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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; text-align:left; width:96%"
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|+ '''Table 54.  Cast of Characters:  Expansive Subtypes of Objects and Operators'''
 +
|- style="background:paleturquoise"
 +
! Item
 +
! Notation
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! Description
 +
! Type
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|-
 +
| ''U''<sup>&nbsp;&bull;</sup>
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| = [''u'', ''v'']
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| Source Universe
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| ['''B'''<sup>2</sup>]
 +
|-
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| ''X''<sup>&nbsp;&bull;</sup>
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| = [''x'']
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| Target Universe
 +
| ['''B'''<sup>1</sup>]
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|-
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| E''U''<sup>&nbsp;&bull;</sup>
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| = [''u'', ''v'', d''u'', d''v'']
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| Extended Source Universe
 +
| ['''B'''<sup>2</sup> &times; '''D'''<sup>2</sup>]
 +
|-
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| E''X''<sup>&nbsp;&bull;</sup>
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| = [''x'', d''x'']
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| Extended Target Universe
 +
| ['''B'''<sup>1</sup> &times; '''D'''<sup>1</sup>]
 +
|-
 +
| ''J''
 +
| ''J'' : ''U'' &rarr; '''B'''
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| Proposition
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| ('''B'''<sup>2</sup> &rarr; '''B''') &isin; ['''B'''<sup>2</sup>]
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|-
 +
| ''J''
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| ''J'' : ''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>
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| Transformation, or Mapping
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| ['''B'''<sup>2</sup>] &rarr; ['''B'''<sup>1</sup>]
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|-
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| valign="top" | <p>W</p>
 +
| valign="top" | <p>W&nbsp;:</p>
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<p>''U''<sup>&nbsp;&bull;</sup>&nbsp;&rarr;&nbsp;E''U''<sup>&nbsp;&bull;</sup>&nbsp;,</p>
 +
<p>''X''<sup>&nbsp;&bull;</sup>&nbsp;&rarr;&nbsp;E''X''<sup>&nbsp;&bull;</sup>&nbsp;,</p>
 +
<p>(''U''<sup>&nbsp;&bull;</sup>&rarr;''X''<sup>&nbsp;&bull;</sup>)&nbsp;&rarr;<br>
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E''U''<sup>&nbsp;&bull;</sup>&rarr;E''X''<sup>&nbsp;&bull;</sup>)&nbsp;,</p>
 +
<p>For each W in the set:<br>
 +
{<math>\epsilon</math>,&nbsp;<math>\eta</math>,&nbsp;E,&nbsp;D,&nbsp;d}</p>
 +
| valign="top" | <p>Operator</p>
 +
| valign="top" | <p>&nbsp;<p>
 +
<p>['''B'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;,</p>
 +
<p>['''B'''<sup>1</sup>]&nbsp;&rarr;&nbsp;['''B'''<sup>1</sup>&nbsp;&times;&nbsp;'''D'''<sup>1</sup>]&nbsp;,</p>
 +
<p>(['''B'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''B'''<sup>1</sup>])&nbsp;&rarr;<br>
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(['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''B'''<sup>1</sup>&nbsp;&times;&nbsp;'''D'''<sup>1</sup>])</p>
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<p>&nbsp;<br>&nbsp;</p>
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|-
 +
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
 +
|-
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| <font face="lucida calligraphy">A<font>
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| {''a''<sub>1</sub>, &hellip;, ''a''<sub>''n''</sub>}
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| Alphabet
 +
| [''n''] = '''n'''
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|-
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| ''A''<sub>''i''</sub>
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| {(''a''<sub>''i''</sub>), ''a''<sub>''i''</sub>}
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| Dimension ''i''
 +
| '''B'''
 +
|-
 +
| ''A''
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|
 +
〈<font face="lucida calligraphy">A</font>〉<br>
 +
〈''a''<sub>1</sub>, &hellip;, ''a''<sub>''n''</sub>〉<br>
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{‹''a''<sub>1</sub>, &hellip;, ''a''<sub>''n''</sub>›}<br>
 +
''A''<sub>1</sub> &times; &hellip; &times; ''A''<sub>''n''</sub><br>
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&prod;<sub>''i''</sub> ''A''<sub>''i''</sub>
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|
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Set of cells,<br>
 +
coordinate tuples,<br>
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points, or vectors<br>
 +
in the universe<br>
 +
of discourse
 +
| '''B'''<sup>''n''</sup>
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|-
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| ''A''*
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| (hom : ''A'' &rarr; '''B''')
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| Linear functions
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| ('''B'''<sup>''n''</sup>)* = '''B'''<sup>''n''</sup>
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|-
 +
| ''A''^
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| (''A'' &rarr; '''B''')
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| Boolean functions
 +
| '''B'''<sup>''n''</sup> &rarr; '''B'''
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|-
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| ''A''<sup>&bull;</sup>
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|
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[<font face="lucida calligraphy">A</font>]<br>
 +
(''A'', ''A''^)<br>
 +
(''A'' +&rarr; '''B''')<br>
 +
(''A'', (''A'' &rarr; '''B'''))<br>
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[''a''<sub>1</sub>, &hellip;, ''a''<sub>''n''</sub>]
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|
 +
Universe of discourse<br>
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based on the features<br>
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{''a''<sub>1</sub>, &hellip;, ''a''<sub>''n''</sub>}
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|
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('''B'''<sup>''n''</sup>, ('''B'''<sup>''n''</sup> &rarr; '''B'''))<br>
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('''B'''<sup>''n''</sup> +&rarr; '''B''')<br>
 +
['''B'''<sup>''n''</sup>]
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|}<br>
    
===Table 55.  Synopsis of Terminology:  Restrictive and Alternative Subtypes===
 
===Table 55.  Synopsis of Terminology:  Restrictive and Alternative Subtypes===
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