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Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Differential Propositional Calculus (view source)
Revision as of 21:31, 28 May 2008
, 21:31, 28 May 2008revert tables back to simple parentheses
| <math>f_{0000}\!</math>
| <math>f_{0000}\!</math>
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| <math>(x)(y)\!</math>
| neither x nor y
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| <math>\lnot x \land \lnot y\!</math>
|-
|-
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| <math>(x)\ y\!</math>
| y and not x
| y and not x
| <math>\lnot x \land y</math>
| <math>\lnot x \land y\!</math>
|-
|-
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| <math>\lnot x\!</math>
|-
|-
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| x and not y
| x and not y
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| <math>x \land \lnot y\!</math>
|-
|-
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| 0 1 0 1
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| not y
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| <math>\lnot y\!</math>
|-
|-
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| <math>f_{6}\!</math>
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| <math>f_{0110}\!</math>
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| <math>(x,\ y)\!</math>
| x not equal to y
| x not equal to y
| <math>x \ne y</math>
| <math>x \ne y\!</math>
|-
|-
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| <math>f_{7}\!</math>
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| 0 1 1 1
| 0 1 1 1
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| <math>(x\ y)\!</math>
| not both x and y
| not both x and y
| <math>\lnot x \lor \lnot y</math>
| <math>\lnot x \lor \lnot y\!</math>
|-
|-
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| <math>f_{8}\!</math>
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| <math>f_{1000}\!</math>
| 1 0 0 0
| 1 0 0 0
| <math>x\ y</math>
| <math>x\ y\!</math>
| x and y
| x and y
| <math>x \land y</math>
| <math>x \land y\!</math>
|-
|-
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| <math>f_{9}\!</math>
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| <math>f_{1001}\!</math>
| 1 0 0 1
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| <math>(\!|(\!|x,\ y|\!)|\!)</math>
| <math>((x,\ y))\!</math>
| x equal to y
| x equal to y
| <math>x = y\!</math>
| <math>x = y\!</math>
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| <math>f_{1011}\!</math>
| 1 0 1 1
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| <math>(x\ (y))\!</math>
| not x without y
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| <math>x \Rightarrow y</math>
| <math>x \Rightarrow y\!</math>
|-
|-
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| <math>f_{12}\!</math>
| <math>f_{1101}\!</math>
| <math>f_{1101}\!</math>
| 1 1 0 1
| 1 1 0 1
| <math>(\!|(\!|x|\!)\ y|\!)</math>
| <math>((x)\ y)\!</math>
| not y without x
| not y without x
| <math>x \Leftarrow y</math>
| <math>x \Leftarrow y\!</math>
|-
|-
| <math>f_{14}\!</math>
| <math>f_{14}\!</math>
| <math>f_{1110}\!</math>
| <math>f_{1110}\!</math>
| 1 1 1 0
| 1 1 1 0
| <math>(\!|(\!|x|\!)(\!|y|\!)|\!)</math>
| <math>((x)(y))\!</math>
| x or y
| x or y
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| <math>x \lor y\!</math>
|-
|-
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| <math>f_{15}\!</math>
| <math>f_{1111}\!</math>
| <math>f_{1111}\!</math>
| 1 1 1 1
| 1 1 1 1
| <math>(\!|(\!|~|\!)|\!)</math>
| <math>((~))\!</math>
| true
| true
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| <math>1\!</math>
| style="width:16%" |
| style="width:16%" |
| style="width:16%" | <math>f\!</math>
| style="width:16%" | <math>f\!</math>
| style="width:16%" | <math>\operatorname{E}f|_{xy}</math>
| style="width:16%" | <math>\operatorname{E}f|_{xy}\!</math>
| style="width:16%" | <math>\operatorname{E}f|_{x(\!|y|\!)}</math>
| style="width:16%" | <math>\operatorname{E}f|_{x(y)}\!</math>
| style="width:16%" | <math>\operatorname{E}f|_{(\!|x|\!)y}</math>
| style="width:16%" | <math>\operatorname{E}f|_{(x)y}\!</math>
| style="width:16%" | <math>\operatorname{E}f|_{(\!|x|\!)(\!|y|\!)}</math>
| style="width:16%" | <math>\operatorname{E}f|_{(x)(y)}\!</math>
|-
|-
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| <math>f_{0}\!</math>
| <math>(\!|~|\!)</math>
| <math>(~)\!</math>
| <math>(\!|~|\!)</math>
| <math>(~)\!</math>
| <math>(\!|~|\!)</math>
| <math>(~)\!</math>
| <math>(\!|~|\!)</math>
| <math>(~)\!</math>
| <math>(\!|~|\!)</math>
| <math>(~)\!</math>
|-
|-
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| <math>f_{1}\!</math>
| <math>(\!|x|\!)(\!|y|\!)</math>
| <math>(x)(y)\!</math>
| <math>\operatorname{d}x\ \operatorname{d}y</math>
| <math>\operatorname{d}x\ \operatorname{d}y\!</math>
| <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math>
| <math>\operatorname{d}x (\operatorname{d}y)\!</math>
| <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math>
| <math>(\operatorname{d}x) \operatorname{d}y\!</math>
| <math>(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x)(\operatorname{d}y)\!</math>
|-
|-
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| <math>f_{2}\!</math>
| <math>(\!|x|\!) y</math>
| <math>(x) y\!</math>
| <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math>
| <math>\operatorname{d}x (\operatorname{d}y)\!</math>
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| <math>\operatorname{d}x\ \operatorname{d}y\!</math>
| <math>(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x)(\operatorname{d}y)\!</math>
| <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math>
| <math>(\operatorname{d}x) \operatorname{d}y\!</math>
|-
|-
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| <math>f_{4}\!</math>
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| <math>(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x)(\operatorname{d}y)\!</math>
| <math>\operatorname{d}x\ \operatorname{d}y</math>
| <math>\operatorname{d}x\ \operatorname{d}y\!</math>
| <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math>
| <math>\operatorname{d}x (\operatorname{d}y)\!</math>
|-
|-
| <math>f_{8}\!</math>
| <math>f_{8}\!</math>
| <math>x y\!</math>
| <math>x y\!</math>
| <math>(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x)(\operatorname{d}y)\!</math>
| <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math>
| <math>(\operatorname{d}x) \operatorname{d}y\!</math>
| <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math>
| <math>\operatorname{d}x (\operatorname{d}y)\!</math>
| <math>\operatorname{d}x\ \operatorname{d}y</math>
| <math>\operatorname{d}x\ \operatorname{d}y\!</math>
|-
|-
| <math>f_{3}\!</math>
| <math>f_{3}\!</math>
| <math>(\!|x|\!)</math>
| <math>(x)\!</math>
| <math>\operatorname{d}x</math>
| <math>\operatorname{d}x\!</math>
| <math>\operatorname{d}x</math>
| <math>\operatorname{d}x\!</math>
| <math>(\!|\operatorname{d}x|\!)</math>
| <math>(\operatorname{d}x)\!</math>
| <math>(\!|\operatorname{d}x|\!)</math>
| <math>(\operatorname{d}x)\!</math>
|-
|-
| <math>f_{12}\!</math>
| <math>f_{12}\!</math>
| <math>x\!</math>
| <math>x\!</math>
| <math>(\!|\operatorname{d}x|\!)</math>
| <math>(\operatorname{d}x)\!</math>
| <math>(\!|\operatorname{d}x|\!)</math>
| <math>(\operatorname{d}x)\!</math>
| <math>\operatorname{d}x</math>
| <math>\operatorname{d}x\!</math>
| <math>\operatorname{d}x</math>
| <math>\operatorname{d}x\!</math>
|-
|-
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| <math>f_{6}\!</math>
| <math>(\!|x, y|\!)</math>
| <math>(x, y)\!</math>
| <math>(\!|\operatorname{d}x, \operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x, \operatorname{d}y)\!</math>
| <math>(\!|(\!|\operatorname{d}x, \operatorname{d}y|\!)|\!)</math>
| <math>((\operatorname{d}x, \operatorname{d}y))\!</math>
| <math>(\!|(\!|\operatorname{d}x, \operatorname{d}y|\!)|\!)</math>
| <math>((\operatorname{d}x, \operatorname{d}y))\!</math>
| <math>(\!|\operatorname{d}x, \operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x, \operatorname{d}y)\!</math>
|-
|-
| <math>f_{9}\!</math>
| <math>f_{9}\!</math>
| <math>(\!|(\!|x, y|\!)|\!)</math>
| <math>((x, y))\!</math>
| <math>(\!|(\!|\operatorname{d}x, \operatorname{d}y|\!)|\!)</math>
| <math>((\operatorname{d}x, \operatorname{d}y))\!</math>
| <math>(\!|\operatorname{d}x, \operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x, \operatorname{d}y)\!</math>
| <math>(\!|\operatorname{d}x, \operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x, \operatorname{d}y)\!</math>
| <math>(\!|(\!|\operatorname{d}x, \operatorname{d}y|\!)|\!)</math>
| <math>((\operatorname{d}x, \operatorname{d}y))\!</math>
|-
|-
| <math>f_{5}\!</math>
| <math>f_{5}\!</math>
| <math>(\!|y|\!)</math>
| <math>(y)\!</math>
| <math>\operatorname{d}y</math>
| <math>\operatorname{d}y\!</math>
| <math>(\!|\operatorname{d}y|\!)</math>
| <math>(\operatorname{d}y)\!</math>
| <math>\operatorname{d}y</math>
| <math>\operatorname{d}y\!</math>
| <math>(\!|\operatorname{d}y|\!)</math>
| <math>(\operatorname{d}y)\!</math>
|-
|-
| <math>f_{10}\!</math>
| <math>f_{10}\!</math>
| <math>y\!</math>
| <math>y\!</math>
| <math>(\!|\operatorname{d}y|\!)</math>
| <math>(\operatorname{d}y)\!</math>
| <math>\operatorname{d}y</math>
| <math>\operatorname{d}y\!</math>
| <math>(\!|\operatorname{d}y|\!)</math>
| <math>(\operatorname{d}y)\!</math>
| <math>\operatorname{d}y</math>
| <math>\operatorname{d}y\!</math>
|-
|-
| <math>f_{7}\!</math>
| <math>f_{7}\!</math>
| <math>(\!|x y|\!)</math>
| <math>(x y)\!</math>
| <math>(\!|(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)|\!)</math>
| <math>((\operatorname{d}x)(\operatorname{d}y))\!</math>
| <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math>
| <math>((\operatorname{d}x) \operatorname{d}y)\!</math>
| <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math>
| <math>(\operatorname{d}x (\operatorname{d}y))\!</math>
| <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x\ \operatorname{d}y)\!</math>
|-
|-
| <math>f_{11}\!</math>
| <math>f_{11}\!</math>
| <math>(\!|x (\!|y|\!)|\!)</math>
| <math>(x (y))\!</math>
| <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math>
| <math>((\operatorname{d}x) \operatorname{d}y)\!</math>
| <math>(\!|(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)|\!)</math>
| <math>((\operatorname{d}x)(\operatorname{d}y))\!</math>
| <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x\ \operatorname{d}y)\!</math>
| <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math>
| <math>(\operatorname{d}x (\operatorname{d}y))\!</math>
|-
|-
| <math>f_{13}\!</math>
| <math>f_{13}\!</math>
| <math>(\!|(\!|x|\!) y|\!)</math>
| <math>((x) y)\!</math>
| <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math>
| <math>(\operatorname{d}x (\operatorname{d}y))\!</math>
| <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x\ \operatorname{d}y)\!</math>
| <math>(\!|(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)|\!)</math>
| <math>((\operatorname{d}x)(\operatorname{d}y))\!</math>
| <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math>
| <math>((\operatorname{d}x) \operatorname{d}y)\!</math>
|-
|-
| <math>f_{14}\!</math>
| <math>f_{14}\!</math>
| <math>(\!|(\!|x|\!)(\!|y|\!)|\!)</math>
| <math>((x)(y))\!</math>
| <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math>
| <math>(\operatorname{d}x\ \operatorname{d}y)\!</math>
| <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math>
| <math>(\operatorname{d}x (\operatorname{d}y))\!</math>
| <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math>
| <math>((\operatorname{d}x) \operatorname{d}y)\!</math>
| <math>(\!|(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)|\!)</math>
| <math>((\operatorname{d}x)(\operatorname{d}y))\!</math>
|-
|-
| <math>f_{15}\!</math>
| <math>f_{15}\!</math>
| <math>(\!|(\!|~|\!)|\!)</math>
| <math>((~))\!</math>
| <math>(\!|(\!|~|\!)|\!)</math>
| <math>((~))\!</math>
| <math>(\!|(\!|~|\!)|\!)</math>
| <math>((~))\!</math>
| <math>(\!|(\!|~|\!)|\!)</math>
| <math>((~))\!</math>
| <math>(\!|(\!|~|\!)|\!)</math>
| <math>((~))\!</math>
|}<br>
|}<br>
