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]

• Explicit substitution

• Corcoran, J. (2006). "Schemata: the Concept of Schema in the History of Logic" (PDF). Bulletin of Symbolic Logic. 12 (2): 219–240. doi:10.2178/bsl/1146620060. S2CID 6909703.
• Hunter, Geoffrey (1996) [1971]. Metalogic: An Introduction to the Metatheory of Standard First-Order Logic. University of California Press (published 1973). ISBN 9780520023567. OCLC 36312727. (accessible to patrons with print disabilities)
• 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.