Valuedefined

Valuedefined is a theoretical term used in philosophy, logic, and computer science to describe a property of expressions or entities whose value is uniquely determined by a given definition or interpretation. In this sense, valuedefined emphasizes the outcome—the actual value—rather than the process by which it is arrived at.

It is related to, but distinct from, well-defined: while a well-defined expression yields consistent results across equivalent representations, valuedefined emphasizes that a single, specific value is assigned under the intended interpretation. The term is often used in theoretical discussions and pedagogical contexts to highlight stability of value in formal systems, including mathematical logic, programming language semantics, and formal semantics in linguistics.

Etymology and scope: valuedefined is a portmanteau of “value” and “defined.” It appears in niche scholarly discussions to differentiate the existence of a determinate value from broader notions of definability or computability. In practice, the use of valuedefined aims to make explicit when an interpretation assigns a precise value to an expression.

Formal notion: An expression E is valuedefined under interpretation I if there exists a unique v in the codomain such that I assigns E the value v; otherwise, E is not valuedefined. This can depend on whether the system provides total or partial definitions, and on the domain and rules of interpretation.

Examples: The expression 2+3 is valuedefined as 5 under standard arithmetic. A function g defined by g(x) = x^2 for x ≥ 0 is valuedefined on the nonnegative domain; g is not valuedefined on negative x if the definition omits those inputs. In programming, a constant literal such as true is valuedefined, while an undefined expression that raises an exception is not.

See also: well-defined, definability, determinacy, semantics, valuation, consistency.