Counterfactual notation
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").
The use of capital letters for both variables and propositions is an effective abbreviation that might admittedly lead to some ambiguity. However, the ambiguity can be resolved (or minimized) through the following syntactic distinction: When A appears in an equation it denotes a name of a variable, and when it appears alone, or in a propositional formula (i.e., without the structural equality sign), it stands for the proposition "A is true". I believe that the benefits of abbreviating "A is true" with "A" outweighs the risks of potential ambiguity.
Best wishes,
========Judea Pearl
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