Assignment (FOL)

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An assignment, [ilmath]\sigma[/ilmath] is a map whose domain is the variable set, [ilmath]V[/ilmath], and the co-domain is the set of a domain[1].

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

The set of all assignments is denoted:

  • [ilmath][V\rightarrow M][/ilmath][1]

See next

See also

  • Substitution assignment, written [ilmath]\sigma[x_i:=a][/ilmath][1] that is the same as [ilmath]\sigma[/ilmath] except it maps the variable [ilmath]x_i[/ilmath] to the value [ilmath]a[/ilmath].


  1. 1.0 1.1 1.2 Mathematical Logic - Foundations for Information Science - Wei Li

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