[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 12

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Cybernetics List, Peirce List,

Cast into the form of a 3-adic sign relation,
the situation before us can now be given the
following shape:

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` Y ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `Semiotic Domain` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` o-------------------o ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` Rooted  Trees ` | ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` o-------------------o ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` Syntactic ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` Reduction ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` v ` ` ` ` ` ` ` ` `
` ` ` ` o-----------o ` ` En_sem` ` o-----------o ` ` ` ` ` `
` ` ` ` | ` ` ` ` ` |<--------------| ` ` ` o ` | ` ` ` ` ` `
` ` ` ` | ` F ` T ` | ` ` ` ` ` ` ` | ` O ` | ` | ` ` ` ` ` `
` ` ` ` | ` ` ` ` ` |<--------------| ` ` ` O ` | ` ` ` ` ` `
` ` ` ` o-----------o ` ` Ex_sem` ` o-----------o ` ` ` ` ` `
` ` ` ` ` ` ` X ` ` ` ` ` ` ` ` ` ` ` ` `Y_0` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` Canonical ` ` ` ` ` ` `
` ` ` ` Object Domain ` ` ` ` ` ` ` `Sign Domain` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

The interpretation maps En, Ex : Y -> X
are factored into a shared syntactic part:

   En_syn = Ex_syn = E_syn : Y -> Y_0

and a couple of differential semantic parts:

   En_sem, Ex_sem : Y_0 -> X

The functional images of the syntactic reduction map E_syn : Y -> Y_0
are the two simplest signs or the most reduced pair of expressions,
regarded as rooted trees taking the shapes O and |, and these may
be treated as the canonical representatives of their respective
equivalence classes.

To be continued ...

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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