In
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
, a metavariable (also metalinguistic variable or syntactical variable) is a
symbol
A symbol is a mark, Sign (semiotics), sign, or word that indicates, signifies, or is understood as representing an idea, physical object, object, or wikt:relationship, relationship. Symbols allow people to go beyond what is known or seen by cr ...
or symbol string which belongs to a
metalanguage
In logic and linguistics, a metalanguage is a language used to describe another language, often called the ''object language''. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics, quota ...
and stands for elements of some object language. For instance, in the sentence
:''Let A and B be two sentences of a language ℒ''
the symbols A and B are part of the metalanguage in which the statement about the object language ℒ is formulated.
John Corcoran considered this terminology unfortunate because it obscures the use of
schema
Schema may refer to:
Science and technology
* SCHEMA (bioinformatics), an algorithm used in protein engineering
* Schema (genetic algorithms), a set of programs or bit strings that have some genotypic similarity
* Schema.org, a web markup vocab ...
ta and because such "variables" do not actually range over a domain.
The convention is that a metavariable is to be uniformly substituted with the same instance in all its appearances in a given schema. This is in contrast with
nonterminal
In formal languages, terminal and nonterminal symbols are parts of the ''vocabulary'' under a formal grammar. ''Vocabulary'' is a finite, nonempty set of symbols. ''Terminal symbols'' are symbols that cannot be replaced by other symbols of the v ...
symbols in
formal grammars
A formal grammar is a set of symbols and the production rules for rewriting some of them into every possible string of a formal language over an alphabet. A grammar does not describe the meaning of the strings — only their form.
In applied m ...
where the nonterminals on the right of a production can be substituted by different instances.
[.]
Attempts to formalize the notion of metavariable result in some kind of
type theory
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems.
Some type theories serve as alternatives to set theory as a foundation of ...
.
[Masahiko Sato, Takafumi Sakurai, Yukiyoshi Kameyama, and Atsushi Igarashi.]
Calculi of Meta-variables
in ''Computer Science Logic. 17th International Workshop CSL 2003. 12th Annual Conference of the EACSL
The European Association for Computer Science Logic (EACSL), founded 14 July 1992,
. Description of goals from EACSL official web ...
. 8th Kurt Gödel Colloquium, KGC 2003, Vienna, Austria, August 25-30, 2003. Proceedings'', Springer Lecture Notes in Computer Science
''Lecture Notes in Computer Science'' is a series of computer science books published by Springer Science+Business Media since 1973.
Overview
The series contains proceedings, post-proceedings, monographs, and Festschrifts. In addition, tutorials ...
2803. . pp. 484–497
See also
*
Explicit substitution
In computer science, lambda calculi are said to have explicit substitutions if they pay special attention to the formalization of the process of substitution. This is in contrast to the standard lambda calculus where substitutions are performed ...
Notes
References
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{{Mathematical logic
Logic symbols
Metalogic
Syntax (logic)
Variables (mathematics)