threevalued

Threevalued refers to a family of non-classical logics that extends classical two-valued logic by introducing a third truth value in addition to true and false. The extra value is used to model aspects such as indeterminacy, partial information, or inconsistency, depending on the particular system. Threevalued logics are studied in logic, computer science, and philosophy as tools for handling uncertainty and incomplete data.

Several well-known systems illustrate the variety of approaches. Kleene's three-valued logics (often called K3) use the values true, false, and indeterminate. Łukasiewicz's three-valued logic (L3) employs a numeric scale, typically 0, 1/2, and 1, with arithmetic-style definitions for the logical connectives. Bochvar's internal three-valued logic introduces a special value that signals meaningless formulas, focusing on the propagation of this value through expressions. Paraconsistent logics, such as Priest's Logic of Paradox (LP), allow some degree of inconsistency without collapsing into triviality, and use their own conventions for handling the third value.

In these logics, the standard connectives—negation, conjunction, disjunction, and implication—are defined to cope with the third value in various ways. For example, negation may swap true and false while leaving the indeterminate value unchanged, and conjunction and disjunction are designed so that the third value propagates in a controlled manner. Implication is usually defined in terms of negation and disjunction or via its own special rule set, reflecting how partial information affects conditional statements.

Applications of threevalued logic include database theory (where nulls represent unknown data), formal models of incomplete or uncertain knowledge, and programming language semantics that need to reason about errors or incomplete computations. They provide a flexible framework for reasoning beyond the limits of classical logic.