Substitution (logic)

A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols with other expressions.

The resulting expression is called a substitution instance, or instance for short, of the original expression.

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Propositional logic[edit]

Definition[edit]

Where ψ and φ represent formulas of propositional logic, ψ is a substitution instance of φ if and only if ψ may be obtained from φ by substituting formulas for propositional variables in φ, replacing each occurrence of the same variable by an occurrence of the same formula. For example:

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Integration by substitution

Lambda calculus § Substitution

String interpolation

Substitution property of Equality

Trigonometric substitution

Universal instantiation

Crabbé, M. (2004). . Logic Journal of the IGPL, 12, 111–124.

On the Notion of Substitution

(1952) On the definition of substitution, replacement and allied notions in an abstract formal system. Revue philosophique de Louvain 50, 251–269.

Curry, H. B.

Hunter, G. (1971). Metalogic: An Introduction to the Metatheory of Standard First Order Logic. University of California Press. 0-520-01822-2

ISBN

(1967). Mathematical Logic. Reprinted 2002, Dover. ISBN 0-486-42533-9

Kleene, S. C.

at the nLab

Substitution

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