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==Examples from semiotics==

==Examples from semiotics==

The study of signs — the full variety of significant forms of expression — in relation to the things that signs are significant ''of'', and in relation to the beings that signs are significant ''to'', is known as ''[[semiotics]]'' or the ''theory of signs''.  As just described, semiotics treats of a 3-place relation among ''signs'', their ''objects'', and their ''interpreters''.

The study of signs — the full variety of significant forms of expression — in relation to the things that signs are significant ''of'', and in relation to the beings that signs are significant ''to'', is known as ''[[semiotics]]'' or the ''theory of signs''.  As just described, semiotics treats of a 3-place relation among ''signs'', their ''objects'', and their ''interpreters''.

The term ''[[semiosis]]'' refers to any activity or process that involves signs.  Studies of semiosis that deal with its more abstract form are not concerned with every concrete detail of the entities that act as signs, as objects, or as agents of semiosis, but only with the most salient patterns of relationship among these three roles.  In particular, the formal theory of signs does not consider all of the properties of the interpretive agent but only the more striking features of the impressions that signs make on a representative interpreter.  In its formal aspects, that impact or influence may be treated as just another sign, called the ''interpretant sign'', or the ''interpretant'' for short.  Such a 3-adic relation, among objects, signs, and interpretants, is called a ''[[sign relation]]''.

The term ''[[semiosis]]'' refers to any activity or process that involves signs.  Studies of semiosis that deal with its more abstract form are not concerned with every concrete detail of the entities that act as signs, as objects, or as agents of semiosis, but only with the most salient patterns of relationship among these three roles.  In particular, the formal theory of signs does not consider all of the properties of the interpretive agent but only the more striking features of the impressions that signs make on a representative interpreter.  In its formal aspects, that impact or influence may be treated as just another sign, called the ''interpretant sign'', or the ''interpretant'' for short.  Such a 3-adic relation, among objects, signs, and interpretants, is called a ''[[sign relation]]''.

&

&

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}), &

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}), &

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}), &

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}), &

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}), &

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}), &

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}) &

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}) &

The triples in <math>L_\operatorname{A}</math> represent the way that interpreter <math>\operatorname{A}</math> uses signs.  For example, the listing of the triple <math>(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime})</math> in <math>L_\operatorname{A}</math> represents the fact that <math>\operatorname{A}</math> uses <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math> to mean the same thing that <math>\operatorname{A}</math> uses <math>^{\backprime\backprime} \operatorname{u} ^{\prime\prime}</math> to mean, namely, <math>\operatorname{B}.</math>

The triples in <math>L_\operatorname{A}</math> represent the way that interpreter <math>\operatorname{A}</math> uses signs.  For example, the listing of the triple <math>(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime})</math> in <math>L_\operatorname{A}</math> represents the fact that <math>\operatorname{A}</math> uses <math>^{\backprime\backprime} \operatorname{B} ^{\prime\prime}</math> to mean the same thing that <math>\operatorname{A}</math> uses <math>^{\backprime\backprime} \operatorname{u} ^{\prime\prime}</math> to mean, namely, <math>\operatorname{B}.</math>

The relation '''L'''_B is the set of eight triples enumerated here:

The relation <math>L_\operatorname{B}</math> is the set of eight triples enumerated here:

: {(A, "A", "A"), (A, "A", "u"), (A, "u", "A"), (A, "u", "u"),

{| align="center" cellpadding="8" width="90%"

: &nbsp;(B, "B", "B"), (B, "B", "i"), (B, "i", "B"), (B, "i", "i")}.

(\operatorname{A}, \, ^{\backprime\backprime} \operatorname{A} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{A} ^{\prime\prime}), &

(\operatorname{A}, \, ^{\backprime\backprime} \operatorname{A} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}), &

(\operatorname{A}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{A} ^{\prime\prime}), &

(\operatorname{A}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{u} ^{\prime\prime}), &

&

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}), &

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{i} ^{\prime\prime}), &

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{i} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{B} ^{\prime\prime}), &

(\operatorname{B}, \, ^{\backprime\backprime} \operatorname{i} ^{\prime\prime}, \, ^{\backprime\backprime} \operatorname{i} ^{\prime\prime}) &

\}.

The triples in '''L'''_B represent the way that interpreter B uses signs.  For example, the listing of the triple (B, "i", "B") in '''L'''_B represents the fact that B uses "B" to mean the same thing that B uses "i" to mean, namely, B.

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'''_A and '''L'''_B are conveniently arranged in the form of ''[[relational database|relational data tables]]'', as follows:

The triples that make up the relations '''L'''_A and '''L'''_B are conveniently arranged in the form of ''[[relational database|relational data tables]]'', as follows: