In  and  D. Lewis formulates his counterfactual logic VC as follows. The language contains the connectives ∧, ∨, ⊃, ¬ and the binary connective ≤. A ≤ B is read as “A is at least as possible as B”. The following connectives are defined in terms of ≤.
A < B: = ¬(B ≤ A) (it is more possible that A than that B).
◊ A ≔ ¬(⊥ ≤ A) (⊥ is the false formula; A is possible).
□ A ≔ ⊥ ≤ ¬A (A is necessary).
(if A were the case, then B would be the case).
(if A were the case, then B might be the case).
and are two counterfactual conditional operators. (AB) iff ¬(A ¬B).
The following axiom system VC is presented by D. Lewis in  and : V: (1) Truthfunctional classical propositional calculus.
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