Three-valued Logic - Representation of Values

Representation of Values

As with bivalent logic, truth values in ternary logic may be represented numerically using various representations of the ternary numeral system. A few of the more common examples are:

• 1 for true, 2 for false, and 0 for unknown, unknowable/undecidable, irrelevant, or both.
• 0 for false, 1 for true, and a third non-integer symbol such as # or ½ for the final value, also known as "maybe".
• Balanced ternary uses −1 for false, +1 for true and 0 for the third value; these values may also be simplified to −, +, and 0, respectively.

This article mainly illustrates a system of ternary propositional logic using the truth values {false, unknown, and 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.