View source for Term (logic)

In [[mathematical logic]], a '''term''' denotes a [[mathematical object]] and a [[Formula (mathematics)|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.

== Description ==

A first-order term is [[Recursive definition|recursively constructed]] from constant symbols, [[Recursive definition|variables]], and [[Uninterpreted logic|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)} {\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} {\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.

== See also ==

* [[Equation]]
* [[Expression (mathematics)]]
* [[Formula (mathematics)]]
* [[Free variables and bound variables]]
* [[Ground expression]]
* [[Mathematical logic]]
* [[Mathematical object]]
* [[Recursive definition]]
* [[Rewriting]]
* [[Uninterpreted logic]]
* [[Universal algebra]]

== External links ==

* [https://en.wikipedia.org/wiki/Term_(logic) Term (logic)] @ Wikipedia

[[Category:Logic]]