ONT Re: Sign Relations
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Semiotic SIG,
Here are a couple of concrete examples of sign relations
that I use to illustrate the basic properties of the genus
in my dissertation. These examples were deliberately chosen
to be as simple as they possibly could and still be interesting,
or at least to fill out the most elementary features that the ilk
of sign relations in general can have. So please do not pick on them
for being too simple-minded, as that is the responsibility of their designer.
If you want complexer examples, well, I liberally have a gadshillion of them.
Indeed, up until the moment when one of my dissertation advisors asked me to
construct something approaching a minimal example, I had never even deigned
to consider any finite models that might happen to fall under the definition
of a sign relation. When this gets down to the business of language learning
and logical modeling, all of the serious examples of sign relations have
sign domains with infinite cardinalities. Peirce thought that the power
of the continuum was probably the minimum meaningful count, but I, in my
computable wisdom, will be content with countable infinities for a while.
We can start out by imagining that we take a sample of a fragment
of a dialogue between two people, A and B, in which their language
is restricted to just their own proper names, "A" and "B", plus the
first and second person pronouns, "I" and "you", which will here be
schematized as "i" and "u", respectively.
To specify a sign relation one has to give three domains,
the Object, Sign, Interpretant domains, schematized here
as O, S, I, respectively.
For this example, let us take the two sign relations, L(A) and L(B),
corresponding to the usages of the two "interpreters", A and B,
respectively.
| L(A) and L(B) are subsets of OxSxI,
| written here as L(A), L(B) c OxSxI,
| where O, S, I are given as follows:
|
| O = {A, B},
|
| S = {"A", "B", "i", "u"},
|
| I = {"A", "B", "i", "u"}.
|
| L(A) has the following eight triples
| of the form <o, s, i> in OxSxI:
|
| <A, "A", "A">
| <A, "A", "i">
| <A, "i", "A">
| <A, "i", "i">
| <B, "B", "B">
| <B, "B", "u">
| <B, "u", "B">
| <B, "u", "u">
|
| L(B) has the following eight triples
| of the form <o, s, i> in OxSxI:
|
| <A, "A", "A">
| <A, "A", "u">
| <A, "u", "A">
| <A, "u", "u">
| <B, "B", "B">
| <B, "B", "i">
| <B, "i", "B">
| <B, "i", "i">
That's the basic set-up. Next time I will discuss
the relevant properties of these two sign relations.
Jon Awbrey
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Sign Relations
http://suo.ieee.org/email/msg00729.html
http://suo.ieee.org/email/msg01224.html
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