undefinedness

Undefinedness refers to a state in which a value, reference, or truth value is not specified or not defined within a given system. It arises when something has no legitimate denotation, lies outside a domain, or cannot be determined from available information. The concept appears across fields such as mathematics, logic, computer science, linguistics, and philosophy, often to flag limits of a framework or to guide precise formulation.

In mathematics and logic, undefinedness commonly appears with partial functions and domain restrictions. For example, division by zero is undefined in the real numbers, and a function is undefined at points outside its domain. Some logical theories accommodate truth-value gaps or partial predicates, while others use extended frameworks to handle undefined terms explicitly.

In computer science, undefined behavior refers to program actions that are not specified by the language standard. Results of such behavior may vary between compilers or hardware, making behavior unpredictable. Languages may address undefinedness with exceptions, error codes, or option types to force explicit handling.

In linguistics and philosophy, undefinedness can occur when terms lack referents, such as empty or non-existent entities, or when reference fails (for instance, presupposition failure or non-existent objects). This can affect the meaningfulness of statements or the truth value of discourse.

Handling undefinedness typically involves clarifying domains, restricting terms, using total functions or explicit error signaling, or adopting logical systems that accommodate partiality or indeterminacy. See also undefined behavior, partial functions, and reference failure.