# Metavariable

In logic, a **metavariable** (also **metalinguistic variable**[1] or **syntactical variable**[2]) is a symbol or symbol string which belongs to a metalanguage 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 considers this terminology unfortunate because it obscures the use of schemata and because such "variables" do not actually range over a domain.[3]^{:220}

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 symbols in formal grammars where the nonterminals on the right of a production can be substituted by different instances.[4]

Attempts to formalize the notion of metavariable result in some kind of type theory.[5]

## See also

## Notes

- Hunter, p. 13.
- Shoenfield 2001, p. 7.
- Corcoran 2006, p. 220.
- Tennent 2002, pp. 36–37, 210.
- 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. 8th Kurt Gödel Colloquium, KGC 2003, Vienna, Austria, August 25-30, 2003. Proceedings*, Springer Lecture Notes in Computer Science 2803. ISBN 3-540-40801-0. pp. 484–497

## References

- Corcoran, J. (2006). "Schemata: the Concept of Schema in the History of Logic" (PDF).
*Bulletin of Symbolic Logic*.**12**: 219–240. - Hunter, Geoffrey.
*Metalogic: An Introduction to the Metatheory of Standard First-Order Logic*. - Shoenfield, Joseph R. (2001) [1967].
*Mathematical Logic*(2nd ed.). A K Peters. ISBN 978-1-56881-135-2. - Tennent, R. D. (2002).
*Specifying Software: A Hands-On Introduction*. Cambridge University Press. ISBN 978-0-521-00401-5.