Ternary

Three-valued logic based on Kleene’s strong logic of indeterminacy.

Truth values

• FALSE (-1)
• UNKNOWN (0)
• TRUE (1)

Truth tables

  NOT(A) - Logical negation
  +---+----+
  | A | ¬A |
  |---+----|
  | F |  T |
  | U |  U |
  | T |  F |
  +---+----+
  AND(A, B) - Logical conjunction. Minimum value of (A, B)
  +--------+-----------+
  |        |     B     |
  | A ∧ B  |---+---+---|
  |        | F | U | T |
  |----+---+---+---+---|
  |    | F | F | F | F |
  | A  | U | F | U | U |
  |    | T | F | U | T |
  +----+---+---+---+---+
  OR(A, B) - Logical disjunction. Maximum value of (A, B)
  +--------+-----------+
  |        |     B     |
  | A ∨ B  |---+---+---|
  |        | F | U | T |
  |----+---+---+---+---|
  |    | F | F | U | T |
  | A  | U | U | U | T |
  |    | T | T | T | T |
  +----+---+---+---+---+
  IMP(A, B) - Logical implication. OR(NOT(A), B)
  +--------+-----------+
  |        |     B     |
  | A → B  |---+---+---|
  |        | F | U | T |
  |----+---+---+---+---|
  |    | F | T | T | T |
  | A  | U | U | U | T |
  |    | T | F | U | T |
  +----+---+---+---+---+
  EQV(A, B) - Logical biconditional. OR(AND(A, B), AND(NOT(A), NOT(B)))
  +--------+-----------+
  |        |     B     |
  | A ↔ B  |---+---+---|
  |        | F | U | T |
  |----+---+---+---+---|
  |    | F | T | U | F |
  | A  | U | U | U | U |
  |    | T | F | U | T |
  +----+---+---+---+---+