On all pure three-valued logics


 We investigate the class of all pure three-valued logics that result from choosing the eight subsets of $\{0, 1, \frac {1}{2}\}$ as designated values on the strong Kleene schema, including the sets that are not (order) filters. We present some of their main characteristics and show some formal relations between these logics. We also suggest a recipe to build philosophical interpretations for most of these logics and show why it is not easy to apply this account to the last two logics in the list.