  The mathematician and logician Kleene used a third truth degree for “undefined” in the context of partial recursive functions. His connectives were the negation, the weak conjunction, and the weak disjunction of the 3-valued Łukasiewicz system together with a definable conjunction \(\wedge_{+}\) and a definable implication \(\rightarrow_{+}\) determined by truth degree functions with the following function tables (these latter have truth degree ½ iff one of their constituents has truth degree ½):