In addition to classic two-valued logic, there are *many* many-valued logics, including Łukasiewicz's and Kleene's three-valued logics, Gödel's many-valued logic $G\_k$, and infinite-valued fuzzy logic and probability logic.


I wonder: Was ever the case that some kind of "0-valued" and "1-valued" logics came up in a natural way in a certain context?



0-valued and 1-valued logics?
There is an article by C. L. Hamblin titled *One-valued Logic,* The Philosophical Quarterly, 66 (1967), 38-45, that you may find interesting.


