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| This results in a higher order sign relation for <math>Q_{\text{AB}},\!</math> that is shown in Table 46. | | This results in a higher order sign relation for <math>Q_{\text{AB}},\!</math> that is shown in Table 46. |
| | | |
− | <pre> | + | <br> |
− | Table 46. Higher Order Sign Relation for Q(A, B) | + | |
− | Object Sign Interpretant
| + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%" |
− | A <R> <R>
| + | |+ style="height:30px" | <math>\text{Table 46.} ~~ \text{Higher Order Sign Relation for} ~ Q(\text{A}, \text{B})\!</math> |
− | B <R> <R>
| + | |- style="height:40px; background:#f0f0ff" |
− | <A> <q> <q>
| + | | <math>\text{Object}\!</math> |
− | <B> <q> <q>
| + | | <math>\text{Sign}\!</math> |
− | <i> <q> <q>
| + | | <math>\text{Interpretant}\!</math> |
− | <u> <q> <q>
| + | |- |
− | <A, <A>, <A>> <A> <A>
| + | | valign="bottom" width="33%" | |
− | <A, <A>, <i>> <A> <A>
| + | <math>\begin{matrix} |
− | <A, <i>, <A>> <A> <A>
| + | \text{A} |
− | <A, <i>, <i>> <A> <A>
| + | \\ |
− | <B, <B>, <B>> <A> <A>
| + | \text{B} |
− | <B, <B>, <u>> <A> <A>
| + | \end{matrix}</math> |
− | <B, <u>, <B>> <A> <A>
| + | | valign="bottom" width="33%" | |
− | <B, <u>, <u>> <A> <A>
| + | <math>\begin{matrix} |
− | <A, <A>, <A>> <B> <B>
| + | {}^{\langle} L {}^{\rangle} |
− | <A, <A>, <u>> <B> <B>
| + | \\ |
− | <A, <u>, <A>> <B> <B>
| + | {}^{\langle} L {}^{\rangle} |
− | <A, <u>, <u>> <B> <B>
| + | \end{matrix}</math> |
− | <B, <B>, <B>> <B> <B>
| + | | valign="bottom" width="33%" | |
− | <B, <B>, <i>> <B> <B>
| + | <math>\begin{matrix} |
− | <B, <i>, <B>> <B> <B>
| + | {}^{\langle} L {}^{\rangle} |
− | <B, <i>, <i>> <B> <B>
| + | \\ |
− | <<<A>, A>, A> <De> <De>
| + | {}^{\langle} L {}^{\rangle} |
− | <<<B>, A>, B> <De> <De>
| + | \end{matrix}</math> |
− | <<<i>, A>, A> <De> <De>
| + | |- |
− | <<<u>, A>, B> <De> <De>
| + | | valign="bottom" width="33%" | |
− | <<<A>, B>, A> <De> <De>
| + | <math>\begin{matrix} |
− | <<<B>, B>, B> <De> <De>
| + | {}^{\langle} \text{A} {}^{\rangle} |
− | <<<i>, B>, B> <De> <De>
| + | \\ |
− | <<<u>, B>, A> <De> <De>
| + | {}^{\langle} \text{B} {}^{\rangle} |
− | </pre> | + | \\ |
| + | {}^{\langle} \text{i} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{u} {}^{\rangle} |
| + | \end{matrix}</math> |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | {}^{\langle} q {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} q {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} q {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} q {}^{\rangle} |
| + | \end{matrix}</math> |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | {}^{\langle} q {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} q {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} q {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} q {}^{\rangle} |
| + | \end{matrix}</math> |
| + | |- |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) |
| + | \end{matrix}</math> |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \end{matrix}</math> |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{A} {}^{\rangle} |
| + | \end{matrix}</math> |
| + | |- |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & ) |
| + | \\ |
| + | ( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & ) |
| + | \end{matrix}</math> |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \end{matrix}</math> |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \text{B} {}^{\rangle} |
| + | \end{matrix}</math> |
| + | |- |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | (( & {}^{\langle} \text{A} {}^{\rangle} & , & \text{A} & ), & \text{A} & ) |
| + | \\ |
| + | (( & {}^{\langle} \text{A} {}^{\rangle} & , & \text{B} & ), & \text{A} & ) |
| + | \\ |
| + | (( & {}^{\langle} \text{B} {}^{\rangle} & , & \text{A} & ), & \text{B} & ) |
| + | \\ |
| + | (( & {}^{\langle} \text{B} {}^{\rangle} & , & \text{B} & ), & \text{B} & ) |
| + | \\ |
| + | (( & {}^{\langle} \text{i} {}^{\rangle} & , & \text{A} & ), & \text{A} & ) |
| + | \\ |
| + | (( & {}^{\langle} \text{i} {}^{\rangle} & , & \text{B} & ), & \text{B} & ) |
| + | \\ |
| + | (( & {}^{\langle} \text{u} {}^{\rangle} & , & \text{A} & ), & \text{B} & ) |
| + | \\ |
| + | (( & {}^{\langle} \text{u} {}^{\rangle} & , & \text{B} & ), & \text{A} & ) |
| + | \end{matrix}</math> |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \end{matrix}</math> |
| + | | valign="bottom" width="33%" | |
| + | <math>\begin{matrix} |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \\ |
| + | {}^{\langle} \operatorname{De} {}^{\rangle} |
| + | \end{matrix}</math> |
| + | |} |
| + | |
| + | <br> |
| | | |
| Following the manner of construction in this extremely reduced example, it is possible to see how answers to the above questions, concerning the meaning of <math>{}^{\backprime\backprime} \operatorname{De}(q, L) {}^{\prime\prime},\!</math> might be worked out. In the present instance: | | Following the manner of construction in this extremely reduced example, it is possible to see how answers to the above questions, concerning the meaning of <math>{}^{\backprime\backprime} \operatorname{De}(q, L) {}^{\prime\prime},\!</math> might be worked out. In the present instance: |