1 I. INTRODUCTIO N Human language is unique among communication systems in nature it is socially learned and offers

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I. INTRODUCTION

Human language is unique among communication systems in nature: it is socially learned and offers

the potential for open communication because of its recursive constituent structure [1]. The structure

of this communication system is not only the result of biological ability evolution but also that of

cultural evolution of language itself [2]. In general, the research purpose of language evolution is:

when, where, and how human language came into being, changed, and died [3], with the objects

including the meaning of language, grammar, and other details [4-6].

Due to the lack of sufficient data support and the extremely slow speed of language evolution in

reality, the most commonly appliable method for historical research on language evolution is based on

computational model [7-9]. One research paradigm is inspired by the idea that language may arise

spontaneously in a communicative group and may hold some adaptive features [10]. This view has led

to a great deal of analysis of multi-agent models that simulate such communication and seek to infer

the attributes of emerging languages and their possible further evolution [11-13].

According to the mathematical realization of the components of the target language phenomenon,

existing language models can be classified to rule-based and equation-based models [14-15]. Rule-

Corresponding Author: Ning Cai (caining91@tsinghua.org.cn)

On Clustering Trend in Language Evolution Based on Dynamical

Behaviors of Multi-Agent Model

Yu Zhang1, Li Liu1, Chen Diao2, Ning Cai*1

1 School of Artificial Intelligence, Beijing University of Posts and Telecommunications, Beijing, China

E-mail: caining91@tsinghua.org.cn

2 School of Information Engineering, Ningxia University, Yinchuan, China

Abstract: Computer model has been extensively adopted to overcome the time limitation of language evolution by

transforming language theory into physical modeling mechanism, which helps to explore the general laws of the

evolution. In this paper, a multi-agent model is designed to simulate the evolution process of language in human

settlements, with the network topology being lattice. The language of each node in the lattice will evolve gradually

under the influence of its own fixed evolutionary direction and neighbors. According to the computational

experiment results, it is discovered that the state points of languages always converge into several clusters during

evolution process, which gives us an insight into language evolution.

Key words: Language Evolution, Multi-Agent Model, Clustering

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based models define concrete or abstract rules to describe or operate language components and related

behaviors, with the interrelation of these rules leading to evolution [16-17]. Equation-based models

tend to convert languages and related behaviors into mathematical equations, and mathematical

analysis and experimental or empirical verification of these equations enable equation-based models

to reasonably approximate the history of language evolution or forecast its future [18]. Many

computational models are proposed based on the above two frameworks. For example, some models

attribute the distribution of phonetic elements to self-organization in the communication process [19-

20], that is, the process in which the global pattern of the system is generated from the local interaction

of its components [21]. Some studies have also proved that the universality of language is naturally

generated through cultural transmission [22-24] or language games [25-28].

In this paper, we design a multi-agent model to simulate the evolution of language over time. First,

the basic unit of language transmission and exchange should be a human settlement and it will act as

an agent [29]. To construct the framework of language communication and variance, we take each

human settlement as a node in the network topology and construct the configuration of topology

between nodes inspired by ecological competition models. Each node in the network has two basic

attributes: weight and state, which correspond to the degree of influence of settlements and the

development state of language and culture respectively. In addition, connecting edge of any two nodes

has a basic attribute of edge weight, which represents the intensity of traffic flow between any two

settlements. As a basic rule of thumb, for example, the higher the weight of a node, the greater the

force it exerts on the surrounding nodes with which it is connected. Then, a language dynamics model

is designed to simulate the linguistic and cultural development of settlements by integrating relevant

principles of multi-disciplines [30], that is, the states of all nodes in the topological network are

iteratively changed through the dynamics model.

Based on the above model, we conducted computer simulation [31] experiments to study the

influence of configuration of topology, variation of state dimensions, and other factors on language

evolution and found an adaptive feature in language evolution. We conclude that this model reasonably

models the dynamics of language evolution by analyzing the feedback of experimental results and

combining relevant empirical conclusions. Moreover, it reveals the inherent commonality between

linguistic, physical, and biological phenomena, since the model itself and its mathematical principles

can reflect a more extensive and general background other than the domain of linguistics. In brief, this

innovative language evolution model enriches our mentality and technique of studying language

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evolution.

The rest of this paper is organized as follows. Sec. 2 elaborates and formulates the model and proves

the condition of relative stability theoretically. Four computational experiments are carried out to

explore the general laws of language evolution in Sec. 3. Finally, Sec. 4 draws the conclusion and

indicates future directions.

II. MODEL CONSTRUCTION

The unit of language evolution is residential settlement with fixed position, possibly being a city,

town, or a village. In ancient society, the communication between any two neighboring settlements

could only rely on the road between them because of the restriction of single form of communication.

Furthermore, the communication between non-adjacent settlements needs to go through multiple

transfer stations, without direct communication. Therefore, the network topology between settlements

must be a planar graph. For simplicity, it is assumed to be a regular lattice, as shown in Fig. 1:

FIGURE 1. Network topology diagram of settlements.

Nodes in the network topology represent settlements and edges represent roads between them. Since

the nodes are in the lattice, the number of each node is denoted by a dyadic array (). For any node

in the network, its language evolution mechanism can be summarized as the following formula:

1

























 (1)

In this formula,  denotes time, and  denotes the -dimensional state vector of the

settlement ( ) . Each entry of the state vector quantitatively corresponds to certain feature of the

language, and an instantaneous portrait of the evolution of language can be expressed by a dynamic

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摘要：

~1~I.INTRODUCTIONHumanlanguageisuniqueamongcommunicationsystemsinnature:itissociallylearnedandoffersthepotentialforopencommunicationbecauseofitsrecursiveconstituentstructure[1].Thestructureofthiscommunicationsystemisnotonlytheresultofbiologicalabilityevolutionbutalsothatofculturalevolutionoflanguage...

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