 As an example for a valuation system based on more that two elements, consider two well-known valuation systems which determine Kleene’s (strong) “logic of indeterminacy” \(K_3\) and Priest’s “logic of paradox” \(P_3\). In a propositional language without implication, \(K_3\) is specified by the Kleene matrix \(\mathbf{K}_3 = \langle \{T, I, F\}, \{T\}, \{ f_c: c \in \{\sim , \wedge , \vee \}\} \rangle\), where the functions \(f_c\) are defined as follows: