Exprimierbare

Exprimierbare is an adjective used in German to describe something that can be expressed or stated, typically within a given formal or symbolic framework. In mathematical, logical and computational contexts, exprimierbar refers to the existence of a finite expression that denotes or yields a particular object, value or property using a prescribed language or syntax.

Etymology and usage: the word derives from exprimieren (to express) with the suffix -bar, meaning “able to be.” In formal settings, exprimierbar indicates that a quantity, statement or concept can be captured by a finite string of symbols, operators and constants from a defined alphabet. The notion is closely related to, but distinct from, notions such as definierbar (definable) or darstellbar (representable).

Examples and contexts: in a fixed arithmetic language that includes symbols for 0, 1, addition, multiplication, and parentheses, every rational number has a finite expression and is exprimierbar. Many constants or objects beyond that language, such as pi or certain transcendental constructions, are not exprimierbar unless the language is extended with explicit constants or definitions. In logic and computer science, a property or function is exprimierbar in a given formal system if there exists a finite formula or program in that system that describes or computes it.

Relation to other concepts: exprimierbar is weaker than computability in the sense that a finite expression may exist without guaranteeing an efficient or practical method for evaluation. It is also distinguished from definierbar, where the emphasis is on a description that uniquely specifies an object within a model.

See also: definierbar, darstellbar, ausdruckbar, formale Sprachen, Berechenbarkeit.