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
External links
- Symbol (formal) @ Wikipedia.org
