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User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 05:02, 28 January 2009

6,439 bytes added ,  05:02, 28 January 2009
→‎Logical Translation Rule 2
Line 1,252: Line 1,252:  
L2b15. [True] = (()) = 1 : U->B.
 
L2b15. [True] = (()) = 1 : U->B.
 
</pre>
 
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{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"
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|
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
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|- style="height:48px; text-align:right"
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| width="98%" | <math>\text{Logical Translation Rule 2}\!</math>
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| width="2%"  | &nbsp;
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|}
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|-
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|
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
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|- style="height:48px"
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| width="2%"  style="border-top:1px solid black" | &nbsp;
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| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
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| width="80%" style="border-top:1px solid black" |
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<math>s, t ~\text{are sentences about things in the universe}~ X</math>
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|- style="height:48px"
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| &nbsp;
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| <math>\text{and}\!</math>
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| <math>p, q ~\text{are propositions} ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:48px"
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| &nbsp;
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| <math>\text{such that:}\!</math>
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| &nbsp;
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|- style="height:48px"
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| &nbsp;
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| <math>\text{L2a.}\!</math>
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| <math>\downharpoonleft s \downharpoonright ~=~ p \quad \operatorname{and} \quad \downharpoonleft t \downharpoonright ~=~ q</math>
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|- style="height:48px"
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| &nbsp;
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| <math>\text{then}\!</math>
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| <math>\text{the following equations hold:}\!</math>
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|}
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|-
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|
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{| align="center" cellpadding="0" cellspacing="0" style="text-align:center" width="100%"
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|- style="height:52px"
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| width="2%"  style="border-top:1px solid black" | &nbsp;
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| width="18%" style="border-top:1px solid black" align="left" | <math>\text{L2b}_{0}.\!</math>
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| width="20%" style="border-top:1px solid black" |
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<math>\downharpoonleft \operatorname{false} \downharpoonright</math>
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| width="5%"  style="border-top:1px solid black" | <math>=\!</math>
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| width="20%" style="border-top:1px solid black" | <math>(~)</math>
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| width="5%"  style="border-top:1px solid black" | <math>=\!</math>
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| width="30%" style="border-top:1px solid black" |
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<math>\underline{0} ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{1}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{2}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{3}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{4}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{5}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{6}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{7}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{8}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{9}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{10}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{11}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{12}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{13}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{14}.\!</math>
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| <math>\downharpoonleft \ldots \downharpoonright</math>
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| <math>=\!</math>
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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>
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| <math>=\!</math>
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| <math>\ldots ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:52px"
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| &nbsp;
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| align="left" | <math>\text{L2b}_{15}.\!</math>
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| <math>\downharpoonleft \operatorname{true} \downharpoonright</math>
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| <math>=\!</math>
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| <math>((~))</math>
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| <math>=\!</math>
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| <math>\underline{1} ~:~ X \to \underline\mathbb{B}</math>
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|}
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|}
    
<br>
 
<br>
Jon Awbrey
12,089

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