Substitution assignment (FOL)
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Revision as of 07:18, 10 September 2016 by Alec (Talk | contribs) (Created page with "{{Stub page|grade=A|msg=This page was created just to document it quickly, it needs fleshing out}} __TOC__ ==Definition== Given an {{link|assignment|FOL}}, {{M|\sigma:V\righta...")
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Contents
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][1], defined as follows[1]:
- [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]
