Formal vs self-organised knowledge systems: a network approach

TL;DR

This paper analyzes formal knowledge systems using network theory, revealing that they exhibit topological properties similar to self-organized systems, through comparison with citation networks and a new topological ordering.

Contribution

It introduces a novel topological ordering for directed acyclic graphs and compares formal systems with self-organized networks, highlighting their topological similarities.

Findings

Formal systems behave similarly to self-organized systems topologically.

A new topological ordering for directed acyclic graphs is proposed.

Comparison with citation networks and models supports the main observation.

Abstract

In this work we consider the topological analysis of symbolic formal systems in the framework of network theory. In particular we analyse the network extracted by Principia Mathematica of B. Russell and A.N. Whitehead, where the vertices are the statements and two statements are connected with a directed link if one statement is used to demonstrate the other one. We compare the obtained network with other directed acyclic graphs, such as a scientific citation network and a stochastic model. We also introduce a novel topological ordering for directed acyclic graphs and we discuss its properties in respect to the classical one. The main result is the observation that formal systems of knowledge topologically behave similarly to self-organised systems.