Formalization of Weak Emergence in Multiagent Systems

This paper explores the concept of formalization of weak emergence in multi-agent systems. It discusses the motivation behind the research, explores related works, and critically analyzes an article by Claudia Szabo and Yong Meng Teo. The paper also discusses the application of emergence in a games model.

Formalization of Weak Emergence in Multiagent Systems
Venkata Sai Rohan Illindra
Department of Computer Science
University of Adelaide
[e-mail]
ABSTRACT
Modern systems are complex and composed of parts that are autonomous in their
interactions. Due to several agents and interactions in a system, emergent behavior can be
exhibited as either desirable or undesirable. As such, formalization is needed to identify the weak
emergence in multi-systems. Formalization is critical to evaluate each agent behavior and how
they are affecting the overall results of the whole system. Simulation is considered one of the
most effective approaches to getting emergence from a system. In this context, this paper
describes the concept of formalization of weak emergence in multi-agent systems. It begins with
a brief introduction which explains the motivation of the research. It then continues to explore
the related works in the field of emergence in multi-agent systems. The following part critically
analyzes the article by Zsabo and Meng Teo. The paper ends with the application of the concept
of emergence in a games model. The researchers concluded that emergence in multi-agent
systems is a fundamental field that tries to solve undesirable results in a complex system like AI,
and hence, developers need to use to verify systems.
KEYWORDS
Multi-agent, emergent behavior, complex systems, simulation
ACM Reference Format:
Sai Rohan IV, In Research Essay for Modelling and Analysis of Complex System Assignment

Changes made
I changed the structure according to the template.
Also, changed inline references to [1] style
Stated the article to be analyzed in the introduction section
Added more information in the case study analysis
1. Introduction
Traditionally, in system development, designers must have basic knowledge and purpose
of the system as well as any other possible situation that may affect the system in the future [1].
The systems have little or no autonomy in operations because of future uncertainties [2]. As
such, there is ever-grown system development due to complexities in systems in the bid to
control the emergence of unintended usage or misuse. In computer science, it has motivated an
increase in various techniques in software development. Therefore, modern systems have many
components that exhibit complex interplays and interconnections. Each of these agents is
autonomous based on their internal logic. The complexity exists because of agent independence
and interdependence [3]. Each of the agents in a system forms the component that is a functional
unit. When a system is made, initially the developer has intended purpose. However, at the time
of the system usage through the interaction of various agents, there might appear some issues in
use or misuse by the agents, which were not intentioned by the developer. In this regard, this
paper will analyze “Formalization of Weak Emergence in Multi-agent Systems” article by
Claudia Szabo and Yong Meng Teo.
1.1 Motivation
When a human can use any deceptive mechanism to take advantage over others. They use
pretense in performing a particular action or pretend not to know so as not to share. This is the

aspect that is exhibited by autonomous agents in multi-agent systems. That the agents can have
hidden actions, resources, or show decoy action to deceive. The paper will focus on evaluating
agents and deception emergence in a game system. As such, there is a need to assess emergence
in a traffic jam as various autonomous agents interact to get the solution.
1.2 Related Work
Relationships and interactions between agents’ cause emergence. Multi-agents are
components of a complex system which act dependently and independently [4]. Emergence is
unexpected behavior in systems which might be negative or positive. Each agent is autonomous
and has particular action and hence affects how the7y interact in a system. The aggregate
interaction between multi-agents may cause emergence in the system.
Although emergence elicits significant concern from developers, there is no definite
approach in evaluating the existence of emergence in the system. Szabo and Meng Tao well
explore emergence in systems in their article “Formalization of Weak Emergence in Multiagent
System” [5]. The report states that when the number of components, interactions, and
connections increase, the level of system complexity also increases. Thus, the article view
emergence from two points of views, including scientific and philosophical [5]. The distinction
between the two depends on the perspective on understanding the behavior of the component
where the philosophical emergence is subjective system behavior as opposed to the scientific
definition. Hence, to identify emergence, a researcher can use variable based, event-based, and
grammar-based approaches.
1.3 History of the Concept
The concept of emergence in multi-agents is not new. It was introduced in ancient Greeks
where it was termed as “the whole before the parts” [6]. The Greeks believed that properties that

do not arise from the addition of the behaviors of each component. Emergence is mainly found in
complex systems. There is no generally accepted definition of the term emergence in complex
systems.
In modern systems, emergence has gained much research owing complex systems in
computer science and software engineering. Developers know the software and the intended use
and application. However, there are situations that the software system may not function by the
developer’s specifications in each of the components. Therefore, emergence has caused systems
developments to be continuous to seal gaps likely to cause emergence.
2. Related Work
2.1 Emergence
According to Szabo and Meng Tao, emergence is defined in terms of science and
philosophy [5]. Philosophically, emergence is a subjective “unexpected behavior in complex
systems, the limitation of the observer’s knowledge, the tool employed, and the scale and level of
abstraction under which the system is observed. On the other hand, scientific perspective view
emergence as intrinsic to the system and an independent view of the system. Thus, emergence is
defined as irreducible properties of the whole system, which are associated with components that
aggregate to form a system. Also, Burmaoglu, Sartenaer, and Porter defined emergence can be
defined as the behavior in the process and during the reorganization process of a complex system
[7]. Moreover, the phenomena have been defined as the appearance of novelty as well as
something unpredictable, unexplainable, and cannot be described in its basic physical terms [8].
Overall, emergence phenomena are considered as the pattern in the results and identifiable in
their rights in a complex system. Though identifiable with a system, it is neither predictable nor
analyzable from the system.

2.2 Multi-Agent Systems
Agents are autonomous components of a system and are adaptable to the environmental
changes in the system [9]. A multi-agent system is made of various agents functioning as an
independent component of the whole. Thus, a complex system constitutes agents that exist at the
same time, share a resource, and interact with each other. In this context, a multi-agent system
can be formalized in the interaction between agents.
2.3 Inter-Relatedness Between the Concepts
Emergence is as a result of interaction between the various agents in the system [10].
Each agent acts in autonomy to achieve a particular result in the system. The results are
considered as the aggregate of all agents’ actions, which are controlled by the environment. At
the time of interaction, the actions of all agents can influence the results of the whole system
[11]. That is, even though the agents’ actions are within the set environment, their actions may
cause undesired results from the system. It can be explained by Lwhole – Lpart = Le, where the whole
is the complex system, and the part is the action of each component in the system. The agent to
agent action in a particular environment determines the whole result system, which might be
desirable or undesirable according to the system specifications. According to Szaba and Meng,
emergence involves chaos and novelty. Chaos is the type of interaction between different
entities. For instance, people at a cocktail party represent different entities interacting randomly.
The chaos emerges because there is no clear pattern or rules of interaction. In a cocktail party,
there is no single culture that prevails. Thus, no one knows how close or far away to stand next
to each other, when and whether to make eye contact or if it is good or wrong to use first or last
name when addressing the other person. In such a novel and more complex system, an emergent
order will occur. The emergent is unexpected and happens magically. In a cocktail party

anything can happen as a surprise, and every participant know where to hide or when to celebrate
a happy birthday. According to them, the results of the whole is dependent on the complexity of
the agent's interactions, which is determined by the set of rules in the system. The interaction
applies some rule and ignores others regarding agents’ interests.
3. Proposed Work
3.1 Emergence Formalism
3.1.1 Varieties and Levels of Emergence
Emergence occurs at various levels, including weak and strong [12]. To understand
whether emergence has occurred requires simulation of the system at both macro and micro
levels. Strong emergence cannot be deduced even in principle following the low-level domain of
the system while weak emergence is only unexpected, given the properties and principles of the
low-level domain of the system [13]. A nominal level was introduced to show that a macro
property in a system cannot exist in the micro properties. A strong emergence exists a
philosophical perspective of the emergence and is strongly emergent concerning a low-level
domain. Weak emergence exists in the scientific view of emergent emerge weakly concerning a
low-level domain. Strong emergent has strong effects than weak emergence.
Therefore, in defining the strong and weak emergence require modeling the system in a
multi-level hierarchy where rule and laws guide the interactions between agents [13]. Reason
being, the interactions that lead to emergence are associated with the multi-level hierarchy. The
whole system is referred to as the micro-level and the parts or agents that interact statically or
dynamically at the lower level are referred to micro-level. The sub-systems at the micro-level
can be viewed as systems on their own when looked at the causation factor and the shift between

the various levels in the system. From the micro-level, the whole encapsulates the parts during
interactions, as shown below.
3.1.2 Characteristics of Emergence
Characterization on whether the change is emergent or not requires abstractions at the
two levels of the system hierarchy [14]. That is the macro and micro level. The whole system is
represented as Lwhole, while the aggregate of the agents in the system is presented as Lsum. Thus,
system emergence state is the difference between the Lwhole - Lsum, which gives Le. Lwhole is the
behavior of the system when the parts are not interacting, and Lsum is the sum of the parts’
behavior without interaction. The system states are then measured when each agent n interactions
are taken in aggregate and measured against the whole state of the system regarding the agent's
interactions. Through simulation, all possible states of the system are calculated for possible
system states and to compare the state differences to get emergence. Emergence in a system is
characterized by state-space and degree of interactions of agents in micro-level.
3.1.3 Managing Emergence Behaviors
Although defining emergence of a complex system is critical, there exist underlying
issues [15]. First, finding the sum of all the individual agents’ behavior is challenging. Secondly,
simulating the system to determine the emergence is time-consuming as it involves repetitive
practice and abstraction of agents. Besides, a researcher is faced with forwarding and inverse

problems. When the emergence is identified, the challenge is to find the cause depending on
whether it is weak or strong emergence.
On the hand, emergence has been a significant concern in artificial intelligence. The
concepts of self-organization where agents in the system learn through action can result in
emergence of unintended learned behavior in the AI system. The phenomena of undesirable
emergence have led to caution in the development of intelligent systems. As a control measure to
emergence of undesirable behavior, developers have to carry out rigorous simulation of the
system to test the probability of emergence particularly the strong emergence which might not be
deductive by principle in the system.
3.1.4 Motivation
When a human can use any deceptive mechanism to take advantage over others. They use
pretense in performing a particular action or pretend not to know so as not to share. This is the
aspect that is exhibited by autonomous agents in multi-agent systems. That the agents can have
hidden actions, resources, or show decoy action to deceive. The paper will focus on evaluating
agents and deception emergence in a game system. As such, there is a need to assess emergence
in a traffic jam as various autonomous agents interact to get the solution.
3.2 Background and Overview
In this case, we consider the game and game encounter. In a competitive game, players
compete against each other, which is interaction. The game competition is carried out by the
defined rules, which is the strategy. The environment of the game defines what action each
player can take [16]. Therefore, when agents take a particular action simultaneously, their actions
are dependent on a combination of actions. The cumulative set of actions performed by all agents
influence the environment to change. The phenomena of changing the environment as a result of

certain cumulative actions by agents raise the question of how agents can influence the
environment if they all want to maximize their utility. The appropriate action to take is
dependent on the goal and the understanding of the actions that lead to emergent behavior. In this
case, the agents have negotiated to achieve a position that is favorable to them.
From the game above, agent I and agent J have the goal of gi and gj, respectively. Each of the
agents can perform or fail to act A and B, as shown below.

3.3 System formalism
The system can be formalized about the actions of the two agents. Agent i can choose to
perform action B, which will give a greater value. Hence, the action for agent i with high utility
is dependent on action by agent B. However; agent j can hide his action but inform agent i will
take action B, agent i may take action B that is delivering highest utility. Then, agent, i take
action A, which gives utility zero for agent i. Hence,
Utility agents = (action A, action B)
3.4 Proposed Process for Emergence Identification
The system will be simulated repeatedly identify the emergence. Each of the agents will
act independently and will be identified as i and j. Lsum and Lpart will be calculated from action A
and B, and the divergence in results over time will be Le (emergence).
4. Case Study Analysis
4.1 Concept Explanation When Modelled in a Multi-Agent System
Szabo and Meng Tao introduce the concept of emergence as the primary trend in
computer science. From the viewpoint of the agent in technologies, there exists

interconnectedness, uncertainty in some functions, intelligence, and developer role of
establishing the presence of emergence and determine whether is it beneficial or harmful. A
system can be abstracted to various functions performed by the relationship between agents. An
agent is independent and autonomous and hence has decision-making, control, and
communication capabilities. Thus, when individual functions of agents are aggregated can result
in equal or different results than the results of the sum of the whole system resulting in
emergence.
4.1.1 Overview
The article proposes an automated approach for the identification of emergent trends in a
system. It continues to show the benefit of the automated emergence identification system using
theory and experimentation. Therefore, through the application of their system, they show that it
reduces state-space through simulation of the rate of interaction between agents. In this regard,
the article uses a grammar-based formalization and process. The approach is based on the
abstraction of individual agents from the complexity of the system. As such, it seeks to reduce
the state-space explosion as the system increase in size while the number of agents and
interactions increase. Therefore, it proposes that to identify emergence using a grammar-based
approach, Le is calculated as the emergence of state property.
Thus, Le = Lwhole –Lsum.
Where Lwhole is the all possible system state agent, the interaction of agents in a particular
environment, Lsum, is the aggregation of all the actions of agents in the system.
The approach shows that the size of Lwhole depends on the rate of agent interactions and state
transition rules by the developer. The phenomena can be explained using different rules

modeling the traffic jam; that is, there is an entire system rule, or rules of interest while ignoring
others.
The case uses a flock of bird model to explore emergence in a multi-agent system using a
grammar-based approach. The modeling uses the bottom-up approach to explain the flocking
phenomena. In this case, the analysis begins with the behavior of each bird, which has a
cumulative effect on the whole system of birds. Weak emergence is observed when birds are
flocking together. For instance, a V-shaped is a physical property that emerges and allows a
flock of birds to migrate than when each of them migrates by themselves easily. The model of
flocking is determined by the interaction between the birds by each bird take the path relative to
its neighbor and hence, V-shaped phenomena. Thus, in such a multisystem, there are m various
types of n agents, which are (L)linked to each other in an environment (E). Notably, each agent
interacts with each other and with environment autonomously with a set of attributes. Therefore,
agents change states depending on the values of attributes at a particular time. As such, bird
interaction with each other and the environment regarding specific rules per bird in a particular
behavior rule given by:
Rule(condition): Sij (t) in connection to Sij(t + 1)
The phenomena in flocking of bird are replicated the computer systems, especially
artificial intelligence and software development. The developers are required to simulate the
system multiple time to have a high probability of emergence occurring. In modern technology
where AI is growing, determination of emergence is critical for any negative behavior in the
system.
4.1.2 Rules and Behaviors to Note

The flock of birds uses behavior exhibited when a group of birds is foraging. The bird
model has three rules, which include separation, alignment, and cohesion. Separation is for the
birds to avoid crowding, alignment means that the birds steer towards the direction of the
neighbor, and cohesion is steering towards the average position of neighbor. The generally,
determination of emergence is dependent on the assumptions that each agent is different from
each other and act autonomously. The interaction between the agent is dependent on the
environment set in the system and behavior rules.
5. Conclusion
Agent-based systems are complex and need thorough knowledge to predict emergence at
development and execution. There are various methods of formalizing emergence, but the most
appropriate one is the grammar system. Emergence is affected by the number of interactions
made by the agents in the system. Thus, the higher the interaction, the higher the possibility of
emergence to occur in a system.
Acknowledgment
The authors wish to thank Luong Ba Linh for discussions about this work.

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