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==Grammar Stuff==
+
==Format Samples • Wiki Text==
 +
 
 +
===MathBB, MathBF, MathCal===
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 +
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 & \}
 +
\\
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& = & \{ & \text{“ ”} & , & \text{“(”} & , & \text{“,”} & , & \text{“)”} & \}
 +
\\
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& = & \{ & \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.
 +
 
 +
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 &bull; Screenshots==
 +
 
 +
===MathJax Fail===
 +
 
 +
[[File:Format Samples &bull; MathJax Fail.png|640px]]
 +
 
 +
===MathML View===
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 +
[[File:Format Samples &bull; MathML View.png|640px]]
 +
 
 +
==Logic of Relatives==
 +
 
 +
<br>
 +
 
 +
{| align="center" cellspacing="6" width="90%"
 +
| align="center" |
 +
<pre>
 +
Table 3.  Relational Composition
 +
o---------o---------o---------o---------o
 +
|        #  !1!  |  !1!  |  !1!  |
 +
o=========o=========o=========o=========o
 +
|    L    #    X    |    Y    |        |
 +
o---------o---------o---------o---------o
 +
|    M    #        |    Y    |    Z    |
 +
o---------o---------o---------o---------o
 +
|  L o M  #    X    |        |    Z    |
 +
o---------o---------o---------o---------o
 +
</pre>
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"
 +
|+ <math>\text{Table 3.  Relational Composition}\!</math>
 +
|-
 +
| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | &nbsp;
 +
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
 +
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
 +
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
 +
|-
 +
| style="border-right:1px solid black" | <math>L\!</math>
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| <math>X\!</math>
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| <math>Y\!</math>
 +
| &nbsp;
 +
|-
 +
| style="border-right:1px solid black" | <math>M\!</math>
 +
| &nbsp;
 +
| <math>Y\!</math>
 +
| <math>Z\!</math>
 +
|-
 +
| style="border-right:1px solid black" | <math>L \circ M</math>
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| <math>X\!</math>
 +
| &nbsp;
 +
| <math>Z\!</math>
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" cellspacing="6" width="90%"
 +
| align="center" |
 +
<pre>
 +
Table 9.  Composite of Triadic and Dyadic Relations
 +
o---------o---------o---------o---------o---------o
 +
|        #  !1!  |  !1!  |  !1!  |  !1!  |
 +
o=========o=========o=========o=========o=========o
 +
|    G    #    T    |    U    |        |    V    |
 +
o---------o---------o---------o---------o---------o
 +
|    L    #        |    U    |    W    |        |
 +
o---------o---------o---------o---------o---------o
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|  G o L  #    T    |        |    W    |    V    |
 +
o---------o---------o---------o---------o---------o
 +
</pre>
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:75%"
 +
|+ <math>\text{Table 9.  Composite of Triadic and Dyadic Relations}\!</math>
 +
|-
 +
| style="border-right:1px solid black; border-bottom:1px solid black; width:20%" | &nbsp;
 +
| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>
 +
| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>
 +
| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>
 +
| style="border-bottom:1px solid black; width:20%" | <math>\mathit{1}\!</math>
 +
|-
 +
| style="border-right:1px solid black" | <math>G\!</math>
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| <math>T\!</math>
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| <math>U\!</math>
 +
| &nbsp;
 +
| <math>V\!</math>
 +
|-
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| style="border-right:1px solid black" | <math>L\!</math>
 +
| &nbsp;
 +
| <math>U\!</math>
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| <math>W\!</math>
 +
| &nbsp;
 +
|-
 +
| style="border-right:1px solid black" | <math>G \circ L</math>
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| <math>T\!</math>
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| &nbsp;
 +
| <math>W\!</math>
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| <math>V\!</math>
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" cellspacing="6" width="90%"
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| align="center" |
 +
<pre>
 +
Table 13.  Another Brand of Composition
 +
o---------o---------o---------o---------o
 +
|        #  !1!  |  !1!  |  !1!  |
 +
o=========o=========o=========o=========o
 +
|    G    #    X    |    Y    |    Z    |
 +
o---------o---------o---------o---------o
 +
|    T    #        |    Y    |    Z    |
 +
o---------o---------o---------o---------o
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|  G o T  #    X    |        |    Z    |
 +
o---------o---------o---------o---------o
 +
</pre>
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"
 +
|+ <math>\text{Table 13.  Another Brand of Composition}\!</math>
 +
|-
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| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | &nbsp;
 +
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
 +
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
 +
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
 +
|-
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| style="border-right:1px solid black" | <math>G\!</math>
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| <math>X\!</math>
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| <math>Y\!</math>
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| <math>Z\!</math>
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|-
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| style="border-right:1px solid black" | <math>T\!</math>
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| &nbsp;
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| <math>Y\!</math>
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| <math>Z\!</math>
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|-
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| style="border-right:1px solid black" | <math>G \circ T</math>
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| <math>X\!</math>
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| &nbsp;
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| <math>Z\!</math>
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|}
 +
 
 +
<br>
 +
 
 +
{| align="center" cellspacing="6" width="90%"
 +
| align="center" |
 +
<pre>
 +
Table 15.  Conjunction Via Composition
 +
o---------o---------o---------o---------o
 +
|        #  !1!  |  !1!  |  !1!  |
 +
o=========o=========o=========o=========o
 +
|    L,  #    X    |    X    |    Y    |
 +
o---------o---------o---------o---------o
 +
|    S    #        |    X    |    Y    |
 +
o---------o---------o---------o---------o
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|  L , S  #    X    |        |    Y    |
 +
o---------o---------o---------o---------o
 +
</pre>
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"
 +
|+ <math>\text{Table 15.  Conjunction Via Composition}\!</math>
 +
|-
 +
| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | &nbsp;
 +
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
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| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
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| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
 +
|-
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| style="border-right:1px solid black" | <math>L,\!</math>
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| <math>X\!</math>
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| <math>X\!</math>
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| <math>Y\!</math>
 +
|-
 +
| style="border-right:1px solid black" | <math>S\!</math>
 +
| &nbsp;
 +
| <math>X\!</math>
 +
| <math>Y\!</math>
 +
|-
 +
| style="border-right:1px solid black" | <math>L,\!S</math>
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| <math>X\!</math>
 +
| &nbsp;
 +
| <math>Y\!</math>
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" cellspacing="6" width="90%"
 +
| align="center" |
 +
<pre>
 +
Table 18.  Relational Composition P o Q
 +
o---------o---------o---------o---------o
 +
|        #  !1!  |  !1!  |  !1!  |
 +
o=========o=========o=========o=========o
 +
|    P    #    X    |    Y    |        |
 +
o---------o---------o---------o---------o
 +
|    Q    #        |    Y    |    Z    |
 +
o---------o---------o---------o---------o
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|  P o Q  #    X    |        |    Z    |
 +
o---------o---------o---------o---------o
 +
</pre>
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"
 +
|+ <math>\text{Table 18.  Relational Composition}~ P \circ Q</math>
 +
|-
 +
| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | &nbsp;
 +
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
 +
| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
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| style="border-bottom:1px solid black; width:25%" | <math>\mathit{1}\!</math>
 +
|-
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| style="border-right:1px solid black" | <math>P\!</math>
 +
| <math>X\!</math>
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| <math>Y\!</math>
 +
| &nbsp;
 +
|-
 +
| style="border-right:1px solid black" | <math>Q\!</math>
 +
| &nbsp;
 +
| <math>Y\!</math>
 +
| <math>Z\!</math>
 +
|-
 +
| style="border-right:1px solid black" | <math>P \circ Q</math>
 +
| <math>X\!</math>
 +
| &nbsp;
 +
| <math>Z\!</math>
 +
|}
 +
 
 +
<br>
    +
{| align="center" cellspacing="6" width="90%"
 +
| align="center" |
 
<pre>
 
<pre>
−
Table 12.  Algorithmic Translation Rules
+
Table 20.  Arrow:  J(L(u, v)) = K(Ju, Jv)
−
o------------------------o---------o------------------------o
+
o---------o---------o---------o---------o
−
|                       | Parse  |                       |
+
|         #    J    |   J    |   J    |
−
| Sentence in PARCE      |   -->  | Graph in PARC          |
+
o=========o=========o=========o=========o
−
o------------------------o---------o------------------------o
+
|   K    #    X    |   X    |   X    |
−
|                       |        |                        |
+
o---------o---------o---------o---------o
−
| Conc^0                |   -->  | Node^0                |
+
|   L    #    Y    |   Y    |   Y    |
−
|                        |        |                        |
+
o---------o---------o---------o---------o
−
| Conc^k_j  S_j          |  -->  | Node^k_j  Parse(S_j)  |
  −
|                        |        |                        |
  −
| Surc^0                |  -->  | Lobe^0                |
  −
|                        |        |                        |
  −
| Surc^k_j  S_j          |  -->  | Lobe^k_j  Parse(S_j)  |
  −
|                        |        |                        |
  −
o------------------------o---------o------------------------o
   
</pre>
 
</pre>
 +
|}
 +
 +
<br>
 +
 +
{| align="center" cellpadding="10" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center; width:60%"
 +
|+ <math>\text{Table 20.  Arrow Equation:}~~ J(L(u, v)) = K(Ju, Jv)</math>
 +
|-
 +
| style="border-right:1px solid black; border-bottom:1px solid black; width:25%" | &nbsp;
 +
| style="border-bottom:1px solid black; width:25%" | <math>J\!</math>
 +
| style="border-bottom:1px solid black; width:25%" | <math>J\!</math>
 +
| style="border-bottom:1px solid black; width:25%" | <math>J\!</math>
 +
|-
 +
| style="border-right:1px solid black" | <math>K\!</math>
 +
| <math>X\!</math>
 +
| <math>X\!</math>
 +
| <math>X\!</math>
 +
|-
 +
| style="border-right:1px solid black" | <math>L\!</math>
 +
| <math>Y\!</math>
 +
| <math>Y\!</math>
 +
| <math>Y\!</math>
 +
|}
 +
 +
<br>
 +
 +
==Grammar Stuff==
 +
 +
<br>
    
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 +
|+ '''Table 13.  Algorithmic Translation Rules'''
 +
|- style="background:whitesmoke"
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:whitesmoke; width:100%"
 +
| width="33%"    | <math>\text{Sentence in PARCE}\!</math>
 +
| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
 +
| width="33%"    | <math>\text{Graph in PARC}\!</math>
 +
|}
 
|-
 
|-
 
|
 
|
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| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
 
| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
 
| width="33%"    | <math>\operatorname{Node}^0</math>
 
| width="33%"    | <math>\operatorname{Node}^0</math>
 +
|-
 +
| width="33%"    | <math>\operatorname{Conc}_{j=1}^k s_j</math>
 +
| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
 +
| width="33%"    | <math>\operatorname{Node}_{j=1}^k \operatorname{Parse} (s_j)</math>
 
|}
 
|}
 
|-
 
|-
 
|
 
|
 
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
−
| width="33%"    | <math>\operatorname{Conc}^0</math>
+
| width="33%"    | <math>\operatorname{Surc}^0</math>
 
| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
 
| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
−
| width="33%"    | <math>\operatorname{Node}^0</math>
+
| width="33%"    | <math>\operatorname{Lobe}^0</math>
 
|-
 
|-
−
| width="33%"    | <math>\operatorname{Conc}^0</math>
+
| width="33%"    | <math>\operatorname{Surc}_{j=1}^k s_j</math>
 
| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
 
| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
−
| width="33%"    | <math>\operatorname{Node}^0</math>
+
| width="33%"    | <math>\operatorname{Lobe}_{j=1}^k \operatorname{Parse} (s_j)</math>
 +
|}
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 +
|+ '''Table 14.1  Semantic Translation : Functional Form'''
 +
|- style="background:whitesmoke"
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:whitesmoke; width:100%"
 +
| width="20%" | <math>\operatorname{Sentence}</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>\xrightarrow[\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}]{\operatorname{Denotation}}</math>
 +
| width="20%" | <math>\operatorname{Proposition}</math>
 +
|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>s_j\!</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>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
 +
| width="20%" | <math>q_j\!</math>
 +
|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>\operatorname{Conc}^0</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>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
 +
| width="20%" | <math>\underline{1}</math>
 +
|-
 +
| width="20%" | <math>\operatorname{Conc}^k_j s_j</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>\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>
 +
|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>\operatorname{Surc}^0</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>\xrightarrow{\operatorname{11:02, 14 October 2025 (UTC)11:02, 14 October 2025 (UTC)}}</math>
 +
| width="20%" | <math>\underline{0}</math>
 +
|-
 +
| width="20%" | <math>\operatorname{Surc}^k_j s_j</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>\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>
 +
|}
 +
|}
 +
 
 +
<br>
 +
 
 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 +
|+ '''Table 14.2  Semantic Translation : Equational Form'''
 +
|- style="background:whitesmoke"
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" style="background:whitesmoke; width:100%"
 +
| width="20%" | <math>\downharpoonleft \operatorname{Sentence} \downharpoonright</math>
 +
| width="20%" | <math>\stackrel{\operatorname{Parse}}{=}</math>
 +
| width="20%" | <math>\downharpoonleft \operatorname{Graph} \downharpoonright</math>
 +
| width="20%" | <math>\stackrel{\operatorname{Denotation}}{=}</math>
 +
| width="20%" | <math>\operatorname{Proposition}</math>
 +
|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>\downharpoonleft s_j \downharpoonright</math>
 +
| width="20%" | <math>=\!</math>
 +
| width="20%" | <math>\downharpoonleft C_j \downharpoonright</math>
 +
| width="20%" | <math>=\!</math>
 +
| width="20%" | <math>q_j\!</math>
 +
|}
 +
|-
 +
|
 +
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 +
| width="20%" | <math>\downharpoonleft \operatorname{Conc}^0 \downharpoonright</math>
 +
| width="20%" | <math>=\!</math>
 +
| width="20%" | <math>\downharpoonleft \operatorname{Node}^0 \downharpoonright</math>
 +
| width="20%" | <math>=\!</math>
 +
| width="20%" | <math>\underline{1}</math>
 +
|-
 +
| width="20%" | <math>\downharpoonleft \operatorname{Conc}^k_j s_j \downharpoonright</math>
 +
| width="20%" | <math>=\!</math>
 +
| width="20%" | <math>\downharpoonleft \operatorname{Node}^k_j C_j \downharpoonright</math>
 +
| width="20%" | <math>=\!</math>
 +
| width="20%" | <math>\operatorname{Conj}^k_j q_j</math>
 
|}
 
|}
 
|-
 
|-
 
|
 
|
 
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
 
{| align="center" border="0" cellpadding="8" cellspacing="0" width="100%"
−
| width="33%"   | <math>\operatorname{Conc}^0</math>
+
| width="20%" | <math>\downharpoonleft \operatorname{Surc}^0 \downharpoonright</math>
−
| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
+
| width="20%" | <math>=\!</math>
−
| width="33%"   | <math>\operatorname{Node}^0</math>
+
| width="20%" | <math>\downharpoonleft \operatorname{Lobe}^0 \downharpoonright</math>
 +
| width="20%" | <math>=\!</math>
 +
| width="20%" | <math>\underline{0}</math>
 
|-
 
|-
−
| width="33%"   | <math>\operatorname{Conc}^0</math>
+
| width="20%" | <math>\downharpoonleft \operatorname{Surc}^k_j s_j \downharpoonright</math>
−
| align="center" | <math>\xrightarrow{\operatorname{Parse}}</math>
+
| width="20%" | <math>=\!</math>
−
| width="33%"   | <math>\operatorname{Node}^0</math>
+
| width="20%" | <math>\downharpoonleft \operatorname{Lobe}^k_j C_j \downharpoonright</math>
 +
| width="20%" | <math>=\!</math>
 +
| width="20%" | <math>\operatorname{Surj}^k_j q_j</math>
 
|}
 
|}
 
|}
 
|}
 +
 +
<br>
    
==Table Stuff==
 
==Table Stuff==
 +
 +
<br>
 +
 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
 +
|+ '''Table 15.  Boolean Functions on Zero Variables'''
 +
|- style="background:whitesmoke"
 +
| width="14%" | <math>F\!</math>
 +
| width="14%" | <math>F\!</math>
 +
| width="48%" | <math>F()\!</math>
 +
| width="24%" | <math>F\!</math>
 +
|-
 +
| <math>\underline{0}</math>
 +
| <math>F_0^{(0)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>(~)</math>
 +
|-
 +
| <math>\underline{1}</math>
 +
| <math>F_1^{(0)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>((~))</math>
 +
|}
 +
 +
<br>
 +
 +
{| align="center" border="1" cellpadding="6" cellspacing="0" style="text-align:center; width:90%"
 +
|+ '''Table 16.  Boolean Functions on One Variable'''
 +
|- style="background:whitesmoke"
 +
| width="14%" | <math>F\!</math>
 +
| width="14%" | <math>F\!</math>
 +
| colspan="2" | <math>F(x)\!</math>
 +
| width="24%" | <math>F\!</math>
 +
|- style="background:whitesmoke"
 +
| width="14%" | &nbsp;
 +
| width="14%" | &nbsp;
 +
| width="24%" | <math>F(\underline{1})</math>
 +
| width="24%" | <math>F(\underline{0})</math>
 +
| width="24%" | &nbsp;
 +
|-
 +
| <math>F_0^{(1)}\!</math>
 +
| <math>F_{00}^{(1)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>(~)</math>
 +
|-
 +
| <math>F_1^{(1)}\!</math>
 +
| <math>F_{01}^{(1)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>(x)\!</math>
 +
|-
 +
| <math>F_2^{(1)}\!</math>
 +
| <math>F_{10}^{(1)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>x\!</math>
 +
|-
 +
| <math>F_3^{(1)}\!</math>
 +
| <math>F_{11}^{(1)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>((~))</math>
 +
|}
 +
 +
<br>
 +
 +
{| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:center; width:90%"
 +
|+ '''Table 17.  Boolean Functions on Two Variables'''
 +
|- style="background:whitesmoke"
 +
| width="14%" | <math>F\!</math>
 +
| width="14%" | <math>F\!</math>
 +
| colspan="4" | <math>F(x, y)\!</math>
 +
| width="24%" | <math>F\!</math>
 +
|- style="background:whitesmoke"
 +
| width="14%" | &nbsp;
 +
| width="14%" | &nbsp;
 +
| width="12%" | <math>F(\underline{1}, \underline{1})</math>
 +
| width="12%" | <math>F(\underline{1}, \underline{0})</math>
 +
| width="12%" | <math>F(\underline{0}, \underline{1})</math>
 +
| width="12%" | <math>F(\underline{0}, \underline{0})</math>
 +
| width="24%" | &nbsp;
 +
|-
 +
| <math>F_{0}^{(2)}\!</math>
 +
| <math>F_{0000}^{(2)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>(~)</math>
 +
|-
 +
| <math>F_{1}^{(2)}\!</math>
 +
| <math>F_{0001}^{(2)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>(x)(y)\!</math>
 +
|-
 +
| <math>F_{2}^{(2)}\!</math>
 +
| <math>F_{0010}^{(2)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>(x) y\!</math>
 +
|-
 +
| <math>F_{3}^{(2)}\!</math>
 +
| <math>F_{0011}^{(2)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>(x)\!</math>
 +
|-
 +
| <math>F_{4}^{(2)}\!</math>
 +
| <math>F_{0100}^{(2)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>x (y)\!</math>
 +
|-
 +
| <math>F_{5}^{(2)}\!</math>
 +
| <math>F_{0101}^{(2)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>(y)\!</math>
 +
|-
 +
| <math>F_{6}^{(2)}\!</math>
 +
| <math>F_{0110}^{(2)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>(x, y)\!</math>
 +
|-
 +
| <math>F_{7}^{(2)}\!</math>
 +
| <math>F_{0111}^{(2)}\!</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>(x y)\!</math>
 +
|-
 +
| <math>F_{8}^{(2)}\!</math>
 +
| <math>F_{1000}^{(2)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>x y\!</math>
 +
|-
 +
| <math>F_{9}^{(2)}\!</math>
 +
| <math>F_{1001}^{(2)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>((x, y))\!</math>
 +
|-
 +
| <math>F_{10}^{(2)}\!</math>
 +
| <math>F_{1010}^{(2)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>y\!</math>
 +
|-
 +
| <math>F_{11}^{(2)}\!</math>
 +
| <math>F_{1011}^{(2)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>(x (y))\!</math>
 +
|-
 +
| <math>F_{12}^{(2)}\!</math>
 +
| <math>F_{1100}^{(2)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{0}</math>
 +
| <math>x\!</math>
 +
|-
 +
| <math>F_{13}^{(2)}\!</math>
 +
| <math>F_{1101}^{(2)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>\underline{1}</math>
 +
| <math>((x)y)\!</math>
 +
|-
 +
| <math>F_{14}^{(2)}\!</math>
 +
| <math>F_{1110}^{(2)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{0}</math>
 +
| <math>((x)(y))\!</math>
 +
|-
 +
| <math>F_{15}^{(2)}\!</math>
 +
| <math>F_{1111}^{(2)}\!</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>\underline{1}</math>
 +
| <math>((~))</math>
 +
|}
 +
 +
<br>
 +
 +
----
    
<br>
 
<br>
Jon Awbrey
12,096

edits

Retrieved from "https://mywikibiz.com/Special:MobileDiff/77467...481137"