substitution instance
English
[edit]Noun
[edit]substitution instance (plural substitution instances)
- (logic) A well-formed formula (wff) that has a constant term in place of a variable; expressed as Q(a/x), where the resulting wff is identical to Q except that the constant a takes the place of every free occurrence of the variable x.
- 1972, Alonzo Church, Introduction to Mathematical Logic, Princeton University Press, page 78:
- The result of substituting a term a for all free occurrences of the variable x in the formula Q is denoted by Q(a/x).
Usage notes
[edit]Substitution instances are fundamental to the rules of universal instantiation and existential generalization. The notation Q(a/x) is read as "Q with a substituted for x." The term a must be free for x in Q, meaning that no free variable in a becomes bound by a quantifier in Q after substitution. e.g. If Q is the wff P(x) → ∃y R(x,y), then Q(c/x) is P(c) → ∃y R(c,y).