Difference between revisions of "Assignment (FOL)"
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(Created page with "{{Stub page|grade=A|msg=Page created quickly so I can reference this stuff without sifting through notes or searching PDFs}} __TOC__ ==Definition== An ''assignment'', {{M|\sig...") |
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* {{M|[V\rightarrow M]}}<ref name="MLFFISWL"/> | * {{M|[V\rightarrow M]}}<ref name="MLFFISWL"/> | ||
==See next== | ==See next== | ||
| − | * | + | * {{link|Model|FOL}} |
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==See also== | ==See also== | ||
* {{link|Substitution assignment|FOL}}, written {{M|1=\sigma[x_i:=a]}}<ref name="MLFFISWL"/> that is the same as {{M|\sigma}} except it maps the variable {{M|x_i}} to the value {{M|a}}. | * {{link|Substitution assignment|FOL}}, written {{M|1=\sigma[x_i:=a]}}<ref name="MLFFISWL"/> that is the same as {{M|\sigma}} except it maps the variable {{M|x_i}} to the value {{M|a}}. | ||
Latest revision as of 07:14, 10 September 2016
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Contents
Definition
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].
