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Revision as of 02:16, 6 July 2008
, 02:16, 6 July 2008→A Functional Conception of Propositional Calculus
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:left; width:96%"
|+ '''Table 2. Propositional Calculus : Basic Notations'''
|+ '''Table 2. Propositional Calculus : Basic Notation'''
|- style="background:ghostwhite"
|- style="background:ghostwhite"
! Symbol
! Symbol
| <math>\mathfrak{A}</math>
| <math>\mathfrak{A}</math>
| <math>\lbrace\!</math> “<math>a_1\!</math>” <math>, \ldots,\!</math> “<math>a_n\!</math>” <math>\rbrace\!</math>
| <math>\lbrace\!</math> “<math>a_1\!</math>” <math>, \ldots,\!</math> “<math>a_n\!</math>” <math>\rbrace\!</math>
| Alphabet
| <math>\operatorname{Alphabet}</math>
| <math>[n] = \mathbf{n}</math>
| <math>[n] = \mathbf{n}</math>
|-
|-
| <math>\mathcal{A}</math>
| <math>\mathcal{A}</math>
| <math>\{a_1, \ldots, a_n\}</math>
| <math>\{a_1, \ldots, a_n\}</math>
| Basis
| <math>\operatorname{Basis}</math>
| <math>[n] = \mathbf{n}</math>
| <math>[n] = \mathbf{n}</math>
|-
|-
| <math>A_i\!</math>
| <math>A_i\!</math>
| <math>\{(a_i), a_i\}\!</math>
| <math>\{(a_i), a_i\}\!</math>
| Dimension <math>i\!</math>
| <math>\operatorname{Dimension}\ i</math>
| <math>\mathbb{B}</math>
| <math>\mathbb{B}</math>
|-
|-
| <math>A\!</math>
| <math>A\!</math>
| <math>\langle \mathcal{A} \rangle</math><br>
|
<math>\langle \mathcal{A} \rangle</math><br>
<math>\langle a_1, \ldots, a_n \rangle</math><br>
<math>\langle a_1, \ldots, a_n \rangle</math><br>
<math>\{(a_1, \ldots, a_n)\}\!</math>
<math>\{(a_1, \ldots, a_n)\}</math><br>
<math>A_1 \times \ldots \times A_n</math><br>
<math>A_1 \times \ldots \times A_n</math><br>
<math>\textstyle \prod_i A_i\!</math>
<math>\textstyle \prod_i A_i</math>
| Set of cells,<br>
|
coordinate tuples,<br>
<math>\operatorname{Set~of~cells},</math><br>
points, or vectors<br>
<math>\operatorname{coordinate~tuples},</math><br>
in the universe<br>
<math>\operatorname{points,~or~vectors}</math><br>
of discourse
<math>\operatorname{in~the~universe}</math><br>
<math>\operatorname{of~discourse}</math>
| <math>\mathbb{B}^n</math>
| <math>\mathbb{B}^n</math>
|-
|-
| <math>A^*\!</math>
| <math>A^*\!</math>
| <math>(\operatorname{hom} : A \to \mathbb{B})</math>
| <math>(\operatorname{hom} : A \to \mathbb{B})</math>
| Linear functions
| <math>\operatorname{Linear~functions}</math>
| <math>(\mathbb{B}^n)^* \cong \mathbb{B}^n</math>
| <math>(\mathbb{B}^n)^* \cong \mathbb{B}^n</math>
|-
|-
| <math>A^\uparrow</math>
| <math>A^\uparrow</math>
| <math>(A \to \mathbb{B})</math>
| <math>(A \to \mathbb{B})</math>
| Boolean functions
| <math>\operatorname{Boolean~functions}</math>
| <math>\mathbb{B}^n \to \mathbb{B}</math>
| <math>\mathbb{B}^n \to \mathbb{B}</math>
|-
|-
| <math>A^\circ</math>
| <math>A^\circ</math>
| <math>[\mathcal{A}]</math><br>
|
<math>[\mathcal{A}]</math><br>
<math>(A, A^\uparrow)</math><br>
<math>(A, A^\uparrow)</math><br>
<math>(A\ +\!\to \mathbb{B})</math><br>
<math>(A\ +\!\to \mathbb{B})</math><br>
<math>(A, (A \to \mathbb{B}))</math><br>
<math>(A, (A \to \mathbb{B}))</math><br>
<math>[a_1, \ldots, a_n]</math>
<math>[a_1, \ldots, a_n]</math>
| Universe of discourse<br>
|
based on the features<br>
<math>\operatorname{Universe~of~discourse}</math><br>
<math>\operatorname{based~on~the~features}</math><br>
<math>\{a_1, \ldots, a_n\}</math>
<math>\{a_1, \ldots, a_n\}</math>
| <math>(\mathbb{B}^n, (\mathbb{B}^n \to \mathbb{B}))</math><br>
|
<math>(\mathbb{B}^n, (\mathbb{B}^n \to \mathbb{B}))</math><br>
<math>(\mathbb{B}^n\ +\!\to \mathbb{B})</math><br>
<math>(\mathbb{B}^n\ +\!\to \mathbb{B})</math><br>
<math>[\mathbb{B}^n]</math>
<math>[\mathbb{B}^n]</math>
