solution

model <- 
  make_model("S -> C -> Y <- R <- X; X -> C -> R") |>
  set_restrictions(labels = list(C = c('1110', '1111'), 
                                 R = c('0000', '0001'), 
                                 Y = '0001'),
                 keep = TRUE)

query <- "Y[X=1] > Y[X=0]"

model$parameters_df |> kable()

	param_names	node	gen	param_set	nodal_type	given	param_value	priors
1	S.0	S	1	S	0		0.5	1
2	S.1	S	1	S	1		0.5	1
3	X.0	X	2	X	0		0.5	1
4	X.1	X	2	X	1		0.5	1
12	C.1110	C	3	C	1110		0.5	1
20	C.1111	C	3	C	1111		0.5	1
21	R.0000	R	4	R	0000		0.5	1
29	R.0001	R	4	R	0001		0.5	1
45	Y.0001	Y	5	Y	0001		1.0	1

my_table <-
  model  |>
  grab(what = "ambiguities_matrix") |>
  data.frame() |>
  mutate(
    in_query = get_query_types(model, query)$types,
    priors   = CausalQueries:::get_type_prob(model)) 

my_table |> kable()

	S1X1C0R0Y0	S0X0C1R0Y0	S1X0C1R0Y0	S0X1C1R0Y0	S1X1C1R0Y0	S0X1C1R1Y1	S1X1C1R1Y1	in_query	priors
S0X0C1110R0000Y0001	0	1	0	0	0	0	0	FALSE	0.0625
S1X0C1110R0000Y0001	0	0	1	0	0	0	0	FALSE	0.0625
S0X1C1110R0000Y0001	0	0	0	1	0	0	0	FALSE	0.0625
S1X1C1110R0000Y0001	1	0	0	0	0	0	0	FALSE	0.0625
S0X0C1111R0000Y0001	0	1	0	0	0	0	0	FALSE	0.0625
S1X0C1111R0000Y0001	0	0	1	0	0	0	0	FALSE	0.0625
S0X1C1111R0000Y0001	0	0	0	1	0	0	0	FALSE	0.0625
S1X1C1111R0000Y0001	0	0	0	0	1	0	0	FALSE	0.0625
S0X0C1110R0001Y0001	0	1	0	0	0	0	0	TRUE	0.0625
S1X0C1110R0001Y0001	0	0	1	0	0	0	0	FALSE	0.0625
S0X1C1110R0001Y0001	0	0	0	0	0	1	0	TRUE	0.0625
S1X1C1110R0001Y0001	1	0	0	0	0	0	0	FALSE	0.0625
S0X0C1111R0001Y0001	0	1	0	0	0	0	0	TRUE	0.0625
S1X0C1111R0001Y0001	0	0	1	0	0	0	0	TRUE	0.0625
S0X1C1111R0001Y0001	0	0	0	0	0	1	0	TRUE	0.0625
S1X1C1111R0001Y0001	0	0	0	0	0	0	1	TRUE	0.0625

Examples of inferences

(using a helper funciton to display the subset of the data we care about)

An inference:

I observe \(S=0, Y=0\) only:

  data_consistent(my_table, seen = c("S0", "Y0"))

[1] "prob_DQ:" "0.125"   
[1] "prob_D:" "0.375"  
[1] "prob_Q|D:"         "0.333333333333333"
                    S0X0C1R0Y0 S0X1C1R0Y0 in_query priors
S0X0C1110R0000Y0001          1          0    FALSE 0.0625
S0X1C1110R0000Y0001          0          1    FALSE 0.0625
S0X0C1111R0000Y0001          1          0    FALSE 0.0625
S0X1C1111R0000Y0001          0          1    FALSE 0.0625
S0X0C1110R0001Y0001          1          0     TRUE 0.0625
S0X0C1111R0001Y0001          1          0     TRUE 0.0625

I observe \(S = 1, X = 1, C = 0\)

data_consistent(my_table, seen = c("S1", "X1", "C0"))

[1] "prob_DQ:" "0"       
[1] "prob_D:" "0.125"  
[1] "prob_Q|D:" "0"        
                    S1X1C0R0Y0 in_query priors
S1X1C1110R0000Y0001          1    FALSE 0.0625
S1X1C1110R0001Y0001          1    FALSE 0.0625