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Directory:Jon Awbrey/Papers/Differential Logic : Introduction (view source)

Revision as of 21:30, 16 June 2009

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as a scalar field, in effect, a potential "plateau" of elevation 1

over the shaded region, with an elevation of 0 everywhere else.

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Figure 24-1. Proposition pq : X -> B

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Given any proposition f : X -> B, the "tacit extension" of f to EX

is notated !e!f : EX -> B and defined by the equation !e!f = f, so

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or scalar field f = pq : X -> B to give the extended proposition

or differential field that we notate as !e!f = !e![pq] : EX -> B.

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Figure 24-2. Tacit Extension !e![pq] : EX -> B

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Thus we have a pictorial way of visualizing the following data:

Jon Awbrey

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