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Because the examples in this section have been artificially constructed to be as simple as possible, their detailed elaboration can run the risk of trivializing the whole theory of sign relations.  Still, these examples have subtleties of their own, and their careful treatment will serve to illustrate important issues in the general theory of signs.

Because the examples in this section have been artificially constructed to be as simple as possible, their detailed elaboration can run the risk of trivializing the whole theory of sign relations.  Still, these examples have subtleties of their own, and their careful treatment will serve to illustrate important issues in the general theory of signs.

In the present Example, '''S''' = '''I''' = Syntactic Domain.

In the present Example, '''S''' = '''I''' = Syntactic Domain.

Tables 1 and 2 give the sign relations associated with the interpreters ''A'' and ''B'', respectively, putting them in the form of relational databases.  Thus, the rows of each Table list the ordered triples of the form ‹''o'', ''s'', ''i''› that make up the corresponding sign relations:  ''A'', ''B'' ⊆ ''O''×''S''×''I''.  The issue of using the same names for objects and for relations involving these objects will be taken up later, after the less problematic features of these relations have been treated.

Tables 1 and 2 give the sign relations associated with the interpreters ''A'' and ''B'', respectively, putting them in the form of ''[[relational database]]s''.  Thus, the rows of each Table list the ordered triples of the form ‹''o'', ''s'', ''i''› that make up the corresponding sign relations, '''L'''_A and '''L'''_B ⊆ '''O''' × '''S''' × '''I'''.  It is often tempting to use the same names for objects and for relations involving these objects, but it is best to avoid this in a first approach, taking up the issues that this practice raises after the less problematic features of these relations have been treated.

These Tables codify a rudimentary level of interpretive practice for the agents ''A'' and ''B'', and provide a basis for formalizing the initial semantics that is appropriate to their common syntactic domain.  Each row of a Table names an object and two co-referent signs, making up an ordered triple of the form ‹''o'', ''s'', ''i''› that is called an ''elementary relation'', that is, one element of the relation's set-theoretic extension.

|+ '''L'''_A = Sign Relation of Interpreter A

| '''A''' || '''"A"''' || '''"i"'''

| '''B''' || '''"B"''' || '''"B"'''

|-

| '''B''' || '''"u"''' || '''"B"'''

|-

Already in this elementary context, there are several different meanings that might attach to the project of a ''formal semantics''.  In the process of discussing these alternatives, I will introduce a few terms that are occasionally used in the philosophy of language to point out the needed distinctions.

|+ '''L'''_B = Sign Relation of Interpreter B

| '''B''' || '''"i"''' || '''"B"'''

These Tables codify a rudimentary level of interpretive practice for the agents ''A'' and ''B'', and provide a basis for formalizing the initial semantics that is appropriate to their common syntactic domain.  Each row of a Table names an object and two co-referent signs, making up an ordered triple of the form ‹''o'', ''s'', ''i''› that is called an ''elementary relation'', that is, one element of the relation's set-theoretic extension.

Table 1.  Sign Relation of Interpreter A

A "A" "i"

Already in this elementary context, there are several different meanings that might attach to the project of a ''formal semiotics'', or a formal theory of meaning for signs.  In the process of discussing these alternatives, it is useful to introduce a few terms that are occasionally used in the philosophy of language to point out the needed distinctions.

Table 2.  Sign Relation of Interpreter B

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