Difference between revisions of "Term (logic)"

Latest revision as of 11:22, 7 December 2016

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.

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 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)} {\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

• Term (logic) @ Wikipedia