mainly illustrates a system of ternary propositional logic using the truth values {false, unknown, true}, and extends conventional Boolean connectives to a trivalent context. Ternary predicate logics exist as well; these may have readings of the quantifier different from classical (binary) predicate logic and may include alternative quantifiers as well. Logics Boolean logic allows 22 = 4 unary operators, the addition of a third value in ternary logic leads to a total of 33 = 27 distinct operators on a single input value. (This may be made clear by considering all possible truth tables for an arbitrary unary operator. Given 2 possible values of the boolean (input) variable there are four different patterns of output (result of the unary operator operating on the variable): TT,TF,FT,FF. Whereas, given three possible values of a ternary variable, and three possible results of a unary operation, there are twenty seven different output patterns:TTT,TTU,TTF, TUT,TUU,TUF, TFT,TFU,TFF, UTT,UTU,UTF, UUT,UUU,UUF, UFT,UFU,UFF, FTT,FTU,FTF, FUT,FUU,FUF, FFT,FFU, and FFF.) Similarly, where Boolean logic has 22×2 = 16 distinct binary operators (operators with 2 inputs) possible, ternary logic has 33×3 = 19,683 such operators. Where we can easily name a significant fraction of the Boolean operators (NOT, AND, NAND, OR, NOR, XOR, XNOR, equivalence, implication), it is unreasonable to attempt to name all but a small fraction of the possible ternary operators. Kleene and Priest logics Below is a set of truth tables showing the logic operations for Stephen Cole Kleene's "strong logic of indeterminacy" and Graham Priest's "logic of paradox". In these truth tables, the unknown state can be thought of as neither true nor false in Kleene logic, or thought of as both true and false in Priest logic. The difference lies in the definition of tautologies. Where Kleene logic's only designated truth value is T, Priest logic's designated truth values are both T and U. In Kleene logic, the knowledge of whether any particular unknown state secretly represents true or false at any moment in time is not available. However, certain logical operations can yield an unambiguous result, even if they involve an unknown operand. For example, because true OR true equals true, and true OR false also equals true, one can infer that true OR unknown equals true, as well. In this example, because either bivalent state could be underlying the unknown state, but either state also yields the same result, a definitive true results in all