nontruthvalued

Nontruthvalued is a term used in logic to describe systems in which truth values extend beyond the classical binary of true and false. In nontruthvalued logics, the evaluation of propositions can yield multiple, partly ordered, or even conflicting values. The designation “nontruthvalued” is not tied to a single formal system, but rather to a family of logics that depart from bivalence and classical truth-conditional semantics.

In these frameworks, truth values come from a set V and entailment is often defined with a subset of V known as designated values. Unlike classical logic, where true is the single designated value, nontruthvalued logics may include indeterminate, both true and false, or partially true values. This allows for nuanced reasoning about incomplete, inconsistent, or evolving information. Truth-functional variants define compound values directly from their components, while others rely on alternative semantic mechanisms such as paraconsistent or Kripke-style semantics.

Several well-known nontruthvalued systems illustrate the idea. Three-valued logics (for example, Kleene or Łukasiewicz) introduce an intermediate value between true and false. Four-valued logics (such as Belnap’s) separate information into values like true, false, both, and neither, supporting reasoning under inconsistency. Fuzzy and probabilistic logics further extend truth beyond a binary scale, though they differ in whether they are considered true-valued in a broad sense or measure degrees of truth.

Applications of nontruthvalued approaches appear in computer science, database theory, and artificial intelligence, where data may be incomplete, inconsistent, or uncertain. The term highlights the broader landscape of formal systems designed to model real-world information beyond simple true/false evaluations.