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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)
Revision as of 04:58, 4 July 2008
, 04:58, 4 July 2008→Review and Transition
! Other Notations
! Other Notations
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| <math>~</math>
| <math>\operatorname{True}</math>
| <math>\operatorname{True}</math>
| <math>1\!</math>
| <math>1\!</math>
| <math>0\!</math>
| <math>0\!</math>
|-
|-
| <math>A\!</math>
| <math>x\!</math>
| <math>A\!</math>
| <math>x\!</math>
| <math>A\!</math>
| <math>x\!</math>
|-
|-
| <math>(A)\!</math>
| <math>(x)\!</math>
| <math>\operatorname{Not}\ A</math>
| <math>\operatorname{Not}\ x</math>
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<math>\begin{matrix}
<math>\begin{matrix}
x' \\
\tilde A \\
\tilde{x} \\
\lnot A \\
\lnot x \\
\end{matrix}</math>
\end{matrix}</math>
|-
|-
| <math>A\ B\ C</math>
| <math>x\ y\ z</math>
| <math>A\ \operatorname{and}\ B\ \operatorname{and}\ C</math>
| <math>x\ \operatorname{and}\ y\ \operatorname{and}\ z</math>
| <math>A \land B \land C</math>
| <math>x \land y \land z</math>
|-
|-
| <math>((A)(B)(C))\!</math>
| <math>((x)(y)(z))\!</math>
| <math>A\ \operatorname{or}\ B\ \operatorname{or}\ C</math>
| <math>x\ \operatorname{or}\ y\ \operatorname{or}\ z</math>
| <math>A \lor B \lor C</math>
| <math>x \lor y \lor z</math>
|-
|-
| <math>(A (B))\!</math>
| <math>(x\ (y))\!</math>
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<math>\begin{matrix}
<math>\begin{matrix}
x\ \operatorname{implies}\ y \\
\operatorname{If}\ A\ \operatorname{then}\ B \\
\operatorname{If}\ x\ \operatorname{then}\ y \\
\end{matrix}</math>
\end{matrix}</math>
| <math>A \Rightarrow B\!</math>
| <math>x \Rightarrow y\!</math>
|-
|-
| <math>(A, B)\!</math>
| <math>(x, y)\!</math>
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<math>\begin{matrix}
<math>\begin{matrix}
x\ \operatorname{not~equal~to}\ y \\
x\ \operatorname{exclusive~or}\ y \\
\end{matrix}</math>
\end{matrix}</math>
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<math>\begin{matrix}
<math>\begin{matrix}
x \neq y \\
x + y \\
\end{matrix}</math>
\end{matrix}</math>
|-
|-
| <math>((A, B))\!</math>
| <math>((x, y))\!</math>
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<math>\begin{matrix}
<math>\begin{matrix}
x\ \operatorname{is~equal~to}\ y \\
x\ \operatorname{if~and~only~if}\ y \\
\end{matrix}</math>
\end{matrix}</math>
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<math>\begin{matrix}
<math>\begin{matrix}
x = y \\
x \Leftrightarrow y \\
\end{matrix}</math>
\end{matrix}</math>
|-
|-
| <math>(A, B, C)\!</math>
| <math>(x, y, z)\!</math>
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<math>\begin{matrix}
<math>\begin{matrix}
\operatorname{Just~one~of} \\
\operatorname{Just~one~of} \\
x, y, z \\
\operatorname{is~false}. \\
\operatorname{is~false}. \\
\end{matrix}</math>
\end{matrix}</math>
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<math>\begin{matrix}
<math>\begin{matrix}
x'y~z~ & \lor \\
x~y'z~ & \lor \\
x~y~z' & \\
\end{matrix}</math>
\end{matrix}</math>
|-
|-
| <math>((A),(B),(C))\!</math>
| <math>((x),(y),(c))\!</math>
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<math>\begin{matrix}
<math>\begin{matrix}
\operatorname{Just~one~of} \\
\operatorname{Just~one~of} \\
x, y, z \\
\operatorname{is~true}. \\
\operatorname{is~true}. \\
& \\
& \\
\operatorname{Partition~all} \\
\operatorname{Partition~all} \\
\operatorname{into}\ A, B, C. \\
\operatorname{into}\ x, y, z. \\
\end{matrix}</math>
\end{matrix}</math>
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<math>\begin{matrix}
<math>\begin{matrix}
x~y'z' & \lor \\
x'y~z' & \lor \\
x'y'z~ & \\
\end{matrix}</math>
\end{matrix}</math>
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<math>\begin{matrix}
<math>\begin{matrix}
((A, B), C) \\
((x, y), z) \\
& \\
& \\
(A, (B, C)) \\
(x, (y, z)) \\
\end{matrix}</math>
\end{matrix}</math>
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<math>\begin{matrix}
<math>\begin{matrix}
\operatorname{Oddly~many~of} \\
\operatorname{Oddly~many~of} \\
x, y, z \\
\operatorname{are~true}. \\
\operatorname{are~true}. \\
\end{matrix}</math>
\end{matrix}</math>
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<p><math>A + B + C\!</math></p>
<p><math>x + y + z\!</math></p>
<br>
<br>
<p><math>\begin{matrix}
<p><math>\begin{matrix}
x~y~z~ & \lor \\
x~y'z' & \lor \\
x'y~z' & \lor \\
x'y'z~ & \\
\end{matrix}</math></p>
\end{matrix}</math></p>
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| <math>(Q, (A),(B),(C))\!</math>
| <math>(w, (x),(y),(z))\!</math>
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<math>\begin{matrix}
<math>\begin{matrix}
\operatorname{Partition}\ Q \\
\operatorname{Partition}\ w \\
\operatorname{into}\ A, B, C. \\
\operatorname{into}\ x, y, z. \\
& \\
& \\
\operatorname{Genus}\ Q\ \operatorname{comprises} \\
\operatorname{Genus}\ w\ \operatorname{comprises} \\
\operatorname{species}\ A, B, C. \\
\operatorname{species}\ x, y, z. \\
\end{matrix}</math>
\end{matrix}</math>
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<math>\begin{matrix}
<math>\begin{matrix}
w'x'y'z' & \lor \\
w~x~y'z' & \lor \\
w~x'y~z' & \lor \\
w~x'y'z~ & \\
\end{matrix}</math>
\end{matrix}</math>
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