Formal versus selforganised knowledge systems: A network approach
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 with respect to the classical one. The main result is the observation that formal systems of knowledge topologically behave similarly to selforganised systems.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 November 2011
 DOI:
 10.1016/j.physa.2011.06.074
 arXiv:
 arXiv:1105.1058
 Bibcode:
 2011PhyA..390.4652M
 Keywords:

 Physics  Physics and Society;
 Computer Science  Social and Information Networks;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 research paper