Causal Analysis in Theory and Practice

From Jos Lehmann (University of Amsterdam):

Jos Lehmann noticed potential ambiguity in the notation used for counterfactual propositions. Capital letters, like "A" or "B," are sometimes used to denote propositional variables, and sometimes to denote propositions. For example, in the function A = C (Model M, page 209) "A" stands for the variable "whether rifleman-A shoots", and takes on values in {true, false}, while in statements S1-S5 (page 208), A stands for a proposition (e.g., "Fireman-A shot").

From Keith A. Markus, John Jay College of Criminal Justice, CUNY 

Can you provide a general method for solving for the parameters a, b, c, and d, to achieve the exact reversal of the alignment of physical and statistical time? In other words, what is the general principle behind the example on page 59 for selecting the alternative coordinate system that will have the intended effect?