Logic as a complex network

TL;DR

This paper introduces a network model representing logical implications as a complex network, which grows similarly to the BA model but with more realistic local referencing, exhibiting power law properties.

Contribution

The paper proposes a new network model for logical implications that references only local parts of the network, making it more realistic while maintaining power law characteristics.

Findings

The model exhibits power law degree distribution.

It is more realistic than the traditional BA model.

The network growth mimics logical implication structures.

Abstract

When we represent logical, connective implications by directed edges, the resulting set of directed edges can be regarded as a complex network. In this article, we compose a network model that represents a deductive-logic-like structure composed solely of implications. The proposed network model grows like the BA model reported by Barabasi and Albert [Science 286, 509 (1999)]. Though the BA model references the whole of the existing network when a node is added, our model references only part of the existing network. In this view, our model is more realistic than the BA model. However, it also exhibits power law characteristics.