View source for Symbol (formal)

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]].

== Description ==

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.

Symbols of a [[formal language]] need not be symbols of anything. 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). Symbols of a formal language must be capable of being specified without any reference to any interpretation of them.

A symbol or string of symbols may comprise a well-formed formula if it is consistent with the formation rules of the language.

In a formal system a symbol may be used as a token in formal operations. 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").

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).

Formal symbols are usually thought of as purely syntactic structures, composed into larger structures using a formal grammar, though sometimes they may be associated with an interpretation or model (a formal semantics).

== See also ==

* [[Formal language]]
* [[List of mathematical symbols]]
* [[List of logic symbols]]
* [[Symbol]]

== External links ==

* [https://en.wikipedia.org/wiki/Symbol_(formal) Symbol (formal)] @ Wikipedia.org 

[[Category:Logic]]
[[Category:Symbols]]