Strict/Tolerant Logics Built Using Generalized Weak Kleene Logics

Abstract

This paper continues my work of [9], which showed there was a broad family of many valued logics that have a strict/tolerant counterpart. Here we consider a generalization of weak Kleene three valued logic, instead of the strong version that was background for that earlier work. We explain the intuition behind that generalization, then determine a subclass of strict/tolerant structures in which a generalization of weak Kleene logic produces the same results that the strong Kleene generalization did. This paper provides much background, but is not self-contained. Some results from [9] are called on, and are not reproved here.

[9]  Melvin C. Fitting. “A Family of Strict/Tolerant Logics”. In: Journal of Philosophical Logic (2020). Online. Print publication forthcoming.