Term (logic)

In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact.

A first-order term is recursively constructed from constant symbols, variables and function symbols. An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation. For example, ⁠${\displaystyle (x+1)*(x+1)}$⁠ is a term built from the constant 1, the variable x, and the binary function symbols ⁠${\displaystyle +}$⁠ and ⁠${\displaystyle *}$⁠; it is part of the atomic formula ⁠${\displaystyle (x+1)*(x+1)\geq 0}$⁠ which evaluates to true for each real-numbered value of x.

Besides in logic, terms play important roles in universal algebra, and rewriting systems.