Herbrand structure

In first-order logic, a Herbrand structure ${\displaystyle S}$ is a structure over a vocabulary ${\displaystyle \sigma }$ (also sometimes called a signature) that is defined solely by the syntactical properties of ${\displaystyle \sigma }$. The idea is to take the symbol strings of terms as their values, e.g. the denotation of a constant symbol ${\displaystyle c}$ is just "${\displaystyle c}$" (the symbol). It is named after Jacques Herbrand.

Herbrand structures play an important role in the foundations of logic programming.