User:Jshflynn/Definition:Linguistic structure

Definition

Let $\Sigma$ be an alphabet.

Let $V$ be a language over $\Sigma$ and $\circ$ denote concatenation.

$(V, \circ)$ is a linguistic structure iff:

$\forall \left({x, y}\right) \in V \times V: x \circ y \in V$.

That is, $V$ is closed under $\circ$.

Note

This term was invented. All linguistic structures are algebraic structures. Hence the name.