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RichardKennaway comments on Causal Diagrams and Causal Models - Less Wrong
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Your thesis deals only with acyclic causal graphs. What is the current state of the art for cyclic causal graphs? You'll know already that I've been looking at that, and I have various papers of other people that attempt to take steps in that direction, but my impression is that none of them actually get very far and there is nothing like a set of substantial results that one can point to. Even my own, were they in print yet, are primarily negative.
The recent stuff I have seen is negative results:
(a) Can't assign Pearlian semantics to cyclic graphs.
(b) If you assign equilibrium semantics, you might as well use a dynamic causal Bayesian network, a cyclic graph does not buy you anything.
(c) A graph representing the Markov property of the equilibrium distribution of a Markov chain represented by a causal DBN is an interesting open question. (This graph wouldn't have a causal interpretation of course).