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<li>The way I have chosen to deal with this issue in the present case is not by injecting more features of the informal discussion into the dialogue of <math>\text{A}\!</math> and <math>\text{B},\!</math> but by trying to imagine how agents like <math>\text{A}\!</math> and <math>\text{B}\!</math> might be enabled to reflect on these aspects of their own discussion.</li>

The way I have chosen to deal with this issue in the present case is not by injecting more features of the informal discussion into the dialogue of <math>\text{A}\!</math> and <math>\text{B},\!</math> but by trying to imagine how agents like <math>\text{A}\!</math> and <math>\text{B}\!</math> might be enabled to reflect on these aspects of their own discussion.

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<li>First, I employ the sign relations A and B to illustrate two basic kinds of set theoretic merges, the ordinary or "simple" union and the indexed or "situated" union of extensional relations.  On review, both forms of combination are observed to fall short of what is needed to constitute the desired characteristics of a shared sign relation.</li>

<li>First, I employ the sign relations <math>L_\text{A}\!</math> and <math>L_\text{B}\!</math> to illustrate two basic kinds of set theoretic merges, the ordinary or ''simple'' union and the indexed or ''situated'' union of extensional relations.  On review, both forms of combination are observed to fall short of what is needed to constitute the desired characteristics of a shared sign relation.</li>

<li>Next, I present two other ways of extending the sign relations A and B into a common SOI.  These extensions succeed in capturing further aspects of what interpreters know about their shared language use.  Although motivated on different grounds, the alternative constructions that develop coincide in exactly the same abstract structure.</li>

<li>Next, I present two other ways of extending the sign relations <math>L_\text{A}\!</math> and <math>L_\text{B}\!</math> into a common system of interpretation.  These extensions succeed in capturing further aspects of what interpreters know about their shared language use.  Although motivated on different grounds, the alternative constructions that develop coincide in exactly the same abstract structure.</li>

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