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Lourival Paulino da Silva (2005)

A Formal Model for the Fifth Discipline

Journal of Artificial Societies and Social Simulation vol. 8, no. 3
<http://jasss.soc.surrey.ac.uk/8/3/6.html>

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Received: 09-Dec-2003    Accepted: 28-Mar-2005    Published: 30-Jun-2005


* Abstract

In this paper we present the main results of our research concerning the development of a formal model for the theory called The Fifth Discipline. Our model is based on a Multi-Agent Systems framework. The contributions of this work include a formal model for the Fifth Discipline, and analyses that highlight key features of that theory, namely the pressupositions that agents must be honest, cooperative, tenacious, and that trust is fundamental in the agents' interactions.

Keywords:
Multi-Agent Systems, Formal Methods, the Fifth Discipline, Organizational Modeling, Learning Organization, Organizational Learning, z

* Introduction

1.1
In this paper we outline a formalization, from a Multi-Agent Systems (MAS) perspective, of an Organizational Theory (OT). Based on this formalization, we highlight some relevant features of this OT: the models and underlying assumptions about an organization that implements this OT; their members and the interactions among members; and the interactions among the organization as a whole and its members.

1.2
The OT selected for this work is Senge's Fifth Discipline [Sen90], and the MAS formal framework that is adopted is SMART [dL01], which in turn uses the Z [Spi92] specification language to formally define MAS related concepts and terms.

1.3
The formal model outlined in this paper corresponds to our personal interpretation of Senge's work and depicts some characteristics of his theory, thus is not intended to be a full detailed translation of the Fifth Discipline theory into a formal model. Furthermore, due to space limitations we present here just an overview of our model. The interested reader should refer to Part II - A Detailed Version, where we describe this model in more detail.

1.4
The contributions of this work include not only a formal model for Senge's theory, but also analyses that indicate that several individual features play an important role in Senge's theory, namely agents must be honest, cooperative, tenacious, and trust is fundamental in the agents' interactions. We intend our formalization also to be an instance of what can be done to check an organization with respect to a specific organizational theory.

1.5
In the next section, we present an overview of the Fifth Discipline theory. Some excerpts of our formal model for this theory are outlined in section 3. In section 4, we discuss some properties of our model. We briefly discuss work that relates to our research in section 5. Finally, in section 6, we present our concluding remarks and discussion.

* Overview of the Fifth Discipline Theory

2.1
The field of OT relates to the structure, design and performance of organizations. The improvement of organizational effectiveness is the main goal of this field.

2.2
Different approaches have been developed through the last hundred years of research in OT, from the work of Taylor [Tay11] and Fayol[Fay49] to the Human Relations School, Theory of Behavior, Systems Theory and Contingency Theory. In this path, it is noticeable a change from prescriptive to descriptive and explanatory paradigms, as well as a change from the concept of man as homo economicus, motivated by material and monetary incentives, to more complex models that also include social motivations [Chi00,MSB99].

2.3
Following this trend, Organizational Learning has been growing in the last 40 years. This school focuses in the processes of learning, innovation, and the creation, storage, manipulation and transfer of knowledge. The purpose is the creation of increased organizational performance and adaptability. Differently from other schools, here, greater attention is paid to the management of intangible assets which may provide competitive advantage to organizations.

2.4
In our research we deal with one of the most recent and influential contributions to the school of Organizational Learning: The Fifth Discipline, presented by Senge in [Sen90], and referred in this work as the LO theory. According to Senge, a learning organization is the one that is "continually expanding its capacity to create its future". Here we outline this theory. A more detailed description can be found in Part II - A Detailed Version.

2.5
The LO theory focuses in ways to overcome learning deficiencies, which are identified as the main reasons for the relatively short life span of most organizations. The "methods, techniques and principles" recommended by Senge must be continually developed and are structured into five learning disciplines: Systems Thinking, Personal Mastery, Mental Models, Shared Vision and Team Learning.

2.6
Senge states that the five disciplines must be developed in consonance, in a coherent body of theory and practice, which is united by the Systems Thinking discipline. However, Systems Thinking also depends on the other four disciplines in order to develop its full potential.

2.7
The LO theory is a modern, influential and successful OT. Many important organizations have used it very successfully, including Shell, Harley-Davidson, Kyocera, and Federal Express.

* Modeling the Fifth Discipline as MAS

3.1
The area of MAS has gained increasing attention during the last decade. In order to provide a sound conceptual foundation to concepts involving agency and agent-based development, [dL01] built the SMART conceptual framework.

3.2
SMART was chosen in our research because it is a formal, unambiguous, structured, and extensible framework created to serve as a foundation for studying and building different agent oriented architectures. For example, in [BCV98, LyLLd01, MLd03] different models based on SMART are presented.

3.3
Similarly, in our work we have taken advantage of such SMART's features and have extended it to include new layers that specify agents that aggregate new capabilities and present increasing complexity.

3.4
SMART is specified in Z. Therefore, in appendix A of Part II - A Detailed Version we present introductory information concerning this notation. However, this basic introduction may not provide sufficient information for the reader with no previous experience with Z. In this case, we suggest [Spi92, Spi89, Jac97] for an introduction to this notation.

3.5
In SMART, the world is made of entities, which are specified as a collection of attributes. Moreover, entities are classified according to additional features they have: objects are entities with an associated collection of capabilities; agents have a set of goals; and autonomous agents have motivations. For example, specifications for objects and agents in SMART are presented below.


\begin{zed}Object \defs [ Entity | capableof \neq \setempty ]  Agent \defs [ Object| goals \neq \setempty ]\end{zed}

Learning Organization Agents

3.6
In our work we apply the same reasoning presented above and specify more complex agent types: agents that are capable of planning, performing roles in organizations, and agents that can be members of a Learning Organization. Furthermore, interactions among agents can be described. Thus, the formal specification of individual, collective, and organizational aspects can be performed. The construction of these types is based on those ones previously defined in SMART.

3.7
We note that this section contains only some excerpts of our model for the Fifth Discipline, just to provide an overview of what has been produced. Due to space limitation, most types and concepts are not presented in this work. The interested reader should refer to Part II - A Detailed Version, where we describe this model in more detail.

3.8
The diagram [3] presented in Figure 1 represents the basic schema structure of our formal model for the Fifth Discipline. In this diagram we have characterized the different layers that our model comprises presenting incremental definitions via refinement of agent types. Consequently, features that are present in the lower layers are incorporated by the types defined in the upper layers. In our model, the first layer that is capable of storing internal representations of the environment is the type StoreAgent [dL01]. In the next layer we introduce the type SAutoAgent that corresponds to an autonomous agent that is also capable of capturing and storing information as internal state. Moreover, since it has the ability to generate its own goals according to its motivations, it is an autonomous agent[4]. The perception of this agent is influenced by its goals and motivations, and its behavior is influenced by the environment and by its motivations. On top of this layer we define an agent with a set of plans associated with a set of goals: a planning agent. This agent type has also a set of resources that are required to instantiate an action within a plan. The actions of a planning agent are influenced by its motivations, the environment, and its plans. In the next layer we present the type organizational agent which participates in a set of organizations, performs some roles and has a set of plans that include both its personal plans and those related to the its roles. Similarly, the agent's set of goals include both the agent's goals and the goals associated with each of its roles.

3.9
In summary, on top of the SMART layers we have specified layers related to organizational capabilities, and on top of these, we have defined the layer related to the agent type that is capable of being member of a Learning Organization. Therefore, in this incremental definition we define a more specialized type of agent which corresponds to a formal specification of the requirements described in Senge's theory. The Learning Organization Agent - LearningOrgAgent - is an organizational agent, develops personal mastery, has mental models and develops systems thinking skills. Among the motivations of this agent we have: reducing creative tension and commitment to a clear perception of reality.
  
Figure 1. Formal model's basic schema structure.
This diagram represents the basic schema structure 
 of our formal model for the Fifth Discipline Theory.



 \begin{schema}{LearningOrgAgent}
 	OrgAgent
 \where
 	personalMasteryCapabilities \neq \emptyset \\
 	mentalModelsCapabilities \neq \emptyset \\
 	systemsThinkingCapabilities \neq \emptyset \\
 	learningTeamCapabilities \neq \emptyset \\
 	buildingSharedVisionCapabilities \neq \emptyset \\
 	personalMasteryCapabilities \subset capableof \\
 	mentalModelsCapabilities \subset capableof \\
 	systemsThinkingCapabilities \subset capableof \\
 	learningTeamCapabilities \subset capableof \\
 	buildingSharedVisionCapabilities \subset capableof
\end{schema}

3.10
Consequently, we define that a LearningOrgAgent develops all of Senge's disciplines. Based on its motivations, on the principles and actions related to each discipline, a given agent develops new capabilities to act. Moreover, the agent's guiding ideas are consistent with all of its goals. In our model we divide Senge's disciplines in two groups: intra-personal and inter-personal, according to the type of skills that such disciplines allow the agent to develop. The first group mainly deals with the agent's internal states and representations, and the second deals with interactions among Learning Organization Agents.



 \begin{schema}{LearningOrgAgentAndDisciplines}
 	LearningOrgAgent \\
 	improveIntraPersonal : \power Motivation \cross \power Action \cross  \\
 \t1	IntraPersonalDisciplines \fun \power Action \\
 	improveInterPersonal : \power Motivation \cross \power Action \cross \\
 \t1	InterPersonalDisciplines \fun \power Action \\
 	personalmastery : PersonalMastery \\
 	mentalmodels : MentalModel \\
 	systemsthinkingskill : SystemsThinking
 \where
 	\exists_1 gi : GuidingIdea | gi = ownguidingideas @ \\
 \t1	(isVisionGoalConsistent (gi.visions, allgoals) = yes  \land \\
 \t1	isPurposeGoalConsistent (gi.purposes, allgoals) = yes \land \\
 \t1	isValueGoalConsistent (gi.values, allgoals) = yes) \\
 	(mapset ~ trifirst) (\dom improveIntraPersonal) = \{ motivations \} \\
 	(mapset ~ trisecond) (\dom improveIntraPersonal) = \{ capableof \} \\
 	(mapset ~ trifirst) (\dom improveInterPersonal) = \{	motivations \} \\
 	(mapset ~ trisecond) (\dom improveInterPersonal) = \{capableof \} \\
 	\ran improveIntraPersonal \neq \emptyset \land
 	\ran improveInterPersonal \neq \emptyset
\end{schema}

The Learning Organization Model

3.11
Initially, we discuss how some basic types used in the definition of a Learning Organization, e.g.: groups, teams organizations and formal organizations, are defined in our model. A group is a set of individuals that share a set of resources. Thus, in such a group there is no need for a joint commitment towards a joint goal. A team is a group where there is a set of goals that is shared among its members. In a learning team all members are agents of the type LearningOrgAgent and it is possible to develop team's guiding ideas that are shared among its members. An organization comprises an organizational structure, sets of teams, roles, norms, and organizational goals. The structure of an organization is specified as a connected graph in which the node set corresponds to teams and the edge set corresponds to relationships among the teams. Roles are specified as sets of actions that must be performed, sets of goals, sets of resources that an agent, while performing this role, has permission to manage, and a level of organizational autonomy. This level defines whether the agent performing such role has some freedom to define new tasks in order to achieve the goals associated with the role (as stipulated in norms), or even to change part of the goals, or no freedom at all. We also define that an organization is formal if there are defined organizational positions and norms defined in its context, and each member in the organization performs at least one role.

3.12
We specify a Learning Organization as a type of formal organization in which all teams are learning teams. In summary, the LearningOrg schema specifies, via schema inclusion, that a Learning Organization is such that it has structure, roles, norms that permit that all teams develop the team learning discipline. Moreover, every agent in the organization develops its personal mastery, reflects on their mental models, have systems thinking skills, collectively develop shared visions, and perform roles in the organization.

3.13
The reference to sharedvision.sharedvisions gives access to the organizational shared vision. We require that this set is non-empty, ie, a Learning Organization must develop shared visions. In addition, sharedvision.learningteams is restricted so that the teams that produce such visions are exactly the teams that constitute the organization.



 \begin{schema}{LearningOrg}
 	FormalOrg \\
 	learningteams : \power LearningTeam \\
 	sharedvision : SharedVision
 \where
 	sharedvision.learningteams = learningteams \\
 	sharedvision.sharedvisions \neq \emptyset \\
 	\forall lt : LearningTeam | lt \in learningteams @ \\
 \t1	(\exists_1 te : Team | te \in teams @ ( 
   	\#(te.membersgroup) = 0 \land \\
 \t1	te.resources = lt.resources \land \\
 \t1	te.commongoals = lt.commongoals \land \\
 \t1	te.teamguidingideas = lt.teamguidingideas \land \\
 \t1	te.commonplans = lt.commonplans \land \\
 \t1	te = (\lambda LearningTeam @ \theta Team) ~ lt)) \\
 	\forall lt : LearningTeam | lt \in learningteams @ \\
 \t1	(\forall la : LearningOrgAgent | la \in lt.learningmembers @\\
 \t1 (\exists r : Role | r \in roles @
   	perform (la, r, regset) = pos)) \\
 	\# teams = \# learningteams
\end{schema}

Interactions, Knowledge and Mental Models

3.14
In Part II - A Detailed Version we present a formalization for some of the processes involving interactions among agents of type LearningOrgAgent and how these interactions affect their knowledge and mental models. Here we just present a brief overview of these processes.

3.15
In our model agents communicate using messages that may carry information about some specific entity or about the environment in general. We assume that all communications occur under a given conversational context that may involve agents' beliefs or goals. In addition, these messages are interpreted by the agents in accordance with their mental models, thus producing internal views. An agent is able to recall views from its memory or to infer views that were not previously stored in it. Agents are also capable of producing messages that are influenced by their mental models.

3.16
We assume that an agent's mental models include its knowledge and beliefs. In our model an agent knows a view if it can be recalled from its memory or if the agent can infer it from the views contained in such memory. Furthermore, an agent capable of interacting has knowledge, extracts, interprets, produces, and exposes messages.

3.17
We also define that the agents interact in sequences of messages and that conversation sessions are composed of sequences of interactions. As we are studying Senge's theory, there are two types of sessions that we are interested in modeling: dialogs and discussions. In our model the agents involved in these sessions are members of learning teams. They perform two alternate roles in these interactions: sender or receiver. This is a broadcast model, so that at a given interaction just one agent may perform the sender role, while the others perform receivers roles. We also require that all members perform the sender role at least once in a given session.

* Properties of the Formal Model

4.1
In this section we investigate some characteristics of the model that we have built for Senge's theory [5].

TRUST Is Necessary for the Formalized Fifth Discipline

4.2
We argue that it is not possible to build a shared set of goals (similarly for visions, values, purposes) if the agents involved in the process do not trust each other.

4.3
First we need some definitions.
  1. An agent ai is trustAgent if it exposes only information that it believes or knows, otherwise it is a nonTrustAgent.
  2. Agent ai is believer if, in the absence of previous interactions with a particular agent aj, ai assumes by default a trustAgent model of aj.
  3. An interaction among agents ai and aj is TRUST if, during this interaction, ai has in its mental models a trustAgent model of aj and, reciprocally, if aj has in its mental models a trustAgent model of ai.
  4. An agent may revise its trustAgent model of its partner to nonTrustAgent if it is able to perceive that there is no consistency between its partner's exposed mental models, proposals (messages), agreements, and performed actions.
  5. A dialog/discussion session involving agents ai and aj successfully produces a set goals of shared goals if at the end of the session all these holds:
    • ai believes in goals and
    • aj believes in goals and
    • ai believes that aj believes in aj's interpretation of goals and
    • aj believes that ai believes in ai's interpretation of goals

4.4
The context of analysis involves two agents ai and aj and an initial sequence of sending and receiving messages performed by both agents in order to formulate a set of goals which both agree upon. Our initial hypotheses include:

(h0). We suppose that there are no records of previous interactions among ai and aj.
(h1). We suppose that both ai and aj are believer agents.

4.5
Let us consider the following process:
  1. Agent ai sends message mi. Thus, first, ai has exposed message mi. Then, the received message is interpreted by aj.
  2. According to (h1), aj is a believer agent, therefore it believes that ai believes in mi.
  3. Thus, aj believes that ai believes in mi, ie, that ai believes that the state of affairs in the environment corresponds to the information contained in mi and aj may proceed and drive its reasoning based on this belief. After this step, aj may send message mj regarding this dialog/discussion session.
  4. Similarly, ai believes that aj believes in what is stated in mj. We may assume that this process proceeds through several interactions involving negotiation/argumentation, so that when the session is considered finished by both ai and aj, each agent will have a richer model about the beliefs of the corresponding partner, in particular concerning goals.

4.6
Regarding the set of shared goals, there are two possibilities at the end of the session: a set was built, or there was no agreement about shared goals. Here, we suppose that there was an agreement about a set of goals goals. Therefore, if ai and aj at the end of the session still model the corresponding partner as trustAgent we can affirm that ai believes that aj believes in its interpretation of the goal goals, and that aj believes that ai believes in its interpretation of the goal goals. If, however, at the end of the session, at least one of ai or aj has revised its partner's trustAgent model to nonTrustAgent, then one of our two previous assertions will not hold, and therefore it will not be possible to build a goals set.

Agents Must Be trustAgent

4.7
One formal formal term that we present in detail in Part II - A Detailed Version is ExposedBelief, which is a type of the agent's beliefs. These are stored in the agent's memory. In addition, in our formal model for Mental Models, we introduce the function advocacy. According to this function, the agent has motivations and performs actions so as to expose its beliefs and reasoning. Therefore, the agent in our model is a trustAgent, ie, it exposes only information that it believes or knows.

Agents' Motivations and Disciplines Must Be Consistent

4.8
First, in our formalization of Mental Models, the reflection and advocacy functions depend on the agent's motivations. In the case of the Personal Mastery discipline, the agent's personalvision, developguidingideas, enhancerealityvisions, clarifypersonalvisions, and creativetension functions are dependent on the agent's motivations.

4.9
The formalization of the Team Learning discipline introduces a set of actions and protocols, among them inquiry and advocacy which, as showed above in the considerations about Mental Models, are influenced by the agent's motivations. In addition, there is also the function developdialogdiscussactions, which also depends on the motivations of the agent.

4.10
As for the Systems Thinking discipline, we have the potentialstatesanalyser function which depends on PersonalVision which, in its turn, depends on the agent's motivations.

4.11
Finally, the Shared Vision discipline is developed by teams of agents that construct agreements via dialogdiscuss function, which uses dialogdiscussactions actions. The development of these actions depend on the agents' motivations. Thus, in summary, an agent that develops the five disciplines must have motivations that are consistent with the actions and protocols defined in each of the mentioned disciplines.

Agents Must Be tenacious

4.12
Following the specification of the LearningOrgAgent schema, such type of agent develops the five disciplines independently of any temporal considerations, ie, the disciplines determines the way the agent thinks, acts and interacts. This is a consequence of the fact that for every interaction (with the environment or with another agent) the learningorgperceives function is used to produce the agent's percepts. This function is affected by the agent's mental models and guiding ideas. Guiding ideas result from the agent's personal mastery and include vision, purpose and values. Accordingly, the agent's action selection function, learningorgact, is affected by Mental Models, Personal Mastery, and Systems Thinking. In addition, the learning organization model, presented in LearnOrg, requires that every team in the organization is a learning team and the organization must build a set of shared visions. Therefore, all disciplines must be continuously developed by the agents.

Agents Must Be cooperative

4.13
According to [Wei01], a cooperation is a type of coordination among non antagonistic agents in which the participants succeed or fail together. In contrast, in a competition the success of one participant implies the failure of others.

4.14
In our formalization of the Mental Models discipline we require that the agent exposes its beliefs so that, in a team of agents, each agent learn the others' mental models. This is also true for building shared vision.

4.15
If we consider that an "index" of success of a learning organization is to what degree it is able to develop shared visions, and that this is a collective achievement, then we conclude that, in fact, the learning organization represents a cooperative scenario: agents succeed (or fail) together in the process of shared visions construction.

4.20
In a competitive scenario an agent exposes its mental models only if it believes that by doing so it will have some type of benefit.

Organizational Change Emerges from Individual's Motivations

4.16
According to our model, all agents in the organization develop the five disciplines and the disciplines determine how the agents think, act and interact. We also know that the development of the disciplines by a given agent is influenced by its motivations. Moreover, in Part II - A Detailed Version we show that shared goals, values, and visions, may emerge from interactions among agents and also depend on the agents development of the disciplines. Taking into account that one of the indicators of a given organizational state is its current set of shared goals, values, and visions; and that the outcomes produced by the organization result from agent's actions, we conclude that organizational change emerge from individual motivations.

Low Turn-Over Is Required in the Organization

4.17
The interaction process described in our model presents a situation where there are no changes in the agents that are members of the team during all the process. However, if we take changes in team membership into account, it is possible to observe that the interaction process underlying the construction of shared vision and shared mental models is affected as follows.

4.18
Let us consider a team with n members.

4.19
We show in Part II - A Detailed Version that at least n rounds of interactions are required so that each agent has the opportunity to play the role of sender.

4.20
Suppose that in round k, with k < n , k agents have already played the sender role when a new agent enters the group. Now the group has n + 1 members and at least n + 1 rounds would be required to allow the new member to play the sender role. However, in this case the new member also needs to play the receiver role for all the k presentations that occurred before he was a member of the team. Thus, at least k + n + 1 rounds are required for each new agent that becomes a member of the team in a given round k.

4.21
Now, considering the case where the new agent substitutes a former member of the team, we notice that k + n rounds are required for each new agent that substitutes a member of the team in a given round k.

4.22
Hence, the more frequent inclusions or substitutions of members of a team, the less efficient is the process of producing common knowledge via interactions.

4.23
In fact, for each agent in the team a certain amount of time is spent in modeling the others mental models and visions. If there is a high frequency of turn-over in the teams, all this effort may be wasted. >

Bounded Number of Members in Learning Teams

4.24
In order to improve the efficiency of the interaction process, the number of members in a given team must be bounded. Otherwise, teams with a large number of members will have to spend too much time deliberating, even if the agent population is constant [7]. Thus, in order to cope with this complexity, the learning organization must be subdivided in a number of teams and must also define an upper limit for the size of its teams.

* Related Work

5.1
Formalizations for the organizational theory Organization in Action (OA) [Tho67] are presented in [KP99] and [MH96]. Similarly to the work reported in this paper, parts of a discursive theory are revised using formal methods. In [KP99], first order predicate logic is used to study the underlying argumentation structure for the propositions of the OA theory. On the other hand, a multi-agent modal logic developed by the authors in [MH96], is used to achieve goals that are similar to the ones mentioned above, and, additionally, to investigate the expressive power and applicability of this logic for the formalization of a discursive theory. The formal model presented in this paper uses the Z notation to build a structured framework that can be used to study Senge's theory and also to investigate hybrid organizations, involving both human and computational agents.

5.2
In [Lin98] the investigation and design of organizations that require a high level of reliability is presented. The approach presented in that work is a generalization of the Contingency Theory [LL67] of administration: the effect of the environment on the organizational performance and the corresponding implications on its structure. Differently, the investigation of organizational structures is beyond the scope of this work, as Senge does not specify them in detail in his theory. In the model presented here, we decided to specify the organizational structure as a graph in which each team is represented by a node, and relationships among teams are represented by edges. However, in our model different organizational structures could have been specified instead.

5.3
The social dilemma involving voluntary cooperation among individuals confronted with conflicting time and effort options is the focus of the work reported in [HG98]. The individual can contribute to build a common good or, alternatively, it may decide to take advantage of the efforts of the other individuals. In the model presented in this paper, the shared vision discipline involves a process in which shared high level goals have to emerge. In this process the motivation of each agent underlies its decision to adopt a set of shared goals. The existence of conflicting time and effort options for a given agent could imply the absence of a motivation for this agent to adopt a shared goal or shared vision. However, in our formal model a learning organization has to develop a shared vision, in a process that involves all agents in the organization. Therefore, confronted with such dilemmas, in our model for the Fifth Discipline the agents choose to cooperate.

5.4
In [CP98] a type of agent, called WebBot is investigated. This agent performs tasks autonomously, acting as an assistent for humans or other WebBots). That work studies the effect of the honesty of the WebBot concerning the individual and collective organizational behavior. Similarly, in our model one of the features that plays an important role is the honesty of the agent in its interactions in a learning organization. In fact, we show that in this model trust interactions among agents are necessary to build a learning organization.

5.5
The goal of the work presented in [YS99] is to study a role based agent-oriented conceptual framework in order to model workflow. In that case, business processes are viewed as a collection of problem solvers autonomous agents that interact when faced with interdependencies. Workflow coordination is achieved via agent communication. In that work, the organizational model results from the definition of organizational roles and description of the coordination and agent performance while performing a given role. Therefore, that model focuses in organizational processes, while our model is based on a specific organizational theory.

5.6
In [K. 99] multi-agent learning is investigated. That work is based on an Organizational Learning approach based on [Arg77] in which four types of learning are considered. The first is called individual single loop learning and enhances performance in the scope of an individual norm. The second, individual double loop learning, enhances performance via changes in an individual norm. The third, known as organizational single loop learning improves performance in the scope of an organizational norm. Finally, the fourth is named organizational double loop learning and improves performance via changes in an organizational norm. Similarly to the work presented in this paper, [K. 99] also presents a computational model that is inspired by an organizational theory associated to the Organizational Learning approach. In that case, however, Machine Learning and genetic algorithms techniques are used instead, to investigate the computational performance in processes involving multi-agent learning via implementation of concepts defined in an organizational theory. Nonetheless, we note that some of the concepts of [Arg77] may be mapped to concepts in Senge's theory. For example, individual and organizational double loop learning may be compared to personal mastery and shared vision, respectively, in the Fifth Discipline.

5.7
In [HSB02] a model for the specification of multi-agent organizations is presented. This model focuses on functional, structural and deontic aspects. The structure is related to the concepts of role, relationships among roles and groups. The functional aspect includes the concepts of global plans and missions that are structured in a type of goal decomposition tree. Functional and structural aspects are independent so that changes in the functional dimension do not require changes in the organizational structure. The only dimension that has to be adapted is the deontic, in order to reflect the modifications on the other two dimensions. Considering the work reported in this paper we note that the concepts of global missions and goals are similar to the concept of shared guiding ideas in our formal model. However, [HSB02] specifies a structure that associates global missions and plans to lower level goals. Instead, in our model, the development of shared guiding ideas is dynamic and results from interactions among agents.

5.8
In summary, some of the papers mentioned above deal with computational tools in general, and MAS technology in particular to model or simulate organizations, or use formal methods to investigate characteristics of a particular organizational theory. Other papers use organizational theories concepts to design models that can be used to implement computational systems or build MAS frameworks. Therefore, there are similarities between our work and the above mentioned research. However, the novelty of our work is the use of a Software Engineering method to build a formal model based on an organizational theory. Moreover, our model is founded on a MAS formal framework, so that our model represents a perspective on the implementation of the Fifth Discipline in the context of a MAS framework. This model presents a formalization for the main concepts of Senge's theory and, as a consequence, it is not restricted to particular organizational aspects like: coordination, team work, cooperation. We also note that in our formal model there are no constraints concerning the representation of different types of agents, so that organizations composed of human agents, computational agents, or both, can be modeled.

* Discussion

6.1
In this work, we presented an overview of the Fifth Discipline theory and outlined a formalization of this theory in the context of a MAS formal framework. In this section we discuss some issues regarding the formalization process of Senge's theory and issues concerning the properties of the formal model presented here.

6.2
Initially, we point out that during the formalization process we observed some situations where the main reference for the LO theory [Sen90] presented some concepts in an ambiguous way. For example, Senge states in [Sen90, p. 147] that goals and objectives are distinct from visions. However, in another part of the book [Sen90, p. 149] he affirms that a vision corresponds to a specific destination, a concrete image of the desired future. In our work clear definitions are required for every concept, thus we consider that visions, either personal or shared, correspond to goals. Additionally, some concepts (or types) used in this formalization are not explicitly specified in Senge's theory, for example there are no details in [Sen90] or [SKR+94] concerning an agent's plans or its capabilities. Therefore, the formalization of these concepts follows an interpretation of the LO theory and its (plausible) mapping to current research in MAS.

6.3
Other issues arose involving the concepts of autonomy, creative tension, and motivation. It is important to note the different issues involving the concept of autonomy as used in SMART and in our formalization. In the former case, autonomy depends on the fact that an agent is capable of (or has) motivations or not, so that the agent is able to generate its own goals. In our case, the LearningOrgAgent is autonomous but is also embedded in an organizational environment. Therefore, it has to adopt the goals associated with a given role in order to perform this role. Otherwise, as it is autonomous, it can refuse to adopt that goals, but it will also refuse to perform that given role in the organization. In addition, roles have an associated autonomy level (in an organizational sense), so that the agent is able to generate its own goals in the context of the role. Additionally, the concept of creative tension in LO seems to be closely related to the concept of motivation in SMART. In fact, as creative tension may be viewed as a measure of the distance between the current state of affairs in the environment the reduction of creative tension can be considered as a motivation itself [6].

6.4
Concerning the properties derived from the formal model and presented in section 4, it is interesting to note the importance that some individual characteristics play in an organization that plans to successfully implement the LO theory. Hence, we observe that the agents must be honest, cooperative, tenacious and the interactions among agents must also be honest. Thus, there are several constraints on individual features of the agents that are members of such type of formal organization.

6.5
It is important to note that the formal model that we have built corresponds to our interpretation of Senge's work and depicts some characteristics of his theory, thus is not intended to be a full detailed translation of the LO theory into a formal model. For example, most of the skills/activities related to systems thinking are encapsulated in functions. However, the level of abstraction presented in this model is appropriate to allow us to study important properties of the LO theory and discuss individual and organizational features that should be taken into account in an implementation of the LO theory, either in artificial or in natural organizations.

6.6
Additionally, we note that our use of formal methods for modeling systems in general presents new perspectives and reveals new, not yet explored, potentialities concerning the use of these methods. For example, consistency checking of an organization with regard to a specific organizational theory can be investigated.

6.7
All these issues should certainly pose a number of interesting problems and questions regarding the construction of formal models for the Fifth Discipline in particular, and for OT theories in general, and also for the study of different implementation processes of such theories in organizations. A further advancement in this direction is the development of a test case which is presented in [Sil04]. It uses parts of the model introduced in this article and was developed in the form of an animation of the specification using [GB03].

6.8
Our future interest lies in the refinement of our model in order to computationally implement it using MAS development tools like actSMART [AL01,dL04] or the SACI [HS00] environment. We are also interested in investigating some aspects not covered in detail by Senge's theory, for example: planning, skills, the process of emergence of the shared vision. In this case, results from other works that present more detailed views of these aspects will be useful, for example, the process of emergence of organizational mental models based on individual mental models, as presented in [Kim93].

* Acknowledgements

We gratefully acknowledge the important comments and suggestions by Nigel Gilbert and two anonymous reviewers.

* Notes

1 Creative tension, in Senge's vocabulary.

2 Personal vision, in Senge's vocabulary.

3 This type of diagram was introduced by Luck and D'Inverno [dL01].

4 This perspective on the concept of autonomy is presented in [dL01] and is also used in our model.

5 In the following sections our explanations are based on several formal terms that are described in detail in Part II - A Detailed Version.

6 The population is constant if turn-over is equal to zero and new members are not admitted.

7 In the PersonalMastery schema, the creativetension function produces goals. See Part II - A Detailed Version.


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