What does "$:[$" mean in $q_{(i,d,j)} ≜ P(S_{[t+1:t+d]}=j\;|S_{[t+1:[}=j)$?

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I am reading through some math on a paper, and I am trying to properly understand some of the proofs / equations. In particular, $$q_{(i,d,j)} ≜ P(S_{[t+1:t+d]}=j|S_{[t+1:[}=j)$$ is fairly confusing to me.

I know that the function q is being defined as that following block, and so on, but I am getting lost at what :[ means. Does anyone know where to point me? Google comes up with nothing on this notation, though I am aware that [] is used to typically denote arrays / sets.

Paper in question is here (formula on page 5)