12,080
edits
Changes
Directory talk:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 19:15, 21 May 2008
, 19:15, 21 May 2008→Current Version @ PlanetMath : TeX Format: update
\PMlinkescapephrase{collection}
\PMlinkescapephrase{collection}
\PMlinkescapephrase{Collection}
\PMlinkescapephrase{Collection}
\PMlinkescapephrase{component}
\PMlinkescapephrase{Component}
\PMlinkescapephrase{cover}
\PMlinkescapephrase{cover}
\PMlinkescapephrase{Cover}
\PMlinkescapephrase{Cover}
\PMlinkescapephrase{divides}
\PMlinkescapephrase{divides}
\PMlinkescapephrase{Divides}
\PMlinkescapephrase{Divides}
\PMlinkescapephrase{entire}
\PMlinkescapephrase{Entire}
\PMlinkescapephrase{even}
\PMlinkescapephrase{Even}
\PMlinkescapephrase{language}
\PMlinkescapephrase{language}
\PMlinkescapephrase{Language}
\PMlinkescapephrase{Language}
\multicolumn{4}{c}{\textbf{Table 4. Propositional Calculus : Basic Notation}} \\[8pt]
\multicolumn{4}{c}{\textbf{Table 4. Propositional Calculus : Basic Notation}} \\[8pt]
\hline
\hline
\textbf{Symbol} & \textbf{Notation} & \textbf{Description} & \textbf{Type} \\[4pt]
\textbf{Symbol} &
\textbf{Notation} &
\textbf{Description} &
\textbf{Type} \\[4pt]
\hline
\hline
$\mathcal{A}$ & $\{ a_1, \ldots, a_n \}$ & Alphabet & $[n] = \mathbf{n}$ \\[4pt]
$\mathfrak{A}$ &
$\{ \mathfrak{a}_1, \ldots, \mathfrak{a}_n \}$ &
Alphabet &
$[n] = \mathbf{n}$ \\[4pt]
\hline
\hline
$A_i$ & $\{ \overline{a_i}, a_i \}$ & Dimension $i$ & $\mathbb{B}$ \\[4pt]
$\mathcal{A}$ &
$\{ a_1, \ldots, a_n \}$
& Basis &
$[n] = \mathbf{n}$ \\[4pt]
\hline
\hline
$A_i$ &
$\{ \overline{a_i}, a_i \}$ &
Dimension $i$ &
$\mathbb{B}$ \\[4pt]
\hline
$A$ & $\langle \mathcal{A} \rangle$ & Set of cells, & $\mathbb{B}^n$ \\[4pt]
$A$ & $\langle \mathcal{A} \rangle$ & Set of cells, & $\mathbb{B}^n$ \\[4pt]
& $\langle a_1, \ldots, a_n \rangle$ & coordinate tuples, & \\[4pt]
& $\langle a_1, \ldots, a_n \rangle$ & coordinate tuples, & \\[4pt]
& $\textstyle \prod_{i=1}^n A_i$ & of discourse & \\[4pt]
& $\textstyle \prod_{i=1}^n A_i$ & of discourse & \\[4pt]
\hline
\hline
$A^*$ & $(\operatorname{hom} : A \to \mathbb{B})$ & Linear functions &
$A^*$ &
$(\operatorname{hom} : A \to \mathbb{B})$ &
Linear functions &
$(\mathbb{B}^n)^* \cong \mathbb{B}^n$ \\[4pt]
$(\mathbb{B}^n)^* \cong \mathbb{B}^n$ \\[4pt]
\hline
\hline
$A^\uparrow$ & $(A \to \mathbb{B})$ & Boolean functions &
$A^\uparrow$ &
$(A \to \mathbb{B})$ &
Boolean functions &
$\mathbb{B}^n \to \mathbb{B}$ \\[4pt]
$\mathbb{B}^n \to \mathbb{B}$ \\[4pt]
\hline
\hline
$A^\circ$ & $[ \mathcal{A} ]$ & Universe of discourse &
$A^\circ$ & $[ \mathcal{A} ]$ & Universe of discourse &
$(\mathbb{B}^n, (\mathbb{B}^n \to \mathbb{B}))$ \\[4pt]
$(\mathbb{B}^n, (\mathbb{B}^n \to \mathbb{B}))$ \\[4pt]
\textbf{Description} &
\textbf{Description} &
\textbf{Type} \\[4pt]
\textbf{Type} \\[4pt]
\hline
$\operatorname{d}\mathfrak{A}$ &
$\{ \operatorname{d}\mathfrak{a}_1, \ldots, \operatorname{d}\mathfrak{a}_n \}$ &
Alphabet of differential symbols &
$[n] = \mathbf{n}$ \\[4pt]
\hline
\hline
$\operatorname{d}\mathcal{A}$ &
$\operatorname{d}\mathcal{A}$ &
$\{ \operatorname{d}a_1, \ldots, \operatorname{d}a_n \}$ &
$\{ \operatorname{d}a_1, \ldots, \operatorname{d}a_n \}$ &
Basis of differential features &
$[n] = \mathbf{n}$ \\[4pt]
$[n] = \mathbf{n}$ \\[4pt]
\hline
\hline