Symbol (formal)

This article is about symbols in formal language theory. For other uses, see Symbol (disambiguation).
This diagram shows the syntactic entities that may be constructed from formal languages. The symbols and strings of symbols may be broadly divided into nonsense and well-formed formulas. A formal language can be thought of as identical to the set of its well-formed formulas. The set of well-formed formulas may be broadly divided into theorems and non-theorems.

A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern.[citation needed] Although the term "symbol" in common use refers at some times to the idea being symbolized, and at other times to the marks on a piece of paper or chalkboard which are being used to express that idea; in the formal languages studied in mathematics and logic, the term "symbol" refers to the idea, and the marks are considered to be a token instance of the symbol.[dubious – discuss] In logic, symbols build literal utility to illustrate ideas.