metavariable
{{for|the term as used in computer science and programming|Metasyntactic variable}}
In logic, a metavariable (also metalinguistic variable{{sfn|Hunter|1996|page=13}} or syntactical variable){{harvnb|Shoenfield|2001|page=7}}. 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 considered this terminology unfortunate because it obscures the use of schemata and because such "variables" do not actually range over a domain.{{harvnb|Corcoran|2006|page=220}}.{{rp|220|date=November 2012}}
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.{{harvnb|Tennent|2002|pages=36–37, 210}}.
Attempts to formalize the notion of metavariable result in some kind of type theory.Masahiko Sato, Takafumi Sakurai, Yukiyoshi Kameyama, and Atsushi Igarashi. "[http://www.sato.kuis.kyoto-u.ac.jp/~masahiko/papers/csl-03.ps Calculi of Meta-variables]{{dead link|date=January 2018 |bot=InternetArchiveBot |fix-attempted=yes }}" 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
See also
Notes
{{Reflist}}
References
- {{cite journal |last1=Corcoran |first1=J. |author-link=John Corcoran (logician) |year=2006 |title=Schemata: the Concept of Schema in the History of Logic |journal=Bulletin of Symbolic Logic |volume=12 |issue=2 |pages=219–240 |doi=10.2178/bsl/1146620060 |s2cid=6909703 |url=https://philpapers.org/archive/CORSTC.pdf}}
- {{cite book
|last1=Hunter
|first1=Geoffrey
|author1-link=Geoffrey Hunter (logician)
|title=Metalogic: An Introduction to the Metatheory of Standard First-Order Logic
|orig-date=1971
|date=1996
|publication-date=1973
|publisher=University of California Press
|isbn=9780520023567
|oclc=36312727
|page=
|pages=
|section=
}} {{#switch: |yes=([https://archive.org/details/metalogicintrodu0000hunt accessible to patrons with print disabilities])|no=|#default=([https://archive.org/details/metalogicintrodu0000hunt accessible to patrons with print disabilities])}}
- {{Cite book | last1=Shoenfield | first1=Joseph R. | author1-link=Joseph R. Shoenfield | title=Mathematical Logic | orig-year=1967 | publisher=A K Peters | edition=2nd | isbn=978-1-56881-135-2 | year=2001}}
- {{cite book|last1=Tennent|first1=R. D.|title=Specifying Software: A Hands-On Introduction|year=2002|publisher=Cambridge University Press|isbn=978-0-521-00401-5}}
{{Mathematical logic}}