A Determination of all Possible Systems of Strict Implication

Abstract

It is known that the postulates chosen by C. I. Lewis for his "system of strict implication" are not categorical, since three distinct types of such a system have been shown to exist. I shall prove here that the three types already discovered are the only ones possible. The inclusion of an additional modal postulate. will therefore make the system categorical, and allow it to be exhibited as a four-valued truth-value system. The corresponding entscheidung problem may then be solved by the matrix method.

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