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Directory:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 20:59, 6 May 2008
, 20:59, 6 May 2008→Note 17: markup
===Note 17===
===Note 17===
Any cell in a venn diagram has a well-defined set of nearest neighbors, and so we can apply a boundary operator of the appropriate rank to the list of signed features that conjoined would indicate the cell in view.
Any cell in a venn diagram has a well-defined set of nearest neighbors,
and so we can apply a boundary operator of the appropriate rank to the
list of signed features that conjoined would indicate the cell in view.
For example, having computed the "boundary", or what is more properly
For example, having computed the ''boundary'', or what is more properly called the ''point omitted neighborhood'' (PON) of the center cell in a 3-dimensional universe of discourse, what is the PON of the cell that is furthest from it, namely, the ''origin cell'' indicated by the proposition <math>(x)(y)(z)\!</math>?
called the "point omitted neighborhood" (PON) of the center cell in a
3-dimensional universe of discourse, what is the PON of the cell that
is furthest from it, namely, the "origin cell" indicated as (x)(y)(z)?
The region bordering the origin cell, (x)(y)(z), can be computed by placing
The region bordering the origin cell, <math>(x)(y)(z),\!</math> can be computed by placing its three signed conjuncts in a 3-place bracket like <math>(\ldots,\ldots,\ldots),\!</math> arriving at the cactus expression that is shown in both graph and string forms below.
its three signed conjuncts in a 3-place bracket like (__, __, __), arriving
at the cactus expression that is shown below in both graph and string forms.
<pre>
o-------------------------------------------------o
o-------------------------------------------------o
| |
| |
| ((x),(y),(z)) |
| ((x),(y),(z)) |
o-------------------------------------------------o
o-------------------------------------------------o
</pre>
Figure 11 shows the venn diagram of this expression,
Figure 11 shows the venn diagram of this expression, whose meaning is adequately suggested by the phrase "just 1 of 3 is true".
whose meaning is adequately suggested by the phrase
"just 1 of 3 is true".
<pre>
o-----------------------------------------------------------o
o-----------------------------------------------------------o
| U |
| U |