C. I. Lewis intended his systems S1–S5 as contributions to the study of “strict implication”, but in his formulation, strict implication is so thoroughly intertwined with other notions, such as possibility and negation, that it remains a problem, to separate out the properties of strict implication itself. I shall solve this problem for S2–5 and von Wright's M. The results for S3–5 are given below, while the implicative parts of S2 and M, which are rather more complicated, are given in §5.
In this presentation, ‘⊃’ stands for strict implication, and missing brackets for ‘⊃’ are restored by association to the right. A strict formula is one of the form A ⊃ B. Axiom schemes are used throughout.
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