Truthvalue

Truthvalue is a value assigned to a statement or proposition indicating its truth status within a logical or semantic system. In classical (bivalent) logic, there are two truth values: true and false. A statement is true if it corresponds to the way the world actually is under a given interpretation, and false otherwise. In propositional and predicate logic, the truth value of composite sentences is determined by the truth values of their components through logical connectives, a relation often captured in truth tables.

Formal semantics uses truth conditions to define when a sentence is true in a model. In standard semantics, a sentence is true in a given model if its atomic parts are assigned truth values that satisfy the interpretation of the connectives. Truth values thus underpin the evaluation of logical consequence and model satisfaction.

Beyond bivalence, many-valued logics allow more than two truth values, such as indeterminate, both true and false, or neither. This accommodates partial information, vagueness, or inconsistencies. Notable systems include Kleene's three-valued logic and Priest's dialetheic logics, which permit true and false to coexist.

In computer science, truth values are typically represented as booleans, with true and false used for control flow and decision-making. Some languages also incorporate truthiness or falsiness notions, where values can be treated as true or false in a wider context.

Historically, the notion of truth values relates to the development of formal semantics and truth definitions, including Tarski-style truth conditions, which link linguistic truth to models and interpretations.