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Consequently, the semiotic equivalence relations for <math>\text{A}\!</math> and <math>\text{B}\!</math> both induce the same semiotic partition on <math>S,\!</math> namely, the following.

Consequently, both SERs now induce the same semantic partition on S:

{{ "A"A, "A"B, "i"A, "u"B }, { "B"A, "B"B, "i"B, "u"A }}.

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{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}},

{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}},

{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}},

{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}

\}~,~\{

{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{A}},

{}^{\backprime\backprime} \text{B} {}^{\prime\prime\text{B}},

{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{B}},

{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{A}}

\} \}.\!

By means of a simple attribution step a certain level of congruity has been reached in the community of interpretation constituted by A and B.  This newfound agreement on what is abstractly a single SER means that its equivalence classes reconstruct the structure of the object domain within the parts of the SEP.  This allows a measure of objectivity or inter subjectivity to be predicated of the sign relation's representation.   

By means of a simple attribution step a certain level of congruity has been reached in the community of interpretation constituted by A and B.  This newfound agreement on what is abstractly a single SER means that its equivalence classes reconstruct the structure of the object domain within the parts of the SEP.  This allows a measure of objectivity or inter subjectivity to be predicated of the sign relation's representation.