PC algorithm rule4

[kenneth-lee-ch]

Hi,

1. Why would the PC implemented in pc.py in the gCastle package strictly use rule 4 even without background knowledge?

  # rule4
                for i, j in permutations(ij, 2):
                    for kj in sep_set.keys():  # k and j are nonadjacent.
                        if j not in kj:
                            continue
                        else:
                            kj = list(kj)
                            kj.remove(j)
                            k = kj[0]
                            ls = [x for x in columns if x not in [i, j, k]]
                            for l in ls:
                                if cpdag[k, l] == 1 \
                                        and cpdag[l, k] == 0 \
                                        and cpdag[i, k] == 1 \
                                        and cpdag[k, i] == 1 \
                                        and cpdag[l, j] == 1 \
                                        and cpdag[j, l] == 0:
                                    cpdag[j, i] = 0

2. One more question, don't we need to have cpdag[l, i] == 1 and cpdag[i, l] ==1 in the if condition?