# Definition:Language of Predicate Logic/Formal Grammar/Term

## Definition

Part of specifying the language of predicate logic $\LL_1$ is the introduction of terms.

The terms of $\LL_1$ are identified by the following bottom-up grammar:

 $(\mathbf T \ \textrm {VAR})$ $:$ Any variable of $\LL_1$ is a term; $(\mathbf T \ \FF_n)$ $:$ Given an $n$-ary function symbol $f \in \FF_n$ and terms $\tau_1, \ldots, \tau_n$: $\map f {\tau_1, \ldots, \tau_n}$ is also a term.

Colloquially, we can think of a term as an expression signifying an object.