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7.46: Example for injective, label-preserving graph morphisms

Verfasst: 7. Jul 2016 16:19
von felicis
Hi,
does someone know a graph morphism \(r=(\operatorname{\mathit{v-f}}, \operatorname{\mathit{e-f}})\) for the De-Jure-Rule "x creates \(\alpha\) for new object y"?
I don't get how we could create the y subject when we only have \(\operatorname{\mathit{v-f}}: V_L \rightarrow V_R\), i.e. we can't tell the function to create anything, which didn't exist before!!
:(
felicis

Re: 7.46: Example for injective, label-preserving graph morphisms

Verfasst: 9. Jul 2016 15:02
von Boddlnagg
This is how I understand it:

The graph morphism \(r\) can't express any newly created objects, that's true. But the rewrite rule \(rr=(L,R,r)\) also contains \(L\) (which consists of x in that case) and \(R\) (which contains x and y). The graph morphism part of the rule only specifies how existing nodes should be changed. Newly created nodes are specified by whatever is in \(R\) and not in \(L\). The m* on Slide 48 (Module 7) would express this, since it captures the relationship between \(R\) and \(PG'\), although the details weren't specified in the lecture.