truevalued

Truevalued is a term used in logic and semantics to denote a proposition, formula, or statement that evaluates to the designated truth value true under a given interpretation or model. The term is sometimes written as true-valued, but some texts and resources employ the compound form truevalued.

In classical propositional logic, where truth values are typically limited to true and false, a sentence is true-valued when its evaluation under a valuation is the value true. In many-valued logics, which include more than two truth values (for example true, false, and undefined), true-valued formulas are those whose evaluation equals the designated true value, as opposed to false-valued ones or other categories found in paraconsistent or dialethic systems.

The concept helps analyze how logical connectives and semantic rules assign truth values across different logics. It is used to distinguish statements that reliably hold true in a model from those that do not or that yield indeterminate or conflicting results.

Applications of the idea appear in areas such as formal verification, model checking, and truth-conditional semantics, where labeling a statement as true-valued indicates it satisfies the conditions of truth within the specified framework. In knowledge representation and database theory, true-valued assessments can describe statements that are true under a given interpretation or dataset.

See also: truth value; truth-functional logic; many-valued logic; paraconsistent logic; model checking.