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<br>
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===Wiki TeX Tables===
+
===Wiki TeX Tables : PQ===
+
+
<br>
+
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
+
|+ <math>\text{Table A1.}~~\text{Propositional Forms on Two Variables}</math>
+
|- style="background:#f0f0ff"
+
| width="15%" |
+
<p><math>\mathcal{L}_1</math></p>
+
<p><math>\text{Decimal}</math></p>
+
| width="15%" |
+
<p><math>\mathcal{L}_2</math></p>
+
<p><math>\text{Binary}</math></p>
+
| width="15%" |
+
<p><math>\mathcal{L}_3</math></p>
+
<p><math>\text{Vector}</math></p>
+
| width="15%" |
+
<p><math>\mathcal{L}_4</math></p>
+
<p><math>\text{Cactus}</math></p>
+
| width="25%" |
+
<p><math>\mathcal{L}_5</math></p>
+
<p><math>\text{English}</math></p>
+
| width="15%" |
+
<p><math>\mathcal{L}_6</math></p>
+
<p><math>\text{Ordinary}</math></p>
+
|- style="background:#f0f0ff"
+
|
+
| align="right" | <math>p\colon\!</math>
+
| <math>1~1~0~0\!</math>
+
|
+
|
+
|
+
|- style="background:#f0f0ff"
+
|
+
| align="right" | <math>q\colon\!</math>
+
| <math>1~0~1~0\!</math>
+
|
+
|
+
|
+
|-
+
|
+
<math>\begin{matrix}
+
f_0
+
\\[4pt]
+
f_1
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\\[4pt]
+
f_2
+
\\[4pt]
+
f_3
+
\\[4pt]
+
f_4
+
\\[4pt]
+
f_5
+
\\[4pt]
+
f_6
+
\\[4pt]
+
f_7
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
f_{0000}
+
\\[4pt]
+
f_{0001}
+
\\[4pt]
+
f_{0010}
+
\\[4pt]
+
f_{0011}
+
\\[4pt]
+
f_{0100}
+
\\[4pt]
+
f_{0101}
+
\\[4pt]
+
f_{0110}
+
\\[4pt]
+
f_{0111}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
0~0~0~0
+
\\[4pt]
+
0~0~0~1
+
\\[4pt]
+
0~0~1~0
+
\\[4pt]
+
0~0~1~1
+
\\[4pt]
+
0~1~0~0
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\\[4pt]
+
0~1~0~1
+
\\[4pt]
+
0~1~1~0
+
\\[4pt]
+
0~1~1~1
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~)
+
\\[4pt]
+
(p)(q)
+
\\[4pt]
+
(p)~q~
+
\\[4pt]
+
(p)~~~
+
\\[4pt]
+
~p~(q)
+
\\[4pt]
+
~~~(q)
+
\\[4pt]
+
(p,~q)
+
\\[4pt]
+
(p~~q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\text{false}
+
\\[4pt]
+
\text{neither}~ p ~\text{nor}~ q
+
\\[4pt]
+
q ~\text{without}~ p
+
\\[4pt]
+
\text{not}~ p
+
\\[4pt]
+
p ~\text{without}~ q
+
\\[4pt]
+
\text{not}~ q
+
\\[4pt]
+
p ~\text{not equal to}~ q
+
\\[4pt]
+
\text{not both}~ p ~\text{and}~ q
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
0
+
\\[4pt]
+
\lnot p \land \lnot q
+
\\[4pt]
+
\lnot p \land q
+
\\[4pt]
+
\lnot p
+
\\[4pt]
+
p \land \lnot q
+
\\[4pt]
+
\lnot q
+
\\[4pt]
+
p \ne q
+
\\[4pt]
+
\lnot p \lor \lnot q
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_8
+
\\[4pt]
+
f_9
+
\\[4pt]
+
f_{10}
+
\\[4pt]
+
f_{11}
+
\\[4pt]
+
f_{12}
+
\\[4pt]
+
f_{13}
+
\\[4pt]
+
f_{14}
+
\\[4pt]
+
f_{15}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
f_{1000}
+
\\[4pt]
+
f_{1001}
+
\\[4pt]
+
f_{1010}
+
\\[4pt]
+
f_{1011}
+
\\[4pt]
+
f_{1100}
+
\\[4pt]
+
f_{1101}
+
\\[4pt]
+
f_{1110}
+
\\[4pt]
+
f_{1111}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
1~0~0~0
+
\\[4pt]
+
1~0~0~1
+
\\[4pt]
+
1~0~1~0
+
\\[4pt]
+
1~0~1~1
+
\\[4pt]
+
1~1~0~0
+
\\[4pt]
+
1~1~0~1
+
\\[4pt]
+
1~1~1~0
+
\\[4pt]
+
1~1~1~1
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~~p~~q~~
+
\\[4pt]
+
((p,~q))
+
\\[4pt]
+
~~~~~q~~
+
\\[4pt]
+
~(p~(q))
+
\\[4pt]
+
~~p~~~~~
+
\\[4pt]
+
((p)~q)~
+
\\[4pt]
+
((p)(q))
+
\\[4pt]
+
((~))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
p ~\text{and}~ q
+
\\[4pt]
+
p ~\text{equal to}~ q
+
\\[4pt]
+
q
+
\\[4pt]
+
\text{not}~ p ~\text{without}~ q
+
\\[4pt]
+
p
+
\\[4pt]
+
\text{not}~ q ~\text{without}~ p
+
\\[4pt]
+
p ~\text{or}~ q
+
\\[4pt]
+
\text{true}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
p \land q
+
\\[4pt]
+
p = q
+
\\[4pt]
+
q
+
\\[4pt]
+
p \Rightarrow q
+
\\[4pt]
+
p
+
\\[4pt]
+
p \Leftarrow q
+
\\[4pt]
+
p \lor q
+
\\[4pt]
+
1
+
\end{matrix}</math>
+
|}
+
+
<br>
+
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
+
|+ <math>\text{Table A2.}~~\text{Propositional Forms on Two Variables}</math>
+
|- style="background:#f0f0ff"
+
| width="15%" |
+
<p><math>\mathcal{L}_1</math></p>
+
<p><math>\text{Decimal}</math></p>
+
| width="15%" |
+
<p><math>\mathcal{L}_2</math></p>
+
<p><math>\text{Binary}</math></p>
+
| width="15%" |
+
<p><math>\mathcal{L}_3</math></p>
+
<p><math>\text{Vector}</math></p>
+
| width="15%" |
+
<p><math>\mathcal{L}_4</math></p>
+
<p><math>\text{Cactus}</math></p>
+
| width="25%" |
+
<p><math>\mathcal{L}_5</math></p>
+
<p><math>\text{English}</math></p>
+
| width="15%" |
+
<p><math>\mathcal{L}_6</math></p>
+
<p><math>\text{Ordinary}</math></p>
+
|- style="background:#f0f0ff"
+
|
+
| align="right" | <math>p\colon\!</math>
+
| <math>1~1~0~0\!</math>
+
|
+
|
+
|
+
|- style="background:#f0f0ff"
+
|
+
| align="right" | <math>q\colon\!</math>
+
| <math>1~0~1~0\!</math>
+
|
+
|
+
|
+
|-
+
| <math>f_0\!</math>
+
| <math>f_{0000}\!</math>
+
| <math>0~0~0~0</math>
+
| <math>(~)</math>
+
| <math>\text{false}\!</math>
+
| <math>0\!</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_1
+
\\[4pt]
+
f_2
+
\\[4pt]
+
f_4
+
\\[4pt]
+
f_8
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
f_{0001}
+
\\[4pt]
+
f_{0010}
+
\\[4pt]
+
f_{0100}
+
\\[4pt]
+
f_{1000}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
0~0~0~1
+
\\[4pt]
+
0~0~1~0
+
\\[4pt]
+
0~1~0~0
+
\\[4pt]
+
1~0~0~0
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)(q)
+
\\[4pt]
+
(p)~q~
+
\\[4pt]
+
~p~(q)
+
\\[4pt]
+
~p~~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\text{neither}~ p ~\text{nor}~ q
+
\\[4pt]
+
q ~\text{without}~ p
+
\\[4pt]
+
p ~\text{without}~ q
+
\\[4pt]
+
p ~\text{and}~ q
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\lnot p \land \lnot q
+
\\[4pt]
+
\lnot p \land q
+
\\[4pt]
+
p \land \lnot q
+
\\[4pt]
+
p \land q
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_3
+
\\[4pt]
+
f_{12}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
f_{0011}
+
\\[4pt]
+
f_{1100}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
0~0~1~1
+
\\[4pt]
+
1~1~0~0
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)
+
\\[4pt]
+
~p~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\text{not}~ p
+
\\[4pt]
+
p
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\lnot p
+
\\[4pt]
+
p
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_6
+
\\[4pt]
+
f_9
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
f_{0110}
+
\\[4pt]
+
f_{1001}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
0~1~1~0
+
\\[4pt]
+
1~0~0~1
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(p,~q)~
+
\\[4pt]
+
((p,~q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
p ~\text{not equal to}~ q
+
\\[4pt]
+
p ~\text{equal to}~ q
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
p \ne q
+
\\[4pt]
+
p = q
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_5
+
\\[4pt]
+
f_{10}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
f_{0101}
+
\\[4pt]
+
f_{1010}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
0~1~0~1
+
\\[4pt]
+
1~0~1~0
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(q)
+
\\[4pt]
+
~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\text{not}~ q
+
\\[4pt]
+
q
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\lnot q
+
\\[4pt]
+
q
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_7
+
\\[4pt]
+
f_{11}
+
\\[4pt]
+
f_{13}
+
\\[4pt]
+
f_{14}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
f_{0111}
+
\\[4pt]
+
f_{1011}
+
\\[4pt]
+
f_{1101}
+
\\[4pt]
+
f_{1110}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
0~1~1~1
+
\\[4pt]
+
1~0~1~1
+
\\[4pt]
+
1~1~0~1
+
\\[4pt]
+
1~1~1~0
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(p~~q)~
+
\\[4pt]
+
~(p~(q))
+
\\[4pt]
+
((p)~q)~
+
\\[4pt]
+
((p)(q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\text{not both}~ p ~\text{and}~ q
+
\\[4pt]
+
\text{not}~ p ~\text{without}~ q
+
\\[4pt]
+
\text{not}~ q ~\text{without}~ p
+
\\[4pt]
+
p ~\text{or}~ q
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\lnot p \lor \lnot q
+
\\[4pt]
+
p \Rightarrow q
+
\\[4pt]
+
p \Leftarrow q
+
\\[4pt]
+
p \lor q
+
\end{matrix}</math>
+
|-
+
| <math>f_{15}\!</math>
+
| <math>f_{1111}\!</math>
+
| <math>1~1~1~1</math>
+
| <math>((~))</math>
+
| <math>\text{true}\!</math>
+
| <math>1\!</math>
+
|}
+
+
<br>
+
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
+
|+ <math>\text{Table A3.}~~\operatorname{E}f ~\text{Expanded Over Differential Features}~ \{ \operatorname{d}p, \operatorname{d}q \}</math>
+
|- style="background:#f0f0ff"
+
| width="10%" |
+
| width="18%" | <math>f\!</math>
+
| width="18%" |
+
<p><math>\operatorname{T}_{11} f</math></p>
+
<p><math>\operatorname{E}f|_{\operatorname{d}p~\operatorname{d}q}</math></p>
+
| width="18%" |
+
<p><math>\operatorname{T}_{10} f</math></p>
+
<p><math>\operatorname{E}f|_{\operatorname{d}p(\operatorname{d}q)}</math></p>
+
| width="18%" |
+
<p><math>\operatorname{T}_{01} f</math></p>
+
<p><math>\operatorname{E}f|_{(\operatorname{d}p)\operatorname{d}q}</math></p>
+
| width="18%" |
+
<p><math>\operatorname{T}_{00} f</math></p>
+
<p><math>\operatorname{E}f|_{(\operatorname{d}p)(\operatorname{d}q)}</math></p>
+
|-
+
| <math>f_0\!</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_1
+
\\[4pt]
+
f_2
+
\\[4pt]
+
f_4
+
\\[4pt]
+
f_8
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)(q)
+
\\[4pt]
+
(p)~q~
+
\\[4pt]
+
~p~(q)
+
\\[4pt]
+
~p~~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~p~~q~
+
\\[4pt]
+
~p~(q)
+
\\[4pt]
+
(p)~q~
+
\\[4pt]
+
(p)(q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~p~(q)
+
\\[4pt]
+
~p~~q~
+
\\[4pt]
+
(p)(q)
+
\\[4pt]
+
(p)~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)~q~
+
\\[4pt]
+
(p)(q)
+
\\[4pt]
+
~p~~q~
+
\\[4pt]
+
~p~(q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)(q)
+
\\[4pt]
+
(p)~q~
+
\\[4pt]
+
~p~(q)
+
\\[4pt]
+
~p~~q~
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_3
+
\\[4pt]
+
f_{12}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)
+
\\[4pt]
+
~p~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~p~
+
\\[4pt]
+
(p)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~p~
+
\\[4pt]
+
(p)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)
+
\\[4pt]
+
~p~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)
+
\\[4pt]
+
~p~
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_6
+
\\[4pt]
+
f_9
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(p,~q)~
+
\\[4pt]
+
((p,~q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(p,~q)~
+
\\[4pt]
+
((p,~q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((p,~q))
+
\\[4pt]
+
~(p,~q)~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((p,~q))
+
\\[4pt]
+
~(p,~q)~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(p,~q)~
+
\\[4pt]
+
((p,~q))
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_5
+
\\[4pt]
+
f_{10}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(q)
+
\\[4pt]
+
~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~q~
+
\\[4pt]
+
(q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(q)
+
\\[4pt]
+
~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~q~
+
\\[4pt]
+
(q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(q)
+
\\[4pt]
+
~q~
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_7
+
\\[4pt]
+
f_{11}
+
\\[4pt]
+
f_{13}
+
\\[4pt]
+
f_{14}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~p~~q~)
+
\\[4pt]
+
(~p~(q))
+
\\[4pt]
+
((p)~q~)
+
\\[4pt]
+
((p)(q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((p)(q))
+
\\[4pt]
+
((p)~q~)
+
\\[4pt]
+
(~p~(q))
+
\\[4pt]
+
(~p~~q~)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((p)~q~)
+
\\[4pt]
+
((p)(q))
+
\\[4pt]
+
(~p~~q~)
+
\\[4pt]
+
(~p~(q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~p~(q))
+
\\[4pt]
+
(~p~~q~)
+
\\[4pt]
+
((p)(q))
+
\\[4pt]
+
((p)~q~)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~p~~q~)
+
\\[4pt]
+
(~p~(q))
+
\\[4pt]
+
((p)~q~)
+
\\[4pt]
+
((p)(q))
+
\end{matrix}</math>
+
|-
+
| <math>f_{15}\!</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
|- style="background:#f0f0ff"
+
| colspan="2" | <math>\text{Fixed Point Total}\!</math>
+
| <math>4\!</math>
+
| <math>4\!</math>
+
| <math>4\!</math>
+
| <math>16\!</math>
+
|}
+
+
<br>
+
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
+
|+ <math>\text{Table A4.}~~\operatorname{D}f ~\text{Expanded Over Differential Features}~ \{ \operatorname{d}p, \operatorname{d}q \}</math>
+
|- style="background:#f0f0ff"
+
| width="10%" |
+
| width="18%" | <math>f\!</math>
+
| width="18%" |
+
<math>\operatorname{D}f|_{\operatorname{d}p~\operatorname{d}q}</math>
+
| width="18%" |
+
<math>\operatorname{D}f|_{\operatorname{d}p(\operatorname{d}q)}</math>
+
| width="18%" |
+
<math>\operatorname{D}f|_{(\operatorname{d}p)\operatorname{d}q}</math>
+
| width="18%" |
+
<math>\operatorname{D}f|_{(\operatorname{d}p)(\operatorname{d}q)}</math>
+
|-
+
| <math>f_0\!</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_1
+
\\[4pt]
+
f_2
+
\\[4pt]
+
f_4
+
\\[4pt]
+
f_8
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)(q)
+
\\[4pt]
+
(p)~q~
+
\\[4pt]
+
~p~(q)
+
\\[4pt]
+
~p~~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((p,~q))
+
\\[4pt]
+
~(p,~q)~
+
\\[4pt]
+
~(p,~q)~
+
\\[4pt]
+
((p,~q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(q)
+
\\[4pt]
+
~q~
+
\\[4pt]
+
(q)
+
\\[4pt]
+
~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)
+
\\[4pt]
+
(p)
+
\\[4pt]
+
~p~
+
\\[4pt]
+
~p~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~)
+
\\[4pt]
+
(~)
+
\\[4pt]
+
(~)
+
\\[4pt]
+
(~)
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_3
+
\\[4pt]
+
f_{12}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)
+
\\[4pt]
+
~p~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((~))
+
\\[4pt]
+
((~))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((~))
+
\\[4pt]
+
((~))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~)
+
\\[4pt]
+
(~)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~)
+
\\[4pt]
+
(~)
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_6
+
\\[4pt]
+
f_9
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(p,~q)~
+
\\[4pt]
+
((p,~q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~)
+
\\[4pt]
+
(~)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((~))
+
\\[4pt]
+
((~))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((~))
+
\\[4pt]
+
((~))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~)
+
\\[4pt]
+
(~)
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_5
+
\\[4pt]
+
f_{10}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(q)
+
\\[4pt]
+
~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((~))
+
\\[4pt]
+
((~))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~)
+
\\[4pt]
+
(~)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((~))
+
\\[4pt]
+
((~))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~)
+
\\[4pt]
+
(~)
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_7
+
\\[4pt]
+
f_{11}
+
\\[4pt]
+
f_{13}
+
\\[4pt]
+
f_{14}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(p~~q)~
+
\\[4pt]
+
~(p~(q))
+
\\[4pt]
+
((p)~q)~
+
\\[4pt]
+
((p)(q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((p,~q))
+
\\[4pt]
+
~(p,~q)~
+
\\[4pt]
+
~(p,~q)~
+
\\[4pt]
+
((p,~q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~q~
+
\\[4pt]
+
(q)
+
\\[4pt]
+
~q~
+
\\[4pt]
+
(q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~p~
+
\\[4pt]
+
~p~
+
\\[4pt]
+
(p)
+
\\[4pt]
+
(p)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~)
+
\\[4pt]
+
(~)
+
\\[4pt]
+
(~)
+
\\[4pt]
+
(~)
+
\end{matrix}</math>
+
|-
+
| <math>f_{15}\!</math>
+
| <math>((~))</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
|}
+
+
<br>
+
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
+
|+ <math>\text{Table A5.}~~\operatorname{E}f ~\text{Expanded Over Ordinary Features}~ \{ p, q \}</math>
+
|- style="background:#f0f0ff"
+
| width="10%" |
+
| width="18%" | <math>f\!</math>
+
| width="18%" | <math>\operatorname{E}f|_{xy}</math>
+
| width="18%" | <math>\operatorname{E}f|_{p(q)}</math>
+
| width="18%" | <math>\operatorname{E}f|_{(p)q}</math>
+
| width="18%" | <math>\operatorname{E}f|_{(p)(q)}</math>
+
|-
+
| <math>f_0\!</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_1
+
\\[4pt]
+
f_2
+
\\[4pt]
+
f_4
+
\\[4pt]
+
f_8
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)(q)
+
\\[4pt]
+
(p)~q~
+
\\[4pt]
+
~p~(q)
+
\\[4pt]
+
~p~~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~\operatorname{d}p~~\operatorname{d}q~
+
\\[4pt]
+
~\operatorname{d}p~(\operatorname{d}q)
+
\\[4pt]
+
(\operatorname{d}p)~\operatorname{d}q~
+
\\[4pt]
+
(\operatorname{d}p)(\operatorname{d}q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~\operatorname{d}p~(\operatorname{d}q)
+
\\[4pt]
+
~\operatorname{d}p~~\operatorname{d}q~
+
\\[4pt]
+
(\operatorname{d}p)(\operatorname{d}q)
+
\\[4pt]
+
(\operatorname{d}p)~\operatorname{d}q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(\operatorname{d}p)~\operatorname{d}q~
+
\\[4pt]
+
(\operatorname{d}p)(\operatorname{d}q)
+
\\[4pt]
+
~\operatorname{d}p~~\operatorname{d}q~
+
\\[4pt]
+
~\operatorname{d}p~(\operatorname{d}q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(\operatorname{d}p)(\operatorname{d}q)
+
\\[4pt]
+
(\operatorname{d}p)~\operatorname{d}q~
+
\\[4pt]
+
~\operatorname{d}p~(\operatorname{d}q)
+
\\[4pt]
+
~\operatorname{d}p~~\operatorname{d}q~
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_3
+
\\[4pt]
+
f_{12}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)
+
\\[4pt]
+
~p~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~\operatorname{d}p~
+
\\[4pt]
+
(\operatorname{d}p)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~\operatorname{d}p~
+
\\[4pt]
+
(\operatorname{d}p)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(\operatorname{d}p)
+
\\[4pt]
+
~\operatorname{d}p~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(\operatorname{d}p)
+
\\[4pt]
+
~\operatorname{d}p~
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_6
+
\\[4pt]
+
f_9
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(p,~q)~
+
\\[4pt]
+
((p,~q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(\operatorname{d}p,~\operatorname{d}q)~
+
\\[4pt]
+
((\operatorname{d}p,~\operatorname{d}q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((\operatorname{d}p,~\operatorname{d}q))
+
\\[4pt]
+
~(\operatorname{d}p,~\operatorname{d}q)~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((\operatorname{d}p,~\operatorname{d}q))
+
\\[4pt]
+
~(\operatorname{d}p,~\operatorname{d}q)~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(\operatorname{d}p,~\operatorname{d}q)~
+
\\[4pt]
+
((\operatorname{d}p,~\operatorname{d}q))
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_5
+
\\[4pt]
+
f_{10}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(q)
+
\\[4pt]
+
~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~\operatorname{d}q~
+
\\[4pt]
+
(\operatorname{d}q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(\operatorname{d}q)
+
\\[4pt]
+
~\operatorname{d}q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~\operatorname{d}q~
+
\\[4pt]
+
(\operatorname{d}q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(\operatorname{d}q)
+
\\[4pt]
+
~\operatorname{d}q~
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_7
+
\\[4pt]
+
f_{11}
+
\\[4pt]
+
f_{13}
+
\\[4pt]
+
f_{14}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~p~~q~)
+
\\[4pt]
+
(~p~(q))
+
\\[4pt]
+
((p)~q~)
+
\\[4pt]
+
((p)(q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((\operatorname{d}p)(\operatorname{d}q))
+
\\[4pt]
+
((\operatorname{d}p)~\operatorname{d}q~)
+
\\[4pt]
+
(~\operatorname{d}p~(\operatorname{d}q))
+
\\[4pt]
+
(~\operatorname{d}p~~\operatorname{d}q~)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((\operatorname{d}p)~\operatorname{d}q~)
+
\\[4pt]
+
((\operatorname{d}p)(\operatorname{d}q))
+
\\[4pt]
+
(~\operatorname{d}p~~\operatorname{d}q~)
+
\\[4pt]
+
(~\operatorname{d}p~(\operatorname{d}q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~\operatorname{d}p~(\operatorname{d}q))
+
\\[4pt]
+
(~\operatorname{d}p~~\operatorname{d}q~)
+
\\[4pt]
+
((\operatorname{d}p)(\operatorname{d}q))
+
\\[4pt]
+
((\operatorname{d}p)~\operatorname{d}q~)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~\operatorname{d}p~~\operatorname{d}q~)
+
\\[4pt]
+
(~\operatorname{d}p~(\operatorname{d}q))
+
\\[4pt]
+
((\operatorname{d}p)~\operatorname{d}q~)
+
\\[4pt]
+
((\operatorname{d}p)(\operatorname{d}q))
+
\end{matrix}</math>
+
|-
+
| <math>f_{15}\!</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
|}
+
+
<br>
+
+
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
+
|+ <math>\text{Table A6.}~~\operatorname{D}f ~\text{Expanded Over Ordinary Features}~ \{ p, q \}</math>
+
|- style="background:#f0f0ff"
+
| width="10%" |
+
| width="18%" | <math>f\!</math>
+
| width="18%" | <math>\operatorname{D}f|_{xy}</math>
+
| width="18%" | <math>\operatorname{D}f|_{p(q)}</math>
+
| width="18%" | <math>\operatorname{D}f|_{(p)q}</math>
+
| width="18%" | <math>\operatorname{D}f|_{(p)(q)}</math>
+
|-
+
| <math>f_0\!</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
| <math>(~)</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_1
+
\\[4pt]
+
f_2
+
\\[4pt]
+
f_4
+
\\[4pt]
+
f_8
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)(q)
+
\\[4pt]
+
(p)~q~
+
\\[4pt]
+
~p~(q)
+
\\[4pt]
+
~p~~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~~\operatorname{d}p~~\operatorname{d}q~~
+
\\[4pt]
+
~~\operatorname{d}p~(\operatorname{d}q)~
+
\\[4pt]
+
~(\operatorname{d}p)~\operatorname{d}q~~
+
\\[4pt]
+
((\operatorname{d}p)(\operatorname{d}q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~~\operatorname{d}p~(\operatorname{d}q)~
+
\\[4pt]
+
~~\operatorname{d}p~~\operatorname{d}q~~
+
\\[4pt]
+
((\operatorname{d}p)(\operatorname{d}q))
+
\\[4pt]
+
~(\operatorname{d}p)~\operatorname{d}q~~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(\operatorname{d}p)~\operatorname{d}q~~
+
\\[4pt]
+
((\operatorname{d}p)(\operatorname{d}q))
+
\\[4pt]
+
~~\operatorname{d}p~~\operatorname{d}q~~
+
\\[4pt]
+
~~\operatorname{d}p~(\operatorname{d}q)~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((\operatorname{d}p)(\operatorname{d}q))
+
\\[4pt]
+
~(\operatorname{d}p)~\operatorname{d}q~~
+
\\[4pt]
+
~~\operatorname{d}p~(\operatorname{d}q)~
+
\\[4pt]
+
~~\operatorname{d}p~~\operatorname{d}q~~
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_3
+
\\[4pt]
+
f_{12}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(p)
+
\\[4pt]
+
~p~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\operatorname{d}p
+
\\[4pt]
+
\operatorname{d}p
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\operatorname{d}p
+
\\[4pt]
+
\operatorname{d}p
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\operatorname{d}p
+
\\[4pt]
+
\operatorname{d}p
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\operatorname{d}p
+
\\[4pt]
+
\operatorname{d}p
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_6
+
\\[4pt]
+
f_9
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(p,~q)~
+
\\[4pt]
+
((p,~q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(\operatorname{d}p,~\operatorname{d}q)
+
\\[4pt]
+
(\operatorname{d}p,~\operatorname{d}q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(\operatorname{d}p,~\operatorname{d}q)
+
\\[4pt]
+
(\operatorname{d}p,~\operatorname{d}q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(\operatorname{d}p,~\operatorname{d}q)
+
\\[4pt]
+
(\operatorname{d}p,~\operatorname{d}q)
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(\operatorname{d}p,~\operatorname{d}q)
+
\\[4pt]
+
(\operatorname{d}p,~\operatorname{d}q)
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_5
+
\\[4pt]
+
f_{10}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(q)
+
\\[4pt]
+
~q~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\operatorname{d}q
+
\\[4pt]
+
\operatorname{d}q
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\operatorname{d}q
+
\\[4pt]
+
\operatorname{d}q
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\operatorname{d}q
+
\\[4pt]
+
\operatorname{d}q
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
\operatorname{d}q
+
\\[4pt]
+
\operatorname{d}q
+
\end{matrix}</math>
+
|-
+
|
+
<math>\begin{matrix}
+
f_7
+
\\[4pt]
+
f_{11}
+
\\[4pt]
+
f_{13}
+
\\[4pt]
+
f_{14}
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
(~p~~q~)
+
\\[4pt]
+
(~p~(q))
+
\\[4pt]
+
((p)~q~)
+
\\[4pt]
+
((p)(q))
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
((\operatorname{d}p)(\operatorname{d}q))
+
\\[4pt]
+
~(\operatorname{d}p)~\operatorname{d}q~~
+
\\[4pt]
+
~~\operatorname{d}p~(\operatorname{d}q)~
+
\\[4pt]
+
~~\operatorname{d}p~~\operatorname{d}q~~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~(\operatorname{d}p)~\operatorname{d}q~~
+
\\[4pt]
+
((\operatorname{d}p)(\operatorname{d}q))
+
\\[4pt]
+
~~\operatorname{d}p~~\operatorname{d}q~~
+
\\[4pt]
+
~~\operatorname{d}p~(\operatorname{d}q)~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~~\operatorname{d}p~(\operatorname{d}q)~
+
\\[4pt]
+
~~\operatorname{d}p~~\operatorname{d}q~~
+
\\[4pt]
+
((\operatorname{d}p)(\operatorname{d}q))
+
\\[4pt]
+
~(\operatorname{d}p)~\operatorname{d}q~~
+
\end{matrix}</math>
+
|
+
<math>\begin{matrix}
+
~~\operatorname{d}p~~\operatorname{d}q~~
+
\\[4pt]
+
~~\operatorname{d}p~(\operatorname{d}q)~
+
\\[4pt]
+
~(\operatorname{d}p)~\operatorname{d}q~~
+
\\[4pt]
+
((\operatorname{d}p)(\operatorname{d}q))
+
\end{matrix}</math>
+
|-
+
| <math>f_{15}\!</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
| <math>((~))</math>
+
|}
+
+
<br>
+
+
===Wiki TeX Tables : XY===
<br>
<br>