In
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...
, a metavariable (also metalinguistic variable or syntactical variable) is a
symbol
A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...
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 considers this terminology unfortunate because it obscures the use of
schema
The word schema comes from the Greek word ('), which means ''shape'', or more generally, ''plan''. The plural is ('). In English, both ''schemas'' and ''schemata'' are used as plural forms.
Schema may refer to:
Science and technology
* SCHEMA ...
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 computer science, terminal and nonterminal symbols are the lexical elements used in specifying the production rules constituting a formal grammar. ''Terminal symbols'' are the elementary symbols of the language defined by a formal grammar. ...
symbols in
formal grammars
In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) describes how to form strings from a language's alphabet that are valid according to the language's syntax. A grammar does not describe ...
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, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a founda ...
.
[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
''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, tutorial ...
2803. . pp. 484–497
See also
*
Explicit substitution In computer science, lambda calculus, lambda calculi are said to have explicit substitutions if they pay special attention to the formalization of the process of substitution of variables, substitution. This is in contrast to the standard lambda cal ...
Notes
References
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{{Mathematical logic
Logic symbols
Metalogic
Syntax (logic)
Variables (mathematics)