fivevalued

Five-valued refers to a class of logical frameworks that use five distinct truth values to evaluate propositions, extending the two-valued (true/false) basis of classical logic. In such logics, the additional values provide finer granularity for representing uncertainty, inconsistency, or partial information. The exact interpretation of the five values varies among systems. Common design choices include values representing true, false, both true and false (an explicit contradiction), neither true nor false (undetermined), and a fifth value used for special status such as indeterminacy, failure, or error. Logical connectives like and, or, not, and implies are defined to operate over this five-valued domain, often with orderings that reflect information content or truth preservation.

Five-valued logics are studied within philosophy of logic and theoretical computer science as part of the broader field of many-valued logics. They are related to paraconsistent logics, which avoid explosion from contradictions, and to logics of partial information used in databases and knowledge representation. In digital circuit design, five-valued logics can model signals with statuses beyond simply high and low, such as unknown or faulty conditions, enabling more robust fault detection and testing.

There is no single canonical five-valued system; references to "five-valued logic" typically denote a family of logics with varying truth-value assignments and algebraic semantics.

See also: multi-valued logic, paraconsistent logic, fuzzy logic.