Symbol (formal)

[dubious – discuss] In logic, symbols build literal utility to illustrate ideas.

For instance there are logical constants which do not refer to any idea, but rather serve as a form of punctuation in the language (e.g. parentheses).

The set of formal symbols in a formal language is referred to as an alphabet (hence each symbol may be referred to as a "letter")[1][page needed] A formal symbol as used in first-order logic may be a variable (member from a universe of discourse), a constant, a function (mapping to another member of universe) or a predicate (mapping to T/F).

The move to view units in natural language (e.g. English) as formal symbols was initiated by Noam Chomsky (it was this work that resulted in the Chomsky hierarchy in formal languages).

The generative grammar model looked upon syntax as autonomous from semantics.

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.