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Directory talk:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 02:34, 18 May 2013
, 02:34, 18 May 2013→Current Work
{| cellpadding="10"
{| cellpadding="10"
| width="10%" |
| width="10%" |
| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime}]_\text{A}\!</math>
| <math>[ {}^{\langle} \text{A} {}^{\rangle} ]_\text{A}\!</math>
| <math>=\!</math>
| <math>=\!</math>
| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime}]_\text{A}\!</math>
| <math>[ {}^{\langle} \text{i} {}^{\rangle} ]_\text{A}\!</math>
| width="20%" |
| width="20%" |
| <math>[{}^{\backprime\backprime} \text{B} {}^{\prime\prime}]_\text{A}\!</math>
| <math>[ {}^{\langle} \text{B} {}^{\rangle} ]_\text{A}\!</math>
| <math>=\!</math>
| <math>=\!</math>
| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime}]_\text{A}\!</math>
| <math>[ {}^{\langle} \text{u} {}^{\rangle} ]_\text{A}\!</math>
|-
|-
| width="10%" | or
| width="10%" | or
| <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}\!</math>
| <math>{}^{\langle} \text{A} {}^{\rangle}\!</math>
| <math>=_\text{A}\!</math>
| <math>=_\text{A}\!</math>
| <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}\!</math>
| <math>{}^{\langle} \text{i} {}^{\rangle}\!</math>
| width="20%" |
| width="20%" |
| <math>{}^{\backprime\backprime} \text{B} {}^{\prime\prime}\!</math>
| <math>{}^{\langle} \text{B} {}^{\rangle}\!</math>
| <math>=_\text{A}\!</math>
| <math>=_\text{A}\!</math>
| <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}\!</math>
| <math>{}^{\langle} \text{u} {}^{\rangle}\!</math>
|}
|}
These equations induce the following semiotic partition.
{| align="center" cellspacing="6" width="90%"
|
<math>
\{
\{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle} \},
\{ {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \},
\{ {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \}
\}.\!
</math>
|}
The semiotic equivalence relation given by <math>\operatorname{Con}^1 (L_\text{B})\!</math> for interpreter <math>\text{B}\!</math> has the following semiotic equations.
The semiotic equivalence relation given by <math>\operatorname{Con}^1 (L_\text{B})\!</math> for interpreter <math>\text{B}\!</math> has the following semiotic equations.
{| cellpadding="10"
{| cellpadding="10"
| width="10%" |
| width="10%" |
| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime}]_\text{B}\!</math>
| <math>[ {}^{\langle} \text{A} {}^{\rangle} ]_\text{B}\!</math>
| <math>=\!</math>
| <math>=\!</math>
| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime}]_\text{B}\!</math>
| <math>[ {}^{\langle} \text{u} {}^{\rangle} ]_\text{B}\!</math>
| width="20%" |
| width="20%" |
| <math>[{}^{\backprime\backprime} \text{B} {}^{\prime\prime}]_\text{B}\!</math>
| <math>[ {}^{\langle} \text{B} {}^{\rangle} ]_\text{B}\!</math>
| <math>=\!</math>
| <math>=\!</math>
| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime}]_\text{B}\!</math>
| <math>[ {}^{\langle} \text{i} {}^{\rangle} ]_\text{B}\!</math>
|-
|-
| width="10%" | or
| width="10%" | or
| <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}\!</math>
| <math>{}^{\langle} \text{A} {}^{\rangle}\!</math>
| <math>=_\text{B}\!</math>
| <math>=_\text{B}\!</math>
| <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}\!</math>
| <math>{}^{\langle} \text{u} {}^{\rangle}\!</math>
| width="20%" |
| width="20%" |
| <math>{}^{\backprime\backprime} \text{B} {}^{\prime\prime}\!</math>
| <math>{}^{\langle} \text{B} {}^{\rangle}\!</math>
| <math>=_\text{B}\!</math>
| <math>=_\text{B}\!</math>
| <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}\!</math>
| <math>{}^{\langle} \text{i} {}^{\rangle}\!</math>
|}
|}
These equations induce the following semiotic partition.
{| align="center" cellspacing="6" width="90%"
|
<math>
\{
\{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \},
\{ {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle} \},
\{ {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \},
\{ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \}
\}.\!
</math>
|}
<br>
<br>