Changes

User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 16:21, 28 January 2009

310 bytes removed , 16:21, 28 January 2009

→‎Logical Translation Rule 2

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|- style="height:48px"

| width="2%" style="border-top:1px solid black" |  

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| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>

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| width="14%" 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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| width="84%" style="border-top:1px solid black" |

<math>s, t ~\text{are sentences about things in the universe}~ X</math>

|- style="height:48px"

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|- style="height:52px"

| width="2%" style="border-top:1px solid black" |  

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| width="18%" style="border-top:1px solid black" align="left" | <math>\text{L2b}_{0}.\!</math>

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| width="14%" 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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| width="28%" style="border-top:1px solid black" |

<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="4%" style="border-top:1px solid black" | <math>=\!</math>

| 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="4%" style="border-top:1px solid black" | <math>=\!</math>

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| width="30%" style="border-top:1px solid black" |

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| width="28%" style="border-top:1px solid black" |

<math>\underline{0} ~:~ X \to \underline\mathbb{B}</math>

|- style="height:52px"

|  

| align="left" | <math>\text{L2b}_{1}.\!</math>

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| <math>\downharpoonleft \~~ldots~~ \downharpoonright</math>

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| <math>\downharpoonleft \operatorname{neither}~ s ~\operatorname{nor}~ t \downharpoonright</math>

| <math>=\!</math>

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| <math>\~~ldots~~ \downharpoonleft ~~\ldots~~ \downharpoonright ~~\ldots~~</math>

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| <math>(\downharpoonleft s \downharpoonright)(\downharpoonleft t \downharpoonright)</math>

| <math>=\!</math>

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| <math>\~~ldots ~:~ X \to \underline\mathbb{B}~~</math>

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| <math>(p)(q)\!</math>

|- style="height:52px"

|  

| align="left" | <math>\text{L2b}_{2}.\!</math>

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| <math>\downharpoonleft \~~ldots~~ \downharpoonright</math>

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| <math>\downharpoonleft \operatorname{not}~ s ~\operatorname{but}~ t \downharpoonright</math>

| <math>=\!</math>

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| <math>\~~ldots~~ \downharpoonleft ~~\ldots~~ \downharpoonright ~~\ldots~~</math>

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| <math>(\downharpoonleft s \downharpoonright) \downharpoonleft t \downharpoonright</math>

| <math>=\!</math>

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| <math>\~~ldots ~:~ X \to \underline\mathbb{B}~~</math>

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| <math>(p) q\!</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

−

| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

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| <math>\ldots \downharpoonleft \ldots \downharpoonright \ldots</math>

| <math>=\!</math>

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| <math>\ldots ~~~:~ X \to \underline\mathbb{B}~~</math>

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| <math>\ldots</math>

|- style="height:52px"

|  

Jon Awbrey

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