Assignment (FOL)

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Definition

An assignment, $\sigma$ is a map whose domain is the variable set, $V$, and the co-domain is the set of a domain.

• If $\mathscr{L}$ is a first order language, $V$ the set of variable symbols of $\mathscr{L}$, and $\mathbb{M}:=(M,\mathcal{F},\mathcal{R})$ is a domain, then an assignment is a mapping:
  • $\sigma:V\rightarrow M$ is an assignment, is associates with each variable symbol a in the domain.

The set of all assignments is denoted:

• $[V\rightarrow M]$

See next

• Model

See also

• Substitution assignment, written $\sigma[x_i:=a]$ that is the same as $\sigma$ except it maps the variable $x_i$ to the value $a$.