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| | | ['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>] | | | ['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>] |
| | |- | | |- |
| − | | valign="top" | W | + | | valign="top" | <p>W</p> |
| − | | valign="top" | W :<br><br> | + | | valign="top" | <p>W :</p> |
| − | ''U''<sup> •</sup> → E''U''<sup> •</sup>,<br><br> | + | <p>''U''<sup> •</sup> → E''U''<sup> •</sup> ,</p> |
| − | ''X''<sup> •</sup> → E''X''<sup> •</sup>,<br><br> | + | <p>''X''<sup> •</sup> → E''X''<sup> •</sup> ,</p> |
| − | (''U''<sup> •</sup>→''X''<sup> •</sup>)<br><br> | + | <p>(''U''<sup> •</sup>→''X''<sup> •</sup>) →<br> |
| − | →<br><br> | + | E''U''<sup> •</sup>→E''X''<sup> •</sup>) ,</p> |
| − | (E''U''<sup> •</sup>→E''X''<sup> •</sup>),<br><br>
| + | <p>For each W in the set:<br> |
| − | For each W in the set:<br> | + | {<math>\epsilon</math>, <math>\eta</math>, E, D, d} .</p> |
| − | {<math>\epsilon</math>, <math>\eta</math>, E, D, d} | + | | valign="top" | <p>Operator</p> |
| − | | valign="top" | Operator | + | | valign="top" | <p> <p> |
| − | | valign="top" | <br><br> | + | <p>['''B'''<sup>2</sup>] → ['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] ,</p> |
| − | ['''B'''<sup>2</sup>] → ['''B'''<sup>2</sup> × '''D'''<sup>2</sup>],<br><br> | + | <p>['''B'''<sup>1</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>] ,</p> |
| − | ['''B'''<sup>1</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>],<br><br> | + | <p>(['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>]) →<br> |
| − | (['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>])<br><br> | + | (['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>]) .</p> |
| − | →<br><br> | + | <p> <br> </p> |
| − | (['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>]) | |
| | |- | | |- |
| | | | | | |
| Line 6,464: |
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| | | | |
| | <pre> | | <pre> |
| − | | W | W : | Operator
| |
| − |
| |
| − | | | U% -> EU%, | | [B^2] -> [B^2 x D^2],
| |
| − |
| |
| − | | | X% -> EX%, | | [B^1] -> [B^1 x D^1],
| |
| − |
| |
| − | | | (U%->X%)->(EU%->EX%), | | ([B^2] -> [B^1])
| |
| − |
| |
| − | | | for each W among: | | ->
| |
| − | | | e!, !h!, E, D, d | | ([B^2 x D^2]->[B^1 x D^1])
| |
| − |
| |
| − | -------------o
| |
| − |
| |
| | | !e! | | Tacit Extension Operator !e! | | | !e! | | Tacit Extension Operator !e! |
| | | !h! | | Trope Extension Operator !h! | | | !h! | | Trope Extension Operator !h! |
| Line 6,506: |
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| | -------------o | | -------------o |
| | </pre> | | </pre> |
| − |
| |
| − |
| |
| − | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; text-align:left; width:96%"
| |
| − | |+ '''Table 54. Cast of Characters: Expansive Subtypes of Objects and Operators'''
| |
| − | |- style="background:paleturquoise"
| |
| − | ! Item
| |
| − | ! Notation
| |
| − | ! Description
| |
| − | ! Type
| |
| − | |-
| |
| − | | ''U''<sup> •</sup>
| |
| − | | = [''u'', ''v'']
| |
| − | | Source Universe
| |
| − | | ['''B'''<sup>2</sup>]
| |
| − | |-
| |
| − | | ''X''<sup> •</sup>
| |
| − | | = [''x'']
| |
| − | | Target Universe
| |
| − | | ['''B'''<sup>1</sup>]
| |
| − | |-
| |
| − | | E''U''<sup> •</sup>
| |
| − | | = [''u'', ''v'', d''u'', d''v'']
| |
| − | | Extended Source Universe
| |
| − | | ['''B'''<sup>2</sup> × '''D'''<sup>2</sup>]
| |
| − | |-
| |
| − | | E''X''<sup> •</sup>
| |
| − | | = [''x'', d''x'']
| |
| − | | Extended Target Universe
| |
| − | | ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>]
| |
| − | |-
| |
| − | | ''J''
| |
| − | | ''J'' : ''U'' → '''B'''
| |
| − | | Proposition
| |
| − | | ('''B'''<sup>2</sup> → '''B''') ∈ ['''B'''<sup>2</sup>]
| |
| − | |-
| |
| − | | ''J''
| |
| − | | ''J'' : ''U''<sup> •</sup> → ''X''<sup> •</sup>
| |
| − | | Transformation, or Mapping
| |
| − | | ['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>]
| |
| − | |-
| |
| − | | valign="top" | <p>W</p>
| |
| − | | valign="top" | <p>W :</p>
| |
| − | <p>''U''<sup> •</sup> → E''U''<sup> •</sup> ,</p>
| |
| − | <p>''X''<sup> •</sup> → E''X''<sup> •</sup> ,</p>
| |
| − | <p>(''U''<sup> •</sup>→''X''<sup> •</sup>) →<br>
| |
| − | E''U''<sup> •</sup>→E''X''<sup> •</sup>) ,</p>
| |
| − | <p>For each W in the set:<br>
| |
| − | {<math>\epsilon</math>, <math>\eta</math>, E, D, d}</p>
| |
| − | | valign="top" | <p>Operator</p>
| |
| − | | valign="top" | <p> <p>
| |
| − | <p>['''B'''<sup>2</sup>] → ['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] ,</p>
| |
| − | <p>['''B'''<sup>1</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>] ,</p>
| |
| − | <p>(['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>]) →<br>
| |
| − | (['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>])</p>
| |
| − | <p> <br> </p>
| |
| − | |-
| |
| − | |
| |
| − | |
| |
| − | |
| |
| − | |
| |
| − | |-
| |
| − | | <font face="lucida calligraphy">A<font>
| |
| − | | {''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>}
| |
| − | | Alphabet
| |
| − | | [''n''] = '''n'''
| |
| − | |-
| |
| − | | ''A''<sub>''i''</sub>
| |
| − | | {(''a''<sub>''i''</sub>), ''a''<sub>''i''</sub>}
| |
| − | | Dimension ''i''
| |
| − | | '''B'''
| |
| − | |-
| |
| − | | ''A''
| |
| − | |
| |
| − | 〈<font face="lucida calligraphy">A</font>〉<br>
| |
| − | 〈''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>〉<br>
| |
| − | {‹''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>›}<br>
| |
| − | ''A''<sub>1</sub> × … × ''A''<sub>''n''</sub><br>
| |
| − | ∏<sub>''i''</sub> ''A''<sub>''i''</sub>
| |
| − | |
| |
| − | Set of cells,<br>
| |
| − | coordinate tuples,<br>
| |
| − | points, or vectors<br>
| |
| − | in the universe<br>
| |
| − | of discourse
| |
| − | | '''B'''<sup>''n''</sup>
| |
| − | |-
| |
| − | | ''A''*
| |
| − | | (hom : ''A'' → '''B''')
| |
| − | | Linear functions
| |
| − | | ('''B'''<sup>''n''</sup>)* = '''B'''<sup>''n''</sup>
| |
| − | |-
| |
| − | | ''A''^
| |
| − | | (''A'' → '''B''')
| |
| − | | Boolean functions
| |
| − | | '''B'''<sup>''n''</sup> → '''B'''
| |
| − | |-
| |
| − | | ''A''<sup>•</sup>
| |
| − | |
| |
| − | [<font face="lucida calligraphy">A</font>]<br>
| |
| − | (''A'', ''A''^)<br>
| |
| − | (''A'' +→ '''B''')<br>
| |
| − | (''A'', (''A'' → '''B'''))<br>
| |
| − | [''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>]
| |
| − | |
| |
| − | Universe of discourse<br>
| |
| − | based on the features<br>
| |
| − | {''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>}
| |
| − | |
| |
| − | ('''B'''<sup>''n''</sup>, ('''B'''<sup>''n''</sup> → '''B'''))<br>
| |
| − | ('''B'''<sup>''n''</sup> +→ '''B''')<br>
| |
| − | ['''B'''<sup>''n''</sup>]
| |
| − | |}<br>
| |
| | | | |
| | ===Table 55. Synopsis of Terminology: Restrictive and Alternative Subtypes=== | | ===Table 55. Synopsis of Terminology: Restrictive and Alternative Subtypes=== |
