Term (logic)
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
