terms

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, (x+1)*(x+1) is a term built from the constant 1, the variable x, and the binary function symbols + and *; it is part of the atomic formula (x+1)*(x+1) 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.