Formal versus self-organised knowledge systems: A network approach

A.P. Masucci

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 23, 4652-4659

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 self-organised systems.

Keywords: Directed acyclic graph; Scale-free networks; Formal system; Citation; Topological ordering (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:23:p:4652-4659

DOI: 10.1016/j.physa.2011.06.074

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