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The triples in <math>L_\operatorname{B}</math> represent the way that interpreter <math>\operatorname{B}</math> uses signs. For example, the listing of the triple <math>(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{i} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime})</math> in <math>L_\operatorname{B}</math> represents the fact that <math>\operatorname{B}</math> uses <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math> to mean the same thing that <math>\operatorname{B}</math> uses <math>^{\backprime\backprime} \operatorname{i} ^{\prime\prime}</math> to mean, namely, <math>\operatorname{B}.</math>
The triples in <math>L_\operatorname{B}</math> represent the way that interpreter <math>\operatorname{B}</math> uses signs. For example, the listing of the triple <math>(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{i} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime})</math> in <math>L_\operatorname{B}</math> represents the fact that <math>\operatorname{B}</math> uses <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math> to mean the same thing that <math>\operatorname{B}</math> uses <math>^{\backprime\backprime} \operatorname{i} ^{\prime\prime}</math> to mean, namely, <math>\operatorname{B}.</math>
The triples that make up the relations '''L'''<sub>A</sub> and '''L'''<sub>B</sub> are conveniently arranged in the form of ''[[relational database|relational data tables]]'', as follows:
The triples that make up the relations <math>L_\operatorname{A}</math> and <math>L_\operatorname{B}</math> are conveniently arranged in the form of ''[[relational database|relational data tables]]'', as follows:
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:60%"
<br>
|+ '''L'''<sub>A</sub> = Sign Relation of Interpreter A
|- style="background:paleturquoise"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:60%"
! style="width:20%" | Object
|+ <math>L_\operatorname{A} ~=~ \operatorname{Sign~Relation~of~Interpreter~A}</math>
! style="width:20%" | Sign
|- style="background:whitesmoke"
! style="width:20%" | Interpretant
! style="width:33%" | <math>\operatorname{Object}</math>
! style="width:33%" | <math>\operatorname{Sign}</math>
! style="width:33%" | <math>\operatorname{Interpretant}</math>
|-
|-
| '''A''' || '''"A"''' || '''"A"'''
| <math>\operatorname{A}</math>
| <math>^{\backprime\backprime} \operatorname{A} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{A} ^{\prime\prime}</math>
|-
|-
| '''A''' || '''"A"''' || '''"i"'''
| <math>\operatorname{A}</math>
| <math>^{\backprime\backprime} \operatorname{A} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{i} ^{\prime\prime}</math>
|-
|-
| '''A''' || '''"i"''' || '''"A"'''
| <math>\operatorname{A}</math>
| <math>^{\backprime\backprime} \operatorname{i} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{A} ^{\prime\prime}</math>
|-
|-
| '''A''' || '''"i"''' || '''"i"'''
| <math>\operatorname{A}</math>
| <math>^{\backprime\backprime} \operatorname{i} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{i} ^{\prime\prime}</math>
|-
|-
| '''B''' || '''"B"''' || '''"B"'''
| <math>\operatorname{B}</math>
| <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math>
|-
|-
| '''B''' || '''"B"''' || '''"u"'''
| <math>\operatorname{B}</math>
| <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{u} ^{\prime\prime}</math>
|-
|-
| '''B''' || '''"u"''' || '''"B"'''
| <math>\operatorname{B}</math>
| <math>^{\backprime\backprime} \operatorname{u} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math>
|-
|-
| '''B''' || '''"u"''' || '''"u"'''
| <math>\operatorname{B}</math>
| <math>^{\backprime\backprime} \operatorname{u} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{u} ^{\prime\prime}</math>
|}
|}
<br>
<br>
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:60%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; text-align:center; width:60%"
|+ '''L'''<sub>B</sub> = Sign Relation of Interpreter B
|+ <math>L_\operatorname{B} ~=~ \operatorname{Sign~Relation~of~Interpreter~B}</math>
|- style="background:paleturquoise"
|- style="background:whitesmoke"
! style="width:20%" | Object
! style="width:33%" | <math>\operatorname{Object}</math>
! style="width:20%" | Sign
! style="width:33%" | <math>\operatorname{Sign}</math>
! style="width:20%" | Interpretant
! style="width:33%" | <math>\operatorname{Interpretant}</math>
|-
|-
| '''A''' || '''"A"''' || '''"A"'''
| <math>\operatorname{A}</math>
| <math>^{\backprime\backprime} \operatorname{A} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{A} ^{\prime\prime}</math>
|-
|-
| '''A''' || '''"A"''' || '''"u"'''
| <math>\operatorname{A}</math>
| <math>^{\backprime\backprime} \operatorname{A} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{u} ^{\prime\prime}</math>
|-
|-
| '''A''' || '''"u"''' || '''"A"'''
|<math>\operatorname{A}</math>
| <math>^{\backprime\backprime} \operatorname{u} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{A} ^{\prime\prime}</math>
|-
|-
| '''A''' || '''"u"''' || '''"u"'''
| <math>\operatorname{A}</math>
| <math>^{\backprime\backprime} \operatorname{u} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{u} ^{\prime\prime}</math>
|-
|-
| '''B''' || '''"B"''' || '''"B"'''
| <math>\operatorname{B}</math>
| <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math>
|-
|-
| '''B''' || '''"B"''' || '''"i"'''
| <math>\operatorname{B}</math>
| <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{i} ^{\prime\prime}</math>
|-
|-
| '''B''' || '''"i"''' || '''"B"'''
| <math>\operatorname{B}</math>
| <math>^{\backprime\backprime} \operatorname{i} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math>
|-
|-
| '''B''' || '''"i"''' || '''"i"'''
| <math>\operatorname{B}</math>
| <math>^{\backprime\backprime} \operatorname{i} ^{\prime\prime}</math>
| <math>^{\backprime\backprime} \operatorname{i} ^{\prime\prime}</math>
|}
|}
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