Primary Arithmetic as Semiotic System (concl.)

Let be the set of rooted trees and let be the 2‑element subset consisting of a rooted node and a rooted edge.  Simple intuition, or a simple inductive proof, will assure us that any rooted tree can be reduced by means of the axioms of the primary arithmetic to either a root node or a rooted edge.

For example, consider the reduction which proceeds as follows.

(16)

Regarded as a semiotic process, this amounts to a sequence of signs, every one after the first serving as an interpretant of its predecessor, ending in a final sign which may be taken as the canonical sign for their common object, in the upshot being the result of the computation process.

Simple as it is, the sequence exhibits the main features of any computation, namely, a semiotic process proceeding from an obscure sign to a clear sign of the same object, being in its aim and effect an action on behalf of clarification.

Resources

• Logical Graphs
• Survey of Animated Logical Graphs

cc: FB | Logical Graphs • Laws of Form • Ma^thstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science