Re: Peirce List • Helmut Raulien
Cf: Relation Reduction • Examples of Projectively Reducible Relations

I constructed the “Ann and Bob” examples of sign relations back at the beginning of my Systems Engineering program when I had to explain how triadic sign relations would naturally come up in building intelligent systems possessed of a capacity for inquiry.

My advisor asked me for a simple, concrete, but not too trivial example of a sign relation and after cudgeling my wits for a while this is what fell out.  Up till then I had never much considered finite examples of sign relation as the cases arising in logic almost always have formal languages with infinite numbers of elements as their syntactic domains if not also infinite numbers of elements in their object domains.

The illustration at hand involves two sign relations:

• is the sign relation that captures how Ann interprets the signs in the set to denote the objects in
• is the sign relation that captures how Bob interprets the signs in the set to denote the objects in

Each of the sign relations, and contains eight triples of the form where is an object in the object domain is a sign in the sign domain and is an interpretant sign in the interpretant domain   These triples are called elementary or individual sign relations, as distinguished from the general sign relations that generally contain many sign relational triples.

If this much is clear we can move on next time to discuss the two types of reducibility and irreducibility that arise in semiotics.

To be continued …