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| + | ==Format Samples • Wiki Text== |
| + | |
| + | ===MathBB, MathBF, MathCal=== |
| + | |
| + | A set of logical features, <math>\mathcal{A} = \{ a_1, \ldots, a_n \},</math> affords a basis for generating an <math>n</math>-dimensional universe of discourse, written <math>A^\bullet = [ \mathcal{A} ] = [ a_1, \ldots, a_n ].</math> It is useful to consider a universe of discourse as a categorical object that incorporates both the set of points <math>A = \langle a_1, \ldots, a_n \rangle</math> and the set of propositions <math>A^\uparrow = \{ f : A \to \mathbb{B} \}</math> that are implicit with the ordinary picture of a venn diagram on <math>n</math> features. Accordingly, the universe of discourse <math>A^\bullet</math> may be regarded as an ordered pair <math>(A, A^\uparrow)</math> having the type <math>(\mathbb{B}^n, (\mathbb{B}^n \to \mathbb{B})),</math> and this last type designation may be abbreviated as <math>\mathbb{B}^n\ +\!\to \mathbb{B},</math> or even more succinctly as <math>[ \mathbb{B}^n ].</math> For convenience, the data type of a finite set on <math>n</math> elements may be indicated by either one of the equivalent notations, <math>[n]</math> or <math>\mathbf{n}.</math> |
| + | |
| + | ===MathFrak=== |
| + | |
| + | <p><math>\begin{array}{lccccccccccc} |
| + | \mathfrak{M} |
| + | & = & \{ & \mathfrak{m}_1 & , & \mathfrak{m}_2 & , & \mathfrak{m}_3 & , & \mathfrak{m}_4 & \} |
| + | \\ |
| + | & = & \{ & \text{“ ”} & , & \text{“(”} & , & \text{“,”} & , & \text{“)”} & \} |
| + | \\ |
| + | & = & \{ & \mathrm{blank} & , & \mathrm{links} & , & \mathrm{comma} & , & \mathrm{right} & \} |
| + | \end{array}</math></p> |
| + | |
| + | ===TextTT=== |
| + | |
| + | For the initial case <math>k = 0,</math> the bound connective is an empty closure, an expression taking one of the forms <math>\texttt{()}, \texttt{( )}, \texttt{( )}, \ldots</math> with any number of spaces between the parentheses, all of which have the same denotation among propositions. |
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| + | For the generic case <math>k > 0,</math> the bound connective takes the form <math>\texttt{(} s_1 \texttt{,} \ldots \texttt{,} s_k \texttt{)}.</math> |
| + | |
| + | ==Format Samples • Screenshots== |
| + | |
| + | ===MathJax Fail=== |
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| + | [[File:Format Samples • MathJax Fail.png|640px]] |
| + | |
| + | ===MathML View=== |
| + | |
| + | [[File:Format Samples • MathML View.png|640px]] |
| + | |
| ==Logic of Relatives== | | ==Logic of Relatives== |
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| {| align="center" border="0" cellpadding="8" cellspacing="0" style="background:whitesmoke; width:100%" | | {| align="center" border="0" cellpadding="8" cellspacing="0" style="background:whitesmoke; width:100%" |
| | width="20%" | <math>\operatorname{Sentence}</math> | | | width="20%" | <math>\operatorname{Sentence}</math> |
− | | width="20%" | <math>\xrightarrow[\operatorname{~~~~~~~~~~}]{\operatorname{Parse}}</math> | + | | width="20%" | <math>\xrightarrow[\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}]{\operatorname{Parse}}</math> |
| | width="20%" | <math>\operatorname{Graph}</math> | | | width="20%" | <math>\operatorname{Graph}</math> |
− | | width="20%" | <math>\xrightarrow[\operatorname{~~~~~~~~~~}]{\operatorname{Denotation}}</math> | + | | width="20%" | <math>\xrightarrow[\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}]{\operatorname{Denotation}}</math> |
| | width="20%" | <math>\operatorname{Proposition}</math> | | | width="20%" | <math>\operatorname{Proposition}</math> |
| |} | | |} |
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| {| align="center" border="0" cellpadding="8" cellspacing="0" width="100%" | | {| align="center" border="0" cellpadding="8" cellspacing="0" width="100%" |
| | width="20%" | <math>s_j\!</math> | | | width="20%" | <math>s_j\!</math> |
− | | width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math> | + | | width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math> |
| | width="20%" | <math>C_j\!</math> | | | width="20%" | <math>C_j\!</math> |
− | | width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math> | + | | width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math> |
| | width="20%" | <math>q_j\!</math> | | | width="20%" | <math>q_j\!</math> |
| |} | | |} |
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| {| align="center" border="0" cellpadding="8" cellspacing="0" width="100%" | | {| align="center" border="0" cellpadding="8" cellspacing="0" width="100%" |
| | width="20%" | <math>\operatorname{Conc}^0</math> | | | width="20%" | <math>\operatorname{Conc}^0</math> |
− | | width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math> | + | | width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math> |
| | width="20%" | <math>\operatorname{Node}^0</math> | | | width="20%" | <math>\operatorname{Node}^0</math> |
− | | width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math> | + | | width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math> |
| | width="20%" | <math>\underline{1}</math> | | | width="20%" | <math>\underline{1}</math> |
| |- | | |- |
| | width="20%" | <math>\operatorname{Conc}^k_j s_j</math> | | | width="20%" | <math>\operatorname{Conc}^k_j s_j</math> |
− | | width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math> | + | | width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math> |
| | width="20%" | <math>\operatorname{Node}^k_j C_j</math> | | | width="20%" | <math>\operatorname{Node}^k_j C_j</math> |
− | | width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math> | + | | width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math> |
| | width="20%" | <math>\operatorname{Conj}^k_j q_j</math> | | | width="20%" | <math>\operatorname{Conj}^k_j q_j</math> |
| |} | | |} |
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| {| align="center" border="0" cellpadding="8" cellspacing="0" width="100%" | | {| align="center" border="0" cellpadding="8" cellspacing="0" width="100%" |
| | width="20%" | <math>\operatorname{Surc}^0</math> | | | width="20%" | <math>\operatorname{Surc}^0</math> |
− | | width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math> | + | | width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math> |
| | width="20%" | <math>\operatorname{Lobe}^0</math> | | | width="20%" | <math>\operatorname{Lobe}^0</math> |
− | | width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math> | + | | width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math> |
| | width="20%" | <math>\underline{0}</math> | | | width="20%" | <math>\underline{0}</math> |
| |- | | |- |
| | width="20%" | <math>\operatorname{Surc}^k_j s_j</math> | | | width="20%" | <math>\operatorname{Surc}^k_j s_j</math> |
− | | width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math> | + | | width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math> |
| | width="20%" | <math>\operatorname{Lobe}^k_j C_j</math> | | | width="20%" | <math>\operatorname{Lobe}^k_j C_j</math> |
− | | width="20%" | <math>\xrightarrow{\operatorname{~~~~~~~~~~}}</math> | + | | width="20%" | <math>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math> |
| | width="20%" | <math>\operatorname{Surj}^k_j q_j</math> | | | width="20%" | <math>\operatorname{Surj}^k_j q_j</math> |
| |} | | |} |