trevärdessystem

A trevärdessystem, or three-valued logic system, is a logical system that extends classical two-valued logic (true and false) by introducing a third truth value. This third value can represent various concepts depending on the specific system, but commonly it signifies uncertainty, irrelevance, or undefinedness.

The most well-known example of a three-valued logic is Kleene's three-valued logic, often denoted as K3. In K3, the truth values are typically represented as True (T), False (F), and Unknown (U). The logical connectives, such as AND, OR, and NOT, are then redefined to accommodate this third value. For instance, in Kleene's AND, if either operand is F, the result is F. If either operand is T, the result is T. If one is T and the other is U, the result is U. Similarly, for OR, if either operand is T, the result is T. If either operand is F, the result is F. If one is F and the other is U, the result is U. The negation of U is U.

Three-valued logic systems have found applications in various fields, including computer science, artificial intelligence, and philosophy. In databases, they can be used to handle missing or inconsistent data. In AI, they can represent states of knowledge that are not definitively known. Philosophical discussions on modality and vagueness also sometimes employ three-valued logics. The development of such systems allows for a more nuanced representation of truth and reasoning than traditional binary logic.