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Directory talk:Jon Awbrey/Papers/Differential Logic : Introduction (view source)

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==Work Area==
 
==Work Area==
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
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|+ <math>\text{Table A3.}~~\mathrm{E}f ~\text{Expanded over Differential Features}~ \{ \mathrm{d}p, \mathrm{d}q \}\!</math>
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|- style="background:#f0f0ff"
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| width="10%" | &nbsp;
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| width="18%" | <math>f\!</math>
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| width="18%" |
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<p><math>\mathrm{T}_{11} f\!</math></p>
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<p><math>\mathrm{E}f|_{\mathrm{d}p~\mathrm{d}q}\!</math></p>
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| width="18%" |
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<p><math>\mathrm{T}_{10} f\!</math></p>
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<p><math>\mathrm{E}f|_{\mathrm{d}p(\mathrm{d}q)}\!</math></p>
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| width="18%" |
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<p><math>\mathrm{T}_{01} f\!</math></p>
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<p><math>\mathrm{E}f|_{(\mathrm{d}p)\mathrm{d}q}\!</math></p>
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| width="18%" |
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<p><math>\mathrm{T}_{00} f\!</math></p>
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<p><math>\mathrm{E}f|_{(\mathrm{d}p)(\mathrm{d}q)}\!</math></p>
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|-
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| <math>f_0\!</math>
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| <math>(~)\!</math>
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| <math>(~)\!</math>
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| <math>(~)\!</math>
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| <math>(~)\!</math>
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| <math>(~)\!</math>
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|-
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|
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<math>\begin{matrix}
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f_1
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\\[4pt]
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f_2
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\\[4pt]
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f_4
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\\[4pt]
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f_8
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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(p)(q)
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\\[4pt]
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(p)~q~
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\\[4pt]
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~p~(q)
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\\[4pt]
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~p~~q~
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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~p~~q~
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\\[4pt]
 +
~p~(q)
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\\[4pt]
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(p)~q~
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\\[4pt]
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(p)(q)
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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~p~(q)
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\\[4pt]
 +
~p~~q~
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\\[4pt]
 +
(p)(q)
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\\[4pt]
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(p)~q~
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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(p)~q~
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\\[4pt]
 +
(p)(q)
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\\[4pt]
 +
~p~~q~
 +
\\[4pt]
 +
~p~(q)
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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(p)(q)
 +
\\[4pt]
 +
(p)~q~
 +
\\[4pt]
 +
~p~(q)
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\\[4pt]
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~p~~q~
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\end{matrix}\!</math>
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|-
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|
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<math>\begin{matrix}
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f_3
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\\[4pt]
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f_{12}
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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(p)
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\\[4pt]
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~p~
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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~p~
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\\[4pt]
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(p)
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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~p~
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\\[4pt]
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(p)
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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(p)
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\\[4pt]
 +
~p~
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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(p)
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\\[4pt]
 +
~p~
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\end{matrix}\!</math>
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|-
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|
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<math>\begin{matrix}
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f_6
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\\[4pt]
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f_9
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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~(p,~q)~
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\\[4pt]
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((p,~q))
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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~(p,~q)~
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\\[4pt]
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((p,~q))
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
 +
((p,~q))
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\\[4pt]
 +
~(p,~q)~
 +
\end{matrix}\!</math>
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|
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<math>\begin{matrix}
 +
((p,~q))
 +
\\[4pt]
 +
~(p,~q)~
 +
\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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~(p,~q)~
 +
\\[4pt]
 +
((p,~q))
 +
\end{matrix}\!</math>
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|-
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|
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<math>\begin{matrix}
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f_5
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\\[4pt]
 +
f_{10}
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
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(q)
 +
\\[4pt]
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~q~
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
 +
~q~
 +
\\[4pt]
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(q)
 +
\end{matrix}\!</math>
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|
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<math>\begin{matrix}
 +
(q)
 +
\\[4pt]
 +
~q~
 +
\end{matrix}\!</math>
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|
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<math>\begin{matrix}
 +
~q~
 +
\\[4pt]
 +
(q)
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\end{matrix}\!</math>
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|
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<math>\begin{matrix}
 +
(q)
 +
\\[4pt]
 +
~q~
 +
\end{matrix}\!</math>
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|-
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|
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<math>\begin{matrix}
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f_7
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\\[4pt]
 +
f_{11}
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\\[4pt]
 +
f_{13}
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\\[4pt]
 +
f_{14}
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\end{matrix}\!</math>
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|
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<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>
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|-
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| <math>f_{15}\!</math>
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| <math>((~))\!</math>
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| <math>((~))\!</math>
 +
| <math>((~))\!</math>
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| <math>((~))\!</math>
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| <math>((~))\!</math>
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|- style="background:#f0f0ff"
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| colspan="2" | <math>\text{Fixed Point Total}\!</math>
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| <math>4\!</math>
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| <math>4\!</math>
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| <math>4\!</math>
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| <math>16\!</math>
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|}
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 +
<br>
    
==Operational Representation==
 
==Operational Representation==
Jon Awbrey
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