Term (logic)

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

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.

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