Abstract
In lectures at Notre Dame University in 1948 I presented what was essentially a semantical analysis of the propositions formed from the elementary propositions of a formal system by compounding with propositional connectives and quantifiers. The system LD is one of the systems treated there in the chapter on negation. It is substantially the minimal calculus with excluded middle, and was first considered by Johansson. It corresponds semantically to the situation where we have refutability with completeness, and so it may be regarded as the natural system of strict implication. This paper gives the details of certain results concerning this system which have been reported elsewhere. Some related remarks concerning other systems will also be included. Acquaintance with the lectures cited is presupposed; they are referred to as TFD.
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