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MANAGEMENT OF VIRTUAL SOCIETIES IN MAS ENVIRONMENT
IFAC MCPL 2007 The 4th International Federation of Automatic Control Conference on Management and Control of Production and Logistics September 27-30, Sibiu - Romania
MANAGEMENT OF VIRTUAL SOCIETIES IN MAS ENVIRONMENT Viktor Oravec, Baltazár Frankovič Institute of Informatics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 07 Bratislava, Slovakia {viktor.oravec,frankovic}@savba.sk
Abstract: Environmental engineering is emerging in multi-agent system research. There are numerous recent state-of-the-art publications defining short and long term challenges. One of these challenges addressed by this paper is incorporating knowledge system into multi-agent system environment. Experience management of agents’ virtual society as application knowledge system is introduced by this paper. This application enhances managerial properties of the environment. The paper also presents several application dependent problems in experience management, such as experience item description, ontology specification and similarity measurement with proof of optimality. Copyright © 2007 IFAC Keywords: agents, knowledge-base systems, environment architecture, management systems, modelling
1. INTRODUCTION
word of interest (Weyns et al., 2007). Each environment has its own processes. The set of executed processes depends on application. Valckenaers et al. (2007) present three types of applications, namely: emulation, interacting information system and adaptive information system. In emulation application, environment is offline emulator of the world of interest. Interacting information system communicates with the world of interest in real time. Adaptive information system is interacting information system dynamically adapting to the changes in the world of interest.
Multi-agent system (MAS) is the new paradigm for solving complex problems utilizing a distribution of computations among several autonomous, proactive, reactive and social computing systems. These four properties made MAS highly modular and flexible which is reflected by another emerging paradigm agent oriented software engineering. There are many publications considering and proving usefulness of agent approach in practical applications (Bloodsworth and Greenwood, 2005). Recent research in MAS is partly concentrating on multiagent system formalization (Zambonelli and Omicini, 2004) and on precise definition of the framework of its architecture (Weyns et al., 2007). The framework presented by Weyns et al. (2007) divides MAS into two parts, namely an agent system and an environment. Agent system can be viewed as a container for agents, and the environment as an instrument to manage them and support their “life”.
JADE and RETSINA are widely used agent's environments tested on many applications (JADE, 2007) (RETSINA, 2007). However, there are open problems still, while this paper addresses some of them. For example, JADE treats agents as single entities which are located in one of numerous containers located in an agent platform. Agents can travel around this virtual electronic network and form complex social structures; however, these structures are not presented explicitly. They can be recognized only by agreements and communication among agents; moreover, they are usually private to agents. Also, MAS infrastructure of RETSINA utilizes this approach; however RETSINA agents build agent system without implicitly defined environment.
Lack of formalism on the environment level of the multi-agent system results in emerging of a new research field called environmental engineering. This environment is divided into the following three levels: abstract, basic and interaction-mediation level. The main objective of the environment in a multi-agent system is to offer interaction and mediation between agents with an abstraction of a 689
According to a Weyn’s reference model of the environment studied in this paper lately, interactions and communication between agents are supported by the environment through communication, perception and interaction subsystems. From this point of view, the environment acts as mediator among agents. These tree subsystems in the environment can be used as monitors of agents’ behaviour as well. Since these interactions are problem solving oriented, their results are problem solutions of particular domain. Bergman (2002) studied complex problem solving deeply especially in internet-based applications. He introduces an experience management as an important tool for effective manipulating of complex problem solutions for further reuse. Bergman was oriented on problems with precise description; however, defined experience management framework can be used in multimedia knowledge management.
organisation, task, agent, knowledge, communication and design model. The organisation model describes setting where the knowledge system is deployed. The model is spread over the following six subsystems of the Weyn’s environment: synchronization, observation, interaction, perception, translation and communication. The synchronization, observation, translation, perception and interaction subsystems cover concepts of the world of interest taken into account by the knowledge system. These subsystems act as interfaces for agents and environment to the world of interest. On the other hand, the communication subsystem is message system for agents and describes agents in the agent system. The task model represents assignments fulfilled by executive subsystems of the knowledge system. These subsystems defined by environmental engineering, such as perception, interaction, synchronization and observation, are important for environment layer’s functionality. Described tasks are assigned to particular subsystems in the environment. However, there can be tasks related to special features of the environment not included in Weyn’s reference model, such as experience management addressed by this paper.
The main objective of this paper is to present experience management of virtual societies in a multi-agent system, which addresses the challenge of mapping knowledge in the environment of a multiagent system presented by Valckenaers et al. (2007). This paper addresses three experience management processes, namely experience item representation, storing in the domain ontology, and retrieval. This paper is divided into five sections. The first section is introduction with agent oriented engineering state-of-the-art. The next section introduces knowledge and knowledge management in the multi-agent system’s environment. The third section describes a virtual society using propositional logic. The following section addresses description of the domain ontology for virtual society formation process. The fifth section presents retrieval of the experience from the experience base. The paper is concluded by conclusion and future work.
The third model in the conceptual layer is agent model including enumeration of agents in knowledge systems. Note that in knowledge system’s agent model agent is an entity assigned to a task in the task model. Thus, agent model in the knowledge system is renamed to environmental entity model in the remaining part of the article. Each environmental entity has one or more tasks assigned, defined in the previously described task model. The knowledge represented in the knowledge system of the environment is described by knowledge model which is a part of a law model characterizing principles of the world of interest. Furthermore, State subsystem of the environment encompasses knowledge about the environment. Communication model describes interactions among environmental processes working with knowledge and fulfilling tasks defined by task model. Communication model is roughly defined by Weyns’ reference model. The last model is the design model which represents implementation of the knowledge system into the setting.
2. KNOWLEDGE IN THE MAS ENVIRONMENT One objective of multi-agent system’s environmental engineering is to implement knowledge into the environment to describe world of interest, environmental knowledge and the agent system. This implementation should have to follow environmental reference model (Weyns, 2007), which divides environment into several active and passive elements supporting communication between agent system and world of interest.
It is obvious from the previous paragraphs that the knowledge system is distributed over whole MAS environment, this is shown in the following figure (Figure Figure 1) utilizing interaction matrix. This figure depicts two types of boxes: solid and dashed. Solid boxes represent parts of the environment’s reference model, while dashed boxes encompass knowledge system models. Each token in the interaction matrix defines implementation of a part of the knowledge system’s model in the particular subsystem in the reference model. For example,
Environment should encompass own knowledge system which is reachable by agents through perceptions and interactions or through a knowledge interaction subsystem offering additional features to the environment and enlarging the above reference model. In general, the knowledge system model consists of three layers (Schreiber, 2003), namely contextual, conceptual and product layers. The three layers include the following six models:
690
Figure 2, conceptual description of structured agent society is presented. In this example, Society A is top-level society, consisting of three agents and two societies, namely Society B and Society C. The important result of this description is the hierarchical distribution of agents over nested societies.
knowledge model is implemented in Laws and State subsystems. However, design model is spread over each subsystem in the reference model, because each subsystem is involved in the knowledge system.
Laws State
Figure 2 Conceptual description of nested virtual agents’ societies.
Synchronization Observation Interaction Dynamics
Perception Communication
Translation
Figure 1 Relation matrix between subsystems of reference model of the environment and models of the knowledge system
Figure 3 Vertical cut of the multi-agent system of nested agents' societies. Interaction and mediation level is taken into account.
3. MANAGEMENT OF VIRTUAL SOCIETIES Agents in a multi-agent system form structured virtual societies with different organizations and purposes. Horling and Lesser (2005) present eight basic agent organizations, namely hierarchies, holarchies, coalitions, teams, federations, congregations, societies and matrix organizations. Each organization is based on a set of agents. However, it is obvious that agents can create more complex structures, where each organization consists of both agents and nested organizations. Note that the structure of organization can vary. Thus, agent system is modularised and encapsulated. In the following figure
Vertical cut over multi-agent system (Figure 3) shows that it is distributed over agent system and its environment. This is an important fact, because society structure is developed in the environment, not in the agent system; the latter is just a container encompassing all agents. Note that agent system can be distributed. Figure 3 also depicts relevant part of information flows in the society. Other information flows, such as communication with perception and interaction subsystems of the MAS environment included in the reference model, are precisely presented by Weyns et al. (2007) and have been omitted here. The fact that virtual societies are distributed over the agent system and its environment impacts the expansion of functionalities of the environment. Developed societies can be registered in the environment; the environment can manage them afterwards. In this point, two approaches to manage societies can be recognized, namely free and controlled. Free management of an agent society just manages existence of the society and does not control behaviour of agents in the agent system. On the other hand, controlled agents’ society management can control behaviour of agents through communication among agents and virtual societies. Controlling of agents and society behaviour are very important in intelligent systems because of negative emergence.
( Figure 2), an example of nested societies is presented.
In
the
Societies are built according to precisely defined problem which is the goal of the directive or 691
negotiation formation process. Agents in a society take actions which can be described by a plan. However, in negotiation processes, actions are usually generated ad hoc. In self interested agent system outcomes has to be distributed. The plans of actions and of outcomes’ distribution are properties of the society. Thus, society can be described by a concept with the following properties: • an activity defining the aim of the society; • a plan describing sequence of activities taken by entities in the society or distribution of the outcomes; • a set of entities located in the society; • a relation into upper level society. The entity concept encompasses both agents and societies. The term activity includes one of the following concepts: • an objective addressed by societies; • a task solved by agents, • an action executed by agents.
where the society includes two agents A2 , A3 and society S 2 is defined. This society has an objective to satisfy p2 proposition when p1 is satisfied. Also, the example defines optimal plan of actions to satisfy the objective of the society. The parent society is defined as well using the fourth element of society definition. Using propositional logic is very efficient because it can be easily translated into the ontology in the knowledge system and processed by computer, while being still readable by human.
4. ONTOLOGY FOR MANAGEMENT OF VIRTUAL SOCIETIES Virtual societies can be the results of complex problem solving processes, and thus they may be objects of the experience management system which stores problems and their solution in the experience base with other reusing knowledge. This experience management is a part of the knowledge system in the environment which manages virtual societies. This section presents a general ontology for the management of virtual society developed in Protégé. General ontology (Figure 4) for the virtual society management introduces the following five fundamental concepts: Context, Experience, Plan, Entity and Activity.
For mathematical description of society with an action plan, propositional logic can be used (Ditmarsh et al., 2003, Wooldridge and van der Hoek, 2005). Since societies are oriented towards actions, concurrent dynamic epistemic logic defined by Ditmarsh et al. (2003) is used properly. This logic defines coalition of agents as a set of agents. A sequence of actions can also be easily described by various operations. Sequential, parallel and conditional execution and testing of proposition are most important for our purposes. According to logic agents, such society can be described by the following sorted set of four elements:
(
)
S = Σ, F , F 0 , Σ 0S ,
(1)
where: • Σ denotes all agents and societies in the multiagent system; • F represents the set of all formulas in particular propositional logic; • F 0 represents the set of all formulas in the particular propositional logic including Ø; this means that the society has not defined a plan of actions; • Σ 0S defines the set of all societies existing in the multi-agent system and symbol Ø denotes that defined society S is the top-level society and has no parent society. Note that the second and the third elements represent activities of society S. However, the former element defines the aim of the society, and the latter introduces an optimal plan if there is any.
Figure 4 Ontology for virtual society experience management Entity represents any entity in the virtual society. This concept has two child concepts, namely Society and Agent. Both concepts have various properties which are mostly application dependent. Their important properties are hasObjective, hasPlan, hasEntity and finally hasParent. hasObjective is property of any Entity and Experience concepts. It defines the activities which are assigned to these concepts. With reference to Experience concept, it is a problem solved by the experience item. hasObjective property in the Entity concept means the activity assigned to the entity. hasParent property is assigned to Society concept addressing society where particular society is nested. Each society contains entities defined by the hasEntity property.
Example of the society description is in the following formula:
({S 2 , A2 , A3 }, [? p1 ] p 2 , [? p1 ; α1 ; α 2 ] p 2 , S 0 ) ,
(2)
692
lines 11-21 define the objective of this society. Lines 2, 3 and 4 define the content of the society. Plan is assigned in line 5 and objective of the society in line 6. Parent of this society is defined by lines 7-9.
Plan represents the plan associated to the entity in the ontology. This concept is generalization of two concepts, namely OutcomesDistribution and ActivityPlan. OutcomessDistribution directs distribution of the society outcome among entities. ActivityPlan includes sequence of activities performed by particular society. Also, ActivityPlan includes the hasActivity property which describes the plan performed by society using a propositional formula in the particular propositional logic.
The second part of Figure 5 introduces the objective of the society. The objective of this society is a transition from the state described by proposition p1 defined in line 20 to the state described by proposition p2 defined by lines 16 and 17. In line 20 the starting proposition of the transition is tested. This test is part of the condition defined in line 12.
Another significant concept in the virtual society experience management is Experience, with four essential properties, namely hasContext, hasObjective, hasSolver and hasEntity. hasContext defines the set of agents in the agent system. The context is very important, because problem solving is dependent on the set of entities which are used in the complex problem solving process. hasObjective represents a problem solved by entity defined by the hasEntity property. The last property of the Entity concept is optional hasSolver property defining an entity which defines the problem described by the particular individual of the Entity concept, usually the parent of the entity. If the hasSolver property is not present, then the instance of the Context concept encompasses every active entity in the environment. However, if hasSolver is presented, then the instance of the Context concept includes entities which are nested in the society defined by the hasSolver property.
5. SIMILARITY MEASUREMENT Experience items stored in the ontology have to be retrieved, and thus experience management system has to search for the most similar experience item in the experience base. Bergman’s model of the experience management utilized in this paper is similar to case base reasoning. Therefore, similarity measurement has to be defined as follows:
similarity : P × P → 0,1 ,
where P is a set of all possible problems. According to previously defined ontology, P is a Cartesian multiplication of all possible individuals of Context and Activity concepts. Similarity measurement describes similarity of a pair of problems. If both problems are the same, the similarity is equal to 1. If both problems have nothing in common, the similarity is equal to 0.
4.1. Example of the societys’ representation in the ontology
Experience item retrieval in virtual society is divided into the following three steps: • experience base is filtered by the objective of the actual problem; • applicability tests based on various rules, such as context intersection or agent similarity; • retrieval of the most similar experience for actual problem.
In the previous subsection the ontology for the virtual society experience management is defined. In this section, example of the society (2) representation in such ontology is presented utilizing RDF/XML code. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
CONDITION P2
(3)
5.1. Definition of similarity measurement Consider general entity similarity matrix Q in the multiagent system with (n, n) dimensions, where n is the number of entities in the MAS and Qij is inverted similarity between the i-th and j-th entities in the MAS. Moreover, Qi is the i-th line in the general entity similarity matrix. Consider a society content matrix S C which encompasses all contents of the societies stored in experience base, where S Cij ∈ {0,1} . If S Cij = 1 , then the j-th entity is included in the content of the i-th entity stored in the experience base. Note that S Ci represents content vector of the society described by the i-th experience item. The context of the actual problem is stored in pC vector with the same properties as the content vector of the society. Measuring includes the following steps: 1. Generate matix S M with dimensions of S C . 2. For each i-th experience in the experience base create similarity matrix as follows
Figure 5 Fragments of the societys’ representation in the ontology Due to lack of space, only two fragments (Figure 5) of the society representation are shown, namely basic definition of society and its objective. In Figure 5, lines 1-10 define the instance of society 1 (2). Then, 693
3. 4.
Create similarity vector of entities in the experience base:
s Mi = 1 −
5.
ontology of the virtual society derived from mathematical representation which presents idea of defining society structure in the environment rather than in an agent system. Experience management includes retrieval of experience item based on similarity measurement which is based on similarity between entities in a multi-agent system with presented proof of optimality.
~ mul (Q, S Ci ); S Ci ≤ pC Qi = , (4) 0; S Ci > pC where mul () is an element multiplication of two vectors or matrix and vector. For each j-th entity ~ (5) S Mij = max(Qij ). pCj .
1 pC
ACKNOWLEDGEMENT
n
∑S
Mij ; i
= 1..m ,
This work has been supported by the following projects: APVV LPP-0231-06, APVT-51-024604; VEGA 2/7101/27
(6)
j =1
where m is the number of items in the experience base. The most similar experience item has the lowest similarity coefficient in similarity vector s M .
REFERENCES Bergman R. (2002) Experience Management: Foundations, Development Methodology and Internet-Based Applications, Lecture Notes in Artificial Intelligence 2432, Springer, ISBN 3540-44191-3 Bloodsworth P. and Greenwood S. (2005) COSMOA an ontology-centric multi-agent system for coordinating medical responses to large-scale disasters, AI Communications 18, pp. 229-240, IOS Press. Ditmarsh, H.P. van, W. van der Hoek and B.P. Kooi, (2003) Concurrent Dynamic Epistemic Logic . In: V.F. Hendricks, K.F. Jørgensen, S.A. Pedersen (eds.), Knowledge Contributors , 105143. Synthese Library Series, volume 322. Kluwer Academic Publishers, 2003. Horling B. and Lesser V. (2005) A Survey of MultiAgent Organizational Paradigms, The Knowledge Engineering Review, Vol. 19, No 4, Cambridge University Press, pp. 281-316. JADE (2007) http://jade.tilab.com/ RETSINA (2007) http://www.cs.cmu.edu/~softagents/retsina.html Schreiber G. and Akkermans H., Anjewierden A., Hoog R. de, Shadbolt N., Van De Velde W., Wielinga B. (2002) Knowledge Engineering and Management The CommonKADS Methodology, The MIT Press, Cambridge (Massachusetts) and London (England), ISBN 0-262-19300-0. Valckenaers P., Sauter J., Sierra C. and RodriguezAguilar J. A. (2007) Application and environments for multi-agent systems, Journal of Autonoumous Agents and Multi-Agent Systems, Vol 14, pp. 61-85, Springer Weyns D., Omicini A. and Odell J. (2007) Environment as first class abstraction in multiagent systems, Journal of Autonoumous Agents and Multi-Agent Systems, Vol 14, pp. 530, DOI 10.1007/s10458-006-0012-0, Springer Wooldridge M. and van der Hoek W. (2005) On the Logic of Cooperation and Propositional Control. Artificial Intelligence, 164(1-2):81--119 Zambonelli F. and Omicini A. (2004) Challenges and Research Directions in Agent-Oriented Software Engineering, Journal of Autonoumous Agents and Multi-Agent Systems, Vol 9, pp. 253-283, Kluwer Academic Publishers
5.2. Proof of optimality The previously mentioned similarity measurement has to satisfy the following theorem: “Experience item is the best experience item in the experience base, while there is not any experience item which has lower similarity factor computed by the same similarity measurement.” This principle can be mathematically described by Pontryagin’s principle of minimum, well known in optimal control theory:
simfQ, pC , s C ) = min ( simf (Q, pC , sC )) , s C ∈S C
(8)
where s C is the content vector of the best society
and
simf : Q × M C × M C → 0,1
is a function
returning similarity factor between problem context vector and content vector of solutions considering general entity similarity matrix, where M C denotes set of all possible content and context vectors. Equation 8 can be rewritten in the following differential form:
simf (Q, pC , s C ) = min ( simf (Q, pC , s C + δ )) , (9) ∀δ
where δ is disturbance of the best content vector. Two types of disturbances can be considered, namely addition or loss of an entity in the content vector. In the case of loss of an entity, similarity factor will be similar or higher, because disturbed content vector has more zeros than the original vector, and thus it will have higher similarity factor. In the case of addition of an entity into the content of a society, similarity factor can decrease, because new features are added into the society. However, similarity measurement algorithm performs exhaustive search and thus there is not such experience item with lower similarity factor. CONCLUSIONS This paper presents a knowledge system distributed over the MAS environment, which manages virtual societies of agents. This knowledge system includes 694
MANAGEMENT OF VIRTUAL SOCIETIES IN MAS ENVIRONMENT Viktor Oravec, Baltazár Frankovič Institute of Informatics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 07 Bratislava, Slovakia {viktor.oravec,frankovic}@savba.sk
Abstract: Environmental engineering is emerging in multi-agent system research. There are numerous recent state-of-the-art publications defining short and long term challenges. One of these challenges addressed by this paper is incorporating knowledge system into multi-agent system environment. Experience management of agents’ virtual society as application knowledge system is introduced by this paper. This application enhances managerial properties of the environment. The paper also presents several application dependent problems in experience management, such as experience item description, ontology specification and similarity measurement with proof of optimality. Copyright © 2007 IFAC Keywords: agents, knowledge-base systems, environment architecture, management systems, modelling
1. INTRODUCTION
word of interest (Weyns et al., 2007). Each environment has its own processes. The set of executed processes depends on application. Valckenaers et al. (2007) present three types of applications, namely: emulation, interacting information system and adaptive information system. In emulation application, environment is offline emulator of the world of interest. Interacting information system communicates with the world of interest in real time. Adaptive information system is interacting information system dynamically adapting to the changes in the world of interest.
Multi-agent system (MAS) is the new paradigm for solving complex problems utilizing a distribution of computations among several autonomous, proactive, reactive and social computing systems. These four properties made MAS highly modular and flexible which is reflected by another emerging paradigm agent oriented software engineering. There are many publications considering and proving usefulness of agent approach in practical applications (Bloodsworth and Greenwood, 2005). Recent research in MAS is partly concentrating on multiagent system formalization (Zambonelli and Omicini, 2004) and on precise definition of the framework of its architecture (Weyns et al., 2007). The framework presented by Weyns et al. (2007) divides MAS into two parts, namely an agent system and an environment. Agent system can be viewed as a container for agents, and the environment as an instrument to manage them and support their “life”.
JADE and RETSINA are widely used agent's environments tested on many applications (JADE, 2007) (RETSINA, 2007). However, there are open problems still, while this paper addresses some of them. For example, JADE treats agents as single entities which are located in one of numerous containers located in an agent platform. Agents can travel around this virtual electronic network and form complex social structures; however, these structures are not presented explicitly. They can be recognized only by agreements and communication among agents; moreover, they are usually private to agents. Also, MAS infrastructure of RETSINA utilizes this approach; however RETSINA agents build agent system without implicitly defined environment.
Lack of formalism on the environment level of the multi-agent system results in emerging of a new research field called environmental engineering. This environment is divided into the following three levels: abstract, basic and interaction-mediation level. The main objective of the environment in a multi-agent system is to offer interaction and mediation between agents with an abstraction of a 689
According to a Weyn’s reference model of the environment studied in this paper lately, interactions and communication between agents are supported by the environment through communication, perception and interaction subsystems. From this point of view, the environment acts as mediator among agents. These tree subsystems in the environment can be used as monitors of agents’ behaviour as well. Since these interactions are problem solving oriented, their results are problem solutions of particular domain. Bergman (2002) studied complex problem solving deeply especially in internet-based applications. He introduces an experience management as an important tool for effective manipulating of complex problem solutions for further reuse. Bergman was oriented on problems with precise description; however, defined experience management framework can be used in multimedia knowledge management.
organisation, task, agent, knowledge, communication and design model. The organisation model describes setting where the knowledge system is deployed. The model is spread over the following six subsystems of the Weyn’s environment: synchronization, observation, interaction, perception, translation and communication. The synchronization, observation, translation, perception and interaction subsystems cover concepts of the world of interest taken into account by the knowledge system. These subsystems act as interfaces for agents and environment to the world of interest. On the other hand, the communication subsystem is message system for agents and describes agents in the agent system. The task model represents assignments fulfilled by executive subsystems of the knowledge system. These subsystems defined by environmental engineering, such as perception, interaction, synchronization and observation, are important for environment layer’s functionality. Described tasks are assigned to particular subsystems in the environment. However, there can be tasks related to special features of the environment not included in Weyn’s reference model, such as experience management addressed by this paper.
The main objective of this paper is to present experience management of virtual societies in a multi-agent system, which addresses the challenge of mapping knowledge in the environment of a multiagent system presented by Valckenaers et al. (2007). This paper addresses three experience management processes, namely experience item representation, storing in the domain ontology, and retrieval. This paper is divided into five sections. The first section is introduction with agent oriented engineering state-of-the-art. The next section introduces knowledge and knowledge management in the multi-agent system’s environment. The third section describes a virtual society using propositional logic. The following section addresses description of the domain ontology for virtual society formation process. The fifth section presents retrieval of the experience from the experience base. The paper is concluded by conclusion and future work.
The third model in the conceptual layer is agent model including enumeration of agents in knowledge systems. Note that in knowledge system’s agent model agent is an entity assigned to a task in the task model. Thus, agent model in the knowledge system is renamed to environmental entity model in the remaining part of the article. Each environmental entity has one or more tasks assigned, defined in the previously described task model. The knowledge represented in the knowledge system of the environment is described by knowledge model which is a part of a law model characterizing principles of the world of interest. Furthermore, State subsystem of the environment encompasses knowledge about the environment. Communication model describes interactions among environmental processes working with knowledge and fulfilling tasks defined by task model. Communication model is roughly defined by Weyns’ reference model. The last model is the design model which represents implementation of the knowledge system into the setting.
2. KNOWLEDGE IN THE MAS ENVIRONMENT One objective of multi-agent system’s environmental engineering is to implement knowledge into the environment to describe world of interest, environmental knowledge and the agent system. This implementation should have to follow environmental reference model (Weyns, 2007), which divides environment into several active and passive elements supporting communication between agent system and world of interest.
It is obvious from the previous paragraphs that the knowledge system is distributed over whole MAS environment, this is shown in the following figure (Figure Figure 1) utilizing interaction matrix. This figure depicts two types of boxes: solid and dashed. Solid boxes represent parts of the environment’s reference model, while dashed boxes encompass knowledge system models. Each token in the interaction matrix defines implementation of a part of the knowledge system’s model in the particular subsystem in the reference model. For example,
Environment should encompass own knowledge system which is reachable by agents through perceptions and interactions or through a knowledge interaction subsystem offering additional features to the environment and enlarging the above reference model. In general, the knowledge system model consists of three layers (Schreiber, 2003), namely contextual, conceptual and product layers. The three layers include the following six models:
690
Figure 2, conceptual description of structured agent society is presented. In this example, Society A is top-level society, consisting of three agents and two societies, namely Society B and Society C. The important result of this description is the hierarchical distribution of agents over nested societies.
knowledge model is implemented in Laws and State subsystems. However, design model is spread over each subsystem in the reference model, because each subsystem is involved in the knowledge system.
Laws State
Figure 2 Conceptual description of nested virtual agents’ societies.
Synchronization Observation Interaction Dynamics
Perception Communication
Translation
Figure 1 Relation matrix between subsystems of reference model of the environment and models of the knowledge system
Figure 3 Vertical cut of the multi-agent system of nested agents' societies. Interaction and mediation level is taken into account.
3. MANAGEMENT OF VIRTUAL SOCIETIES Agents in a multi-agent system form structured virtual societies with different organizations and purposes. Horling and Lesser (2005) present eight basic agent organizations, namely hierarchies, holarchies, coalitions, teams, federations, congregations, societies and matrix organizations. Each organization is based on a set of agents. However, it is obvious that agents can create more complex structures, where each organization consists of both agents and nested organizations. Note that the structure of organization can vary. Thus, agent system is modularised and encapsulated. In the following figure
Vertical cut over multi-agent system (Figure 3) shows that it is distributed over agent system and its environment. This is an important fact, because society structure is developed in the environment, not in the agent system; the latter is just a container encompassing all agents. Note that agent system can be distributed. Figure 3 also depicts relevant part of information flows in the society. Other information flows, such as communication with perception and interaction subsystems of the MAS environment included in the reference model, are precisely presented by Weyns et al. (2007) and have been omitted here. The fact that virtual societies are distributed over the agent system and its environment impacts the expansion of functionalities of the environment. Developed societies can be registered in the environment; the environment can manage them afterwards. In this point, two approaches to manage societies can be recognized, namely free and controlled. Free management of an agent society just manages existence of the society and does not control behaviour of agents in the agent system. On the other hand, controlled agents’ society management can control behaviour of agents through communication among agents and virtual societies. Controlling of agents and society behaviour are very important in intelligent systems because of negative emergence.
( Figure 2), an example of nested societies is presented.
In
the
Societies are built according to precisely defined problem which is the goal of the directive or 691
negotiation formation process. Agents in a society take actions which can be described by a plan. However, in negotiation processes, actions are usually generated ad hoc. In self interested agent system outcomes has to be distributed. The plans of actions and of outcomes’ distribution are properties of the society. Thus, society can be described by a concept with the following properties: • an activity defining the aim of the society; • a plan describing sequence of activities taken by entities in the society or distribution of the outcomes; • a set of entities located in the society; • a relation into upper level society. The entity concept encompasses both agents and societies. The term activity includes one of the following concepts: • an objective addressed by societies; • a task solved by agents, • an action executed by agents.
where the society includes two agents A2 , A3 and society S 2 is defined. This society has an objective to satisfy p2 proposition when p1 is satisfied. Also, the example defines optimal plan of actions to satisfy the objective of the society. The parent society is defined as well using the fourth element of society definition. Using propositional logic is very efficient because it can be easily translated into the ontology in the knowledge system and processed by computer, while being still readable by human.
4. ONTOLOGY FOR MANAGEMENT OF VIRTUAL SOCIETIES Virtual societies can be the results of complex problem solving processes, and thus they may be objects of the experience management system which stores problems and their solution in the experience base with other reusing knowledge. This experience management is a part of the knowledge system in the environment which manages virtual societies. This section presents a general ontology for the management of virtual society developed in Protégé. General ontology (Figure 4) for the virtual society management introduces the following five fundamental concepts: Context, Experience, Plan, Entity and Activity.
For mathematical description of society with an action plan, propositional logic can be used (Ditmarsh et al., 2003, Wooldridge and van der Hoek, 2005). Since societies are oriented towards actions, concurrent dynamic epistemic logic defined by Ditmarsh et al. (2003) is used properly. This logic defines coalition of agents as a set of agents. A sequence of actions can also be easily described by various operations. Sequential, parallel and conditional execution and testing of proposition are most important for our purposes. According to logic agents, such society can be described by the following sorted set of four elements:
(
)
S = Σ, F , F 0 , Σ 0S ,
(1)
where: • Σ denotes all agents and societies in the multiagent system; • F represents the set of all formulas in particular propositional logic; • F 0 represents the set of all formulas in the particular propositional logic including Ø; this means that the society has not defined a plan of actions; • Σ 0S defines the set of all societies existing in the multi-agent system and symbol Ø denotes that defined society S is the top-level society and has no parent society. Note that the second and the third elements represent activities of society S. However, the former element defines the aim of the society, and the latter introduces an optimal plan if there is any.
Figure 4 Ontology for virtual society experience management Entity represents any entity in the virtual society. This concept has two child concepts, namely Society and Agent. Both concepts have various properties which are mostly application dependent. Their important properties are hasObjective, hasPlan, hasEntity and finally hasParent. hasObjective is property of any Entity and Experience concepts. It defines the activities which are assigned to these concepts. With reference to Experience concept, it is a problem solved by the experience item. hasObjective property in the Entity concept means the activity assigned to the entity. hasParent property is assigned to Society concept addressing society where particular society is nested. Each society contains entities defined by the hasEntity property.
Example of the society description is in the following formula:
({S 2 , A2 , A3 }, [? p1 ] p 2 , [? p1 ; α1 ; α 2 ] p 2 , S 0 ) ,
(2)
692
lines 11-21 define the objective of this society. Lines 2, 3 and 4 define the content of the society. Plan is assigned in line 5 and objective of the society in line 6. Parent of this society is defined by lines 7-9.
Plan represents the plan associated to the entity in the ontology. This concept is generalization of two concepts, namely OutcomesDistribution and ActivityPlan. OutcomessDistribution directs distribution of the society outcome among entities. ActivityPlan includes sequence of activities performed by particular society. Also, ActivityPlan includes the hasActivity property which describes the plan performed by society using a propositional formula in the particular propositional logic.
The second part of Figure 5 introduces the objective of the society. The objective of this society is a transition from the state described by proposition p1 defined in line 20 to the state described by proposition p2 defined by lines 16 and 17. In line 20 the starting proposition of the transition is tested. This test is part of the condition defined in line 12.
Another significant concept in the virtual society experience management is Experience, with four essential properties, namely hasContext, hasObjective, hasSolver and hasEntity. hasContext defines the set of agents in the agent system. The context is very important, because problem solving is dependent on the set of entities which are used in the complex problem solving process. hasObjective represents a problem solved by entity defined by the hasEntity property. The last property of the Entity concept is optional hasSolver property defining an entity which defines the problem described by the particular individual of the Entity concept, usually the parent of the entity. If the hasSolver property is not present, then the instance of the Context concept encompasses every active entity in the environment. However, if hasSolver is presented, then the instance of the Context concept includes entities which are nested in the society defined by the hasSolver property.
5. SIMILARITY MEASUREMENT Experience items stored in the ontology have to be retrieved, and thus experience management system has to search for the most similar experience item in the experience base. Bergman’s model of the experience management utilized in this paper is similar to case base reasoning. Therefore, similarity measurement has to be defined as follows:
similarity : P × P → 0,1 ,
where P is a set of all possible problems. According to previously defined ontology, P is a Cartesian multiplication of all possible individuals of Context and Activity concepts. Similarity measurement describes similarity of a pair of problems. If both problems are the same, the similarity is equal to 1. If both problems have nothing in common, the similarity is equal to 0.
4.1. Example of the societys’ representation in the ontology
Experience item retrieval in virtual society is divided into the following three steps: • experience base is filtered by the objective of the actual problem; • applicability tests based on various rules, such as context intersection or agent similarity; • retrieval of the most similar experience for actual problem.
In the previous subsection the ontology for the virtual society experience management is defined. In this section, example of the society (2) representation in such ontology is presented utilizing RDF/XML code. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
(3)
5.1. Definition of similarity measurement Consider general entity similarity matrix Q in the multiagent system with (n, n) dimensions, where n is the number of entities in the MAS and Qij is inverted similarity between the i-th and j-th entities in the MAS. Moreover, Qi is the i-th line in the general entity similarity matrix. Consider a society content matrix S C which encompasses all contents of the societies stored in experience base, where S Cij ∈ {0,1} . If S Cij = 1 , then the j-th entity is included in the content of the i-th entity stored in the experience base. Note that S Ci represents content vector of the society described by the i-th experience item. The context of the actual problem is stored in pC vector with the same properties as the content vector of the society. Measuring includes the following steps: 1. Generate matix S M with dimensions of S C . 2. For each i-th experience in the experience base create similarity matrix as follows
Figure 5 Fragments of the societys’ representation in the ontology Due to lack of space, only two fragments (Figure 5) of the society representation are shown, namely basic definition of society and its objective. In Figure 5, lines 1-10 define the instance of society 1 (2). Then, 693
3. 4.
Create similarity vector of entities in the experience base:
s Mi = 1 −
5.
ontology of the virtual society derived from mathematical representation which presents idea of defining society structure in the environment rather than in an agent system. Experience management includes retrieval of experience item based on similarity measurement which is based on similarity between entities in a multi-agent system with presented proof of optimality.
~ mul (Q, S Ci ); S Ci ≤ pC Qi = , (4) 0; S Ci > pC where mul () is an element multiplication of two vectors or matrix and vector. For each j-th entity ~ (5) S Mij = max(Qij ). pCj .
1 pC
ACKNOWLEDGEMENT
n
∑S
Mij ; i
= 1..m ,
This work has been supported by the following projects: APVV LPP-0231-06, APVT-51-024604; VEGA 2/7101/27
(6)
j =1
where m is the number of items in the experience base. The most similar experience item has the lowest similarity coefficient in similarity vector s M .
REFERENCES Bergman R. (2002) Experience Management: Foundations, Development Methodology and Internet-Based Applications, Lecture Notes in Artificial Intelligence 2432, Springer, ISBN 3540-44191-3 Bloodsworth P. and Greenwood S. (2005) COSMOA an ontology-centric multi-agent system for coordinating medical responses to large-scale disasters, AI Communications 18, pp. 229-240, IOS Press. Ditmarsh, H.P. van, W. van der Hoek and B.P. Kooi, (2003) Concurrent Dynamic Epistemic Logic . In: V.F. Hendricks, K.F. Jørgensen, S.A. Pedersen (eds.), Knowledge Contributors , 105143. Synthese Library Series, volume 322. Kluwer Academic Publishers, 2003. Horling B. and Lesser V. (2005) A Survey of MultiAgent Organizational Paradigms, The Knowledge Engineering Review, Vol. 19, No 4, Cambridge University Press, pp. 281-316. JADE (2007) http://jade.tilab.com/ RETSINA (2007) http://www.cs.cmu.edu/~softagents/retsina.html Schreiber G. and Akkermans H., Anjewierden A., Hoog R. de, Shadbolt N., Van De Velde W., Wielinga B. (2002) Knowledge Engineering and Management The CommonKADS Methodology, The MIT Press, Cambridge (Massachusetts) and London (England), ISBN 0-262-19300-0. Valckenaers P., Sauter J., Sierra C. and RodriguezAguilar J. A. (2007) Application and environments for multi-agent systems, Journal of Autonoumous Agents and Multi-Agent Systems, Vol 14, pp. 61-85, Springer Weyns D., Omicini A. and Odell J. (2007) Environment as first class abstraction in multiagent systems, Journal of Autonoumous Agents and Multi-Agent Systems, Vol 14, pp. 530, DOI 10.1007/s10458-006-0012-0, Springer Wooldridge M. and van der Hoek W. (2005) On the Logic of Cooperation and Propositional Control. Artificial Intelligence, 164(1-2):81--119 Zambonelli F. and Omicini A. (2004) Challenges and Research Directions in Agent-Oriented Software Engineering, Journal of Autonoumous Agents and Multi-Agent Systems, Vol 9, pp. 253-283, Kluwer Academic Publishers
5.2. Proof of optimality The previously mentioned similarity measurement has to satisfy the following theorem: “Experience item is the best experience item in the experience base, while there is not any experience item which has lower similarity factor computed by the same similarity measurement.” This principle can be mathematically described by Pontryagin’s principle of minimum, well known in optimal control theory:
simfQ, pC , s C ) = min ( simf (Q, pC , sC )) , s C ∈S C
(8)
where s C is the content vector of the best society
and
simf : Q × M C × M C → 0,1
is a function
returning similarity factor between problem context vector and content vector of solutions considering general entity similarity matrix, where M C denotes set of all possible content and context vectors. Equation 8 can be rewritten in the following differential form:
simf (Q, pC , s C ) = min ( simf (Q, pC , s C + δ )) , (9) ∀δ
where δ is disturbance of the best content vector. Two types of disturbances can be considered, namely addition or loss of an entity in the content vector. In the case of loss of an entity, similarity factor will be similar or higher, because disturbed content vector has more zeros than the original vector, and thus it will have higher similarity factor. In the case of addition of an entity into the content of a society, similarity factor can decrease, because new features are added into the society. However, similarity measurement algorithm performs exhaustive search and thus there is not such experience item with lower similarity factor. CONCLUSIONS This paper presents a knowledge system distributed over the MAS environment, which manages virtual societies of agents. This knowledge system includes 694