Substitution assignment (FOL)

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Definition

Given an assignment, [ilmath]\sigma:V\rightarrow M[/ilmath] we can define a new assignment that assigns the variable [ilmath]x_i\in V[/ilmath] the value value [ilmath]a\in M[/ilmath] but is otherwise identical to [ilmath]\sigma[/ilmath] using a substitution assignment operator.

• Denoted: [ilmath]\sigma[x_i:=a][/ilmath], defined as follows:
  • [ilmath]\sigma[x_i:=a]:y\mapsto\left\{\begin{array}{lr}a & \text{if }y=x_i\\ \sigma(y) & \text{otherwise}\end{array}\right.[/ilmath]

See also

• Model