Substitution assignment (FOL)

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Definition

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

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

See also

• Model