Independence of the primitive symbols of Lewis's calculi of propositions
M. J. Alban · Journal of Symbolic Logic · 1943
In this paper it will be shown that the three primitive symbols used by Lewis are independent in each one of his systems S1–S6. Lemma I. “·” is not definable in terms of “∼” and “◊” in any one of the systems S1–S6. Proof. This is obvious, since no binary operation can be defined by unary operations alone. Lemma II. “∼” is not definable in terms of “˙” and “◊” in any one of the systems S1–S5.