 An initial proposal, first developed in Halldén 1949 and Körner 1960 and revamped in Tye 1994, uses a three-valued logic. The motivation for such a logic is similar to the supervaluationist’s. Just as a vague predicate divides objects into the positive extension, negative extension and penumbra, vague sentences can be divided into the true, the false and the indeterminate. Unlike supervaluation semantics, however, the connectives are all defined truth-functionally. Though Halldén proposed Kleene’s weak three-valued tables, Kleene’s strong three-valued tables have dominated as the preferred choice. (For the relevant tables see Haack 1974: Appendix.) A recent variation on this theme is Field 2003, which supplements Kleene’s strong tables with an improved, non-truth-functional conditional and distinguishes the three-valued semantics from the common truth-value gap approach.