MyWikiBiz, Author Your Legacy — Thursday October 31, 2024
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, 15:18, 17 May 2008
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| + | Table 2 exhibits the scheme of notation I use to formalize the domain of propositional calculus, corresponding to the logical content of truth tables and venn diagrams. Although it overworks the square brackets a bit, I also use either one of the equivalent notations [''n''] or '''''n''''' to denote the data type of a finite set on n elements. |
| + | |
| + | <font face="courier new"> |
| + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; text-align:left; width:96%" |
| + | |+ '''Table 2. Fundamental Notations for Propositional Calculus''' |
| + | |- style="background:paleturquoise" |
| + | ! Symbol |
| + | ! Notation |
| + | ! Description |
| + | ! Type |
| + | |- |
| + | | <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>] |
| + | |} |
| + | </font><br> |