threevalue

Threevalue is a term used in logic and computer science to denote a framework or system that uses three truth values rather than the traditional two. The most common instantiation designates the values as true, false, and unknown (or indeterminate). Three-valued logics define the evaluation of logical connectives—such as and, or, and not—differently from classical two-valued logic, allowing reasoning with partial or incomplete information.

Several distinct three-valued logics have been proposed. Kleene's three-valued logic (K3) represents unknown as an intermediary value and emphasizes partial information; Lukasiewicz's three-valued logic (Ł3) uses a different truth-functional structure; Bochvar's logic introduces a meaningless value used to isolate ill-formed propositions. Some systems also consider a value that is both true and false, or other variants used in paraconsistent semantics.

In practical computing, three-valued logic appears in the handling of NULLs. SQL, for example, evaluates conditions with true, false, or unknown, which can affect the outcome of queries and constraints. Three-valued semantics are also used in type systems and data integration to model missing or uncertain data.

Historically, the study of tri-valued logics emerged in the early to mid-20th century, influencing philosophy of language, linguistics, and artificial intelligence. Today, threevalue is relevant in formal semantics, database theory, and programming language design, where it supports robust reasoning about incomplete information and error states.