=4__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
D directly affects F.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=4__causal_relation=child__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
D influences F through some mediator(s).
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=4__causal_relation=non-child_descendant__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F and D together cause some other variable(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=4__causal_relation=has_collider__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both F and D.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=4__causal_relation=has_confounder__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F directly affects E.
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=5__causal_relation=parent__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F influences E through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=5__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E directly affects F.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=5__causal_relation=child__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
E influences F through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=5__causal_relation=non-child_descendant__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
F and E together cause some other variable(s).
|
contradiction
|
num_nodes=6__mec_id=2180__node_i=6__node_j=5__causal_relation=has_collider__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with C. A correlates with D. A correlates with E. A correlates with F. B correlates with C. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of B. A and E are independent given B, C and D. B and D are independent given A and C. B and F are independent given A, C, D and E.
|
Some variable(s) cause(s) both F and E.
|
entailment
|
num_nodes=6__mec_id=2180__node_i=6__node_j=5__causal_relation=has_confounder__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A directly affects B.
|
neutral
|
num_nodes=6__mec_id=2051__node_i=1__node_j=2__causal_relation=parent__prob=0.50
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A influences B through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=2__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
B directly affects A.
|
neutral
|
num_nodes=6__mec_id=2051__node_i=1__node_j=2__causal_relation=child__prob=0.50
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
B influences A through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=2__causal_relation=non-child_descendant__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A and B together cause some other variable(s).
|
entailment
|
num_nodes=6__mec_id=2051__node_i=1__node_j=2__causal_relation=has_collider__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
Some variable(s) cause(s) both A and B.
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=2__causal_relation=has_confounder__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A directly affects C.
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=3__causal_relation=parent__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A influences C through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=3__causal_relation=non-parent_ancestor__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
C directly affects A.
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=3__causal_relation=child__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
C influences A through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=3__causal_relation=non-child_descendant__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A and C together cause some other variable(s).
|
entailment
|
num_nodes=6__mec_id=2051__node_i=1__node_j=3__causal_relation=has_collider__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
Some variable(s) cause(s) both A and C.
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=3__causal_relation=has_confounder__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A directly affects D.
|
entailment
|
num_nodes=6__mec_id=2051__node_i=1__node_j=4__causal_relation=parent__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A influences D through some mediator(s).
|
neutral
|
num_nodes=6__mec_id=2051__node_i=1__node_j=4__causal_relation=non-parent_ancestor__prob=0.50
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
D directly affects A.
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=4__causal_relation=child__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
D influences A through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=4__causal_relation=non-child_descendant__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A and D together cause some other variable(s).
|
entailment
|
num_nodes=6__mec_id=2051__node_i=1__node_j=4__causal_relation=has_collider__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
Some variable(s) cause(s) both A and D.
|
neutral
|
num_nodes=6__mec_id=2051__node_i=1__node_j=4__causal_relation=has_confounder__prob=0.50
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A directly affects E.
|
entailment
|
num_nodes=6__mec_id=2051__node_i=1__node_j=5__causal_relation=parent__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A influences E through some mediator(s).
|
entailment
|
num_nodes=6__mec_id=2051__node_i=1__node_j=5__causal_relation=non-parent_ancestor__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
E directly affects A.
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=5__causal_relation=child__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
E influences A through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=5__causal_relation=non-child_descendant__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A and E together cause some other variable(s).
|
entailment
|
num_nodes=6__mec_id=2051__node_i=1__node_j=5__causal_relation=has_collider__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
Some variable(s) cause(s) both A and E.
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=5__causal_relation=has_confounder__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A directly affects F.
|
entailment
|
num_nodes=6__mec_id=2051__node_i=1__node_j=6__causal_relation=parent__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
A influences F through some mediator(s).
|
entailment
|
num_nodes=6__mec_id=2051__node_i=1__node_j=6__causal_relation=non-parent_ancestor__prob=1.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
F directly affects A.
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=6__causal_relation=child__prob=0.00
|
Suppose there is a closed system of 6 variables, A, B, C, D, E and F. All the statistical relations among these 6 variables are as follows: A correlates with B. A correlates with D. A correlates with E. A correlates with F. B correlates with D. B correlates with E. B correlates with F. C correlates with D. C correlates with E. C correlates with F. D correlates with E. D correlates with F. E correlates with F. However, A is independent of C. A and C are independent given B. B is independent of C. B and C are independent given A. B and E are independent given A, C and D. C and F are independent given A, B, D and E.
|
F influences A through some mediator(s).
|
contradiction
|
num_nodes=6__mec_id=2051__node_i=1__node_j=6__causal_relation=non-child_descendant__prob=0.00
|
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