 There are natural intuitive interpretations of \(I\) in \(\mathbf{K}_3\) and in \(\mathbf{P}_3\) as the underdetermined and the overdetermined value respectively—a truth-value gap and a truth-value glut. Formally these interpretations can be modeled by presenting the values as certain subsets of the set of classical truth values \(\{T, F\}\). Then \(T\) turns into \(\mathbf{T} = \{T\}\) (understood as “true only”), \(F\) into \(\mathbf{F} = \{F\}\) (“false only”), \(I\) is interpreted in \(K_3\) as \(\mathbf{N} = \{\} = \varnothing\) (“neither true nor false”), and in \(P_3\) as \(\mathbf{B} = \{T, F\}\) (“both true and false”). (Note that also Asenjo (1966) considers the same truth-tables with an interpretation of the third value as “antinomic”.) The designatedness of a truth value can be understood in both cases as containment of the classical \(T\) as a member.