Changes

The main trouble with this notion of semantics in the present situation is that the two semiotic partitions for ''A'' and ''B'' are not the same, indeed, they are orthogonal to each other.  This makes it difficult to interpret either one of the partitions or equivalence relations on the syntactic domain as corresponding to any sort of objective structure or invariant reality, independent of the individual interpreter's point of view (POV).

The main trouble with this notion of semantics in the present situation is that the two semiotic partitions for ''A'' and ''B'' are not the same, indeed, they are orthogonal to each other.  This makes it difficult to interpret either one of the partitions or equivalence relations on the syntactic domain as corresponding to any sort of objective structure or invariant reality, independent of the individual interpreter's point of view (POV).

The form of these Tables should suffice to explain what is meant by saying that the SEP's for A and B are orthogonal to each other.

Information about the different forms of semiotic equivalence induced by the interpreters ''A'' and ''B'' is summarized in Tables 3 and 4.  The form of these Tables should suffice to explain what is meant by saying that the SEP's for ''A'' and ''B'' are orthogonal to each other.

Table 3.  Semiotic Partition of Interpreter A

|+ Table 3.  Semiotic Partition of Interpreter ''A''

"A"

"i"

"u"

| width="50%" | "A"

"B"

| width="50%" | "i"

</pre>

| width="50%" | "u"

| width="50%" | "B"

<br>

Table 4.  Semiotic Partition of Interpreter B

|+ Table 4.  Semiotic Partition of Interpreter ''B''

"A"

"i"

"u"

| "A"

"B"

</pre>

{| align="center" border="0" cellpadding="12" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:50%"

| "i"

| "B"

<br>

To discuss these types of situations further, I introduce the square bracket notation "[x]E" for ''the equivalence class of the element x under the equivalence relation E''.  A statement that the elements x and y are equivalent under E is called an ''equation'', and can be written in either one of two ways, as  "[x]E = [y]E"  or as  "x =E y".

To discuss these types of situations further, I introduce the square bracket notation "[x]E" for ''the equivalence class of the element x under the equivalence relation E''.  A statement that the elements x and y are equivalent under E is called an ''equation'', and can be written in either one of two ways, as  "[x]E = [y]E"  or as  "x =E y".