FORMALIZING VIRTUAL ORGANIZATIONS

Sergio Esparcia and Estefan´ıa Argente

Grupo de Tecnolog´ıa Inform´atica - Inteligencia Artiﬁcial, Departamento de Sistemas Inform´aticos y Computaci´on

Universidad Polit´ecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

Keywords:

Virtual organizations, Formalization, Multiagent systems.

Abstract:

This work presents a formalization of Virtual Organizations, which are designed by means of their structural

entities, such as roles, organizational units or norms, and the dynamic entities that change through time like

agents and groups. Entities are grouped by means of the Organizational Dimensions, explicitly represented in

the proposed formalization. Additionally, a study of existing formalizations of Organization Centered Multia-

gent Systems is presented.

1 INTRODUCTION

During last years, the development of Multiagent sys-

tems (MAS) has turned from an agent centered per-

spective to an organization centered perspective. Or-

ganizations describe system functionality, structure,

environment and dynamics. In Organization Centered

MAS (OCMAS), the organization exists as an explicit

entity of the system (Picard et al., 2009), deﬁned by

its designers following a top-down approach. In OC-

MAS, agents are aware of the organization in which

they are participating and they are provided with a

representation of it. Agents can use this knowledge

to reason about it and to establish relationships and

interactions to reach their objectives.

OCMAS can be deﬁned and described by means

of a formal approach. To formalize them it is neces-

sary to introduce concepts taken from maths and logic

theories, such as LAO (Dignum and Dignum, 2007),

whose syntax to deﬁne a system follows the tempo-

ral logic language CTL (Emerson, 1991). Other pro-

posals not only provide a formal way to describe an

OCMAS, but also a language to describe it, such as

the proposal in (Grossi et al., 2005), which employs

a multimodal propositional logic language to model

agent organizations, based on Kripke models. Formal

approaches are very useful in order to obtain a clear

deﬁnition of OCMAS, improving the study and anal-

ysis of the different issues regarding them. Addition-

ally, these formalizations are commonly used tocheck

the correctness and integrity of an OCMAS, by means

of techniques like model checking (Clarke, 1999).

However, formal approaches are not always able

to represent all the concepts that compose an agent

organization. Using the current proposals it is not

possible to completely deﬁne a paradigm for devel-

oping agent systems such as Virtual Organizations

(VO) (Foster et al., 2001), which are sets of individ-

uals and institutions that need to coordinate resources

and services. Thus, they are open systems (Gonzalez-

Palacios and Luck, 2007) formed by the grouping and

collaboration of heterogeneous entities, and allowing

model systems at a high level of abstraction. They in-

clude the integration of organizational and individual

perspectives and also the dynamic adaptation of mod-

els to organizational and environmental changes.

VOs can be structured by means of the Organiza-

tional Dimensions (Criado et al., 2009), which should

be considered when modeling an organization. These

dimensions describe all the entities that compose the

organization, distributed by the functionality of the

entities that they are providing to it. These dimen-

sions are: structural, functional, dynamical, environ-

ment and normative. Current formal proposals only

deﬁne a subset of the dimensions and concepts pre-

sented in the Organizational Dimensions. Thus, it

seems necessary to provide with a formalization that

clearly models the Organizational Dimensions, mak-

ing a clear difference between them.

The objective of this work is to present a formal

framework to deﬁne a VO, taking the Organizational

Dimensions as a basis. The rest of this work is struc-

tured as follows: Section 2 describes the Organiza-

tional Dimensions. Section 3 describes formal frame-

works related with our work. Section 4 presents the

Virtual Organization Formalization (VOF), a formal

Esparcia S. and Argente E..

FORMALIZING VIRTUAL ORGANIZATIONS.

DOI: 10.5220/0003156500840093

In Proceedings of the 3rd International Conference on Agents and Artiﬁcial Intelligence (ICAART-2011), pages 84-93

ISBN: 978-989-8425-41-6

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

framework to deﬁne VOs. Section 5 presents a dis-

cussion between our proposal and the analyzed frame-

works. Finally, section 6 gives our conclusions.

2 ORGANIZATIONAL

DIMENSIONS

When modeling an organization, the following di-

mensions should be taken into account (Criado et al.,

2009): (i) structural, describing the entities that popu-

late the system; (ii) functional, which details the func-

tions, goals and services of the organization; (iii) dy-

namical, which considers the interactions between the

elements and their effects; (iv) environment, describ-

ing the elements that surround the system; and (v)

normative, which deﬁnes the mechanisms used by the

society to inﬂuence the behavior of its members.

The Structural Dimension comprises all the el-

ements of the organization that are independent from

the agents that are part of it. Thus, it is based on roles,

groups and their patterns of interrelationship (inheri-

tance, compatibility, communication, and so on). Ad-

ditionally, the topology of the system is established.

The Functional Dimension speciﬁes the global

goals of the organization, its offered functions and

services, the goals followed by different components

of the organization and the tasks and plans that must

be executed to reach these goals.

The Dynamical Dimension speciﬁes how the or-

ganization evolves through time, detailing the way in

which agents enter and leave it, how they adopt cer-

tain roles according to their capabilities and abilities,

and how they can participate in the units or groups

of the organization where they are admitted. This di-

mension also details the interactions that take place

between internal and external entities.

The Environment Dimension describes how

agents are connected with other types of entities such

as artifacts, applications or resources; and how agents

can perceive and act on the environment.

Finally, the Normative Dimension determines the

set of deﬁned actions and rules to manage the behav-

ior of the members of the organization. Norms are

widely used to limit the autonomy inside societies and

to solve coordination problems, specially when it is

not possible to exercise a total social control.

3 RELATED WORK

Based on different logics and formal methods, some

proposals to model OCMAS have been deﬁned, each

giving its particular vision and adapting its formaliza-

tion to the speciﬁc kind of system that they are look-

ing to build. In this section, a set of relevant propos-

als on this ﬁeld has been reviewed: OperA (Dignum,

2003), LAO (Dignum and Dignum, 2007), Process-

Oriented Modeling Framework (POMF) (Popova and

Sharpanskykh, 2006), MOISE

Inst

(Gˆateau et al.,

2005), MACODO (Haesevoets et al., 2009), PopOrg

(da Rocha Costa and Dimuro, 2008) and the propos-

als from (Grossi et al., 2005) and (Jonker et al., 2007).

All these proposals are analyzed following the Orga-

nizational Dimensions described in the previous sec-

tion, in order to check whether they are taking into

account the entities and concepts from each dimen-

sion.

Table 1 compares these proposals, analyzing the

organizational elements that they take into account.

Next, we will depict in detail the contents of this ta-

ble, describing each studied proposal.

OperA proposes an Organizational Model to de-

scribe organizations that deﬁnes the social, normative,

interaction and communicative structures of the soci-

ety. The Social Structure of OperA is related with the

Structural Dimension, since it contains roles, groups

and dependency relations between roles. Also, its So-

cial Structure is related with the Functional Dimen-

sion since it takes into account the objectives associ-

ated with roles. The Normative Structure is obviously

related with the Normative Dimension, as both con-

sider norms. The Interaction Structure models the ac-

tivity of the system, which is considered as the dy-

namics taken from the Dynamical Dimension. Fi-

nally, the Communicative Structure manages commu-

nication between agents, like interactions in the Dy-

namical Dimension. Nevertheless, this framework

does not model the environment of an OCMAS.

The logic for agent organizations (LAO) is an ex-

tension of CTL logic. The Functional Dimension is

completely represented in LAO, including agents, ob-

jectives, groups, the topology of the system (estab-

lishing links between agents), and roles, which are

represented by means of capabilities and abilities, el-

ements taken from this dimension. LAO additionally

deﬁnes different states of the world where the system

is located (related to the EnvironmentDimension) and

its transitions (related to the Dynamical Dimension).

LAO is a very complete proposal, since it takes into

account a large subset of the elements of the Organi-

zational Dimensions, but it does not provide a formal-

ization for the Normative Dimension.

The Process Oriented Modeling Framework

(POMF) is structured by means of four views. The

main one is the process oriented view, where tasks,

processes and workﬂows are deﬁned. This view in-

FORMALIZING VIRTUAL ORGANIZATIONS

Table 1: Comparison between different formal representations.

Organizational concepts

OperA MOISE PopOrg LAO POMF MACODO Grossi Jonker

Structural Dimension

Roles X X X X X X X X

Groups X X X X

Agents X X X X X X X

Relations X X X X X X

Topology X

Functional Dimension

Capabilities X X X X

Abilities X X

Services X X

Objectives X X X X X

Dynamical Dimension

Interactions X X X X X

Dynamics X X X X X X

Environment Dimension

Environment X X X X

Resources X

Normative Dimension

Norms X X X X

Syntax CTL L

Z Org TTL

Semantics LCR CTL* T

Org

cludes the concept of service from the Functional Di-

mension, being a workﬂowdivided into processes that

are split into tasks. It also includes the resources of

the Environment Dimension. The organization ori-

ented view includes the role entity, which describes

the set of capabilities of the organizational processes

in a concrete workﬂow that are then assigned to agent

entities, deﬁned in the agent view, where groups of

agents are not able to be modeled. Therefore, the or-

ganization oriented view is related with both Struc-

tural and Functional Dimensions and the agent view

is related with the Structural Dimension. Finally,

the performance oriented view describes the organiza-

tional goals, such as the Functional Dimension does.

However, POMF does not provide a formalization for

neither Dynamical nor Normative Dimensions.

MOISE

Inst

is composed of four speciﬁcations, dis-

tributed in a similar way to the OrganizationalDimen-

sions. The Structural Speciﬁcation (SS) deﬁnes the

roles that agents will play, including the relations be-

tween them, and an additional structural level named

group, where the roles belong to and the interactions

are carried out. The SS contains elements from the

Structural Dimension, but it does not model the topol-

ogy of the system. The Functional Speciﬁcation (FS),

related with the Functional Dimension, only deﬁnes

here the goals that the system must achieve. The Con-

textual Speciﬁcation (CS) deﬁnes the different con-

texts that inﬂuence the organizational dynamics and

the transitions between them. This speciﬁcation de-

ﬁnes the environment, taken from the Environment

Dimension, and its dynamics, just like the Dynami-

cal Dimension does. Unfortunately, the CS does not

model the resources populating the environment or

the interactions between agents. Finally, the Norma-

tive Speciﬁcation (NS) deﬁnes the rights and duties

of roles and groups inside the organization, which are

known as norms in the Normative Dimension. All

agents that have adopted a role from the SS compose

the Organizational Entity (OE), which is the element

of the system that controls the dynamic elements of

the organization, including agents and all events that

they generate, such as their interactions.

The organizational formalization proposed in

(Grossi et al., 2005) pursues to represent the orga-

nizational structure. This formal method takes the

concepts of role, establishing relations between them;

and agent from the Structural Dimension. The roles

of the organization are conceived around three basic

notions: objectives, norms and information. Objec-

tives are the only elements related with the Functional

Dimension that are presented in this proposal; and

the Normative Dimension is taken into account using

norms. Regarding information, knowledge about the

current state of the organization can be given to agents

by other agents, so this is a type of interaction from

the Dynamical Dimension. Since this proposal is fo-

cused on modeling the organization structure, it does

not take into account the Environment Dimension.

In (Jonker et al., 2007), a framework for model-

ing and providing a formal analysis of organizations

is deﬁned, based on a generic representation of them

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

by means of a set of roles. Apart from the roles,

this proposal also formalizes two concepts from the

Structural Dimension: agents and relations between

roles. These relations enable the interactions from the

Dynamical Dimension, which is completed by taking

into account the dynamics of the organization. One of

the main advantages of this work is that it is able to

explicitly model the environment of the Environment

Dimension, although it does not model environmental

resources. The main lack of this formalization is that

it does not formalize any concept from the Functional

and Normative Dimensions, so designers are not able

to model concepts such as objectives and norms.

The MACODO framework is centered on the dy-

namics of organizations with self-organization con-

cepts, offering a model with concepts related to the

Functional Dimension, such as roles (establishing the

concept of position, similar to a job offer), contracts

of roles (an agreement between an agent and an orga-

nization for a concrete position to control the access

to an available role), agents (including their context

and local environment, which is related to the En-

vironment Dimension), and organizations (groups of

agents deﬁned by a set of open role positions and cur-

rent role contracts). Relations of hierarchy and com-

munication between roles are not considered. A role

is described as a set of capabilities, which is the only

entity from the Functional Dimension that MACODO

takes into account. Since MACODO is focused on

self-organization, the dynamics of the system from

the Dynamical Dimension, including changes in its

context or in its set of agents, are formalized. To

control the activities that the organization carries out,

MACODO is enhanced with a set of laws, similar

to norms from the Normative Dimension. Although

MACODO does not model other relevant organiza-

tional concepts such as objectives, it deals with ele-

ments from all the Organizational Dimensions.

Finally, to manage the structural dynamics of a

MAS, PopOrg is a model based on two basic con-

cepts: the population of an organization and its struc-

ture. The population of a MAS is its set of agents, as

well as the behaviors and actions (which represent the

capabilities and abilities from the Functional Dimen-

sion); and the exchange processes (services from the

Functional Dimension) that agents are able to carry

out. Therefore, the population of a PopOrg organi-

zation mainly takes concepts from the Functional Di-

mension plus agents from the Structural Dimension.

Moreover, the structure of the organization is com-

posed by roles and the links between them, which are

elements that belong to the Structural Dimension. To

relate the population and the structure, PopOrg has a

third element called implementation that relates the

roles with the agents, and the links with the exchange

processes. Also, PopOrg stores the different states

that the system goes throughduring its execution. Un-

fortunately, PopOrg does not model any of the entities

from the Environment or Normative Dimensions.

Generally, all the analyzed formalizations present

a good approach to deﬁne an organization in a for-

mal way. Nevertheless, none of the proposals takes

into account all the entities from the Organizational

Dimensions, which are not clearly depicted in these

frameworks. Thus, it seems interesting to provide

with an explicit description of the Organizational Di-

mensions, which are useful for representing the orga-

nization elements. Therefore, in section 4 our pro-

posal to model organizations will be presented, which

models an organization clearly deﬁning its dimen-

sions. This proposal also integrates some features

taken from some proposals presented in this section.

4 FORMAL DESCRIPTION OF A

VIRTUAL ORGANIZATION

In this section the concept of Virtual Organization

(VO) will be deﬁned in a formal way, taking into ac-

count its organizational dimensions. This formaliza-

tion, named VOF (Virtual Organization Formaliza-

tion), will be focused on three elements: (i) the Orga-

nizational Speciﬁcation (OS), which details the set of

static elements of the organization; (ii) the Organiza-

tional Entity (OE), which represents the instantiation

of the elements in OS; and (iii) the Organizational

Dynamics (φ), which relates elements from OS with

elements from OE.

Deﬁnition 1. A Virtual Organization is deﬁned, at a

given time t, as a tuple O

= hOS

, OE

, φ

i where:

• OS refers to the Organizational Speciﬁcation. It

is deﬁned as OS = hSD, FD, ED, NDi where:

– SD is the Structural Dimension.

– FD is the Functional Dimension.

– ED is the Environment Dimension.

– ND is the Normative Dimension.

• OE refers to the Organizational Entity, which rep-

resents the dynamic elements of the system.

• φ allows to relate OS with OE, thus deﬁning the

Dynamic Dimension, together with the OE.

The VO will change through time modifying its

states, occurredafter a change in the environment,and

it will change from one state to another by means of a

transition. The following subsections will describe in

detail these three elements.

FORMALIZING VIRTUAL ORGANIZATIONS

4.1 Organizational Speciﬁcation

The Organizational Speciﬁcation details the set of

’static’ elements of the organization, containing orga-

nizational units, roles, norms, and the rest of elements

that build the dimensions of a Virtual Organization.

The Organizational Structure is composed by: (i) the

Structural Dimension, which contains roles, organi-

zational units and their relationships; (ii) the Func-

tional Dimension, describing objectives, functional-

ities and services of an organization; (iii) the Envi-

ronment Dimension, which describes the artifacts and

workspaces from the environmentof the organization;

and (iv) the Normative Dimension, which deﬁnes the

norms that rule the system.

4.1.1 Structural Dimension

The Structural Dimension describes the components

of the system and their relations. It allows deﬁning

the static components of an organization, i.e. all the

elements that are independent from the entities that

are ﬁnally executed. In a more speciﬁc way, it deﬁnes

the organizational units and the structural elements,

roles and relationships between roles.

Deﬁnition 2. The Structural Dimension

(SD) of a Virtual Organization is deﬁned as

SD = hR, OU, Relationsi where:

• R refers to the roles of the organization.

• OU is the set of organizational units.

• Relations is a set of relation-

ships, deﬁned as Relations =

hSocialRelations, StructRelations, DimRelationsi

where:

– SocialRelations refers to the social relation-

ships between roles, which can be formalized

as:

SocialRelations =











inf : R → R

col : R → R

sup : R → R

comp : R → R

where: inf (information) refers to the informa-

tion relations, which allows communications

between roles; col (collaboration) allows a role

to monitor the activities of other roles; sup

(supervision) deﬁnes that an agent playing a

speciﬁc role can transfer or delegate one or

some of his objectives to a subordinate role;

and comp (compatibility) depicts that an agent

playing a speciﬁc role can also play another

compatible role in the organization at the same

time.

– StructRelations refers to the structural rela-

tionships deﬁned by the structure of the orga-

nization, which can be formalized as:

StructRelations =







RoleHier : R → R

Contains : OU → 2

Roles : OU → 2

where: RoleHier represents the hierarchy be-

tween roles of the organization; Contains de-

ﬁnes the topology of the organization by means

of relations between organizational units; and

Roles deﬁnes the roles that are located inside

an organizational unit.

– DimRelations allows relating this dimension

with others, through the element OU, and can

be formalized as:

DimRelations =











Norms : OU → 2

Services : OU → 2

Goals : OU → 2

Workspaces : OU → 2

where: Norms deﬁnes the norms, described in

the normative dimension, which rule an OU;

Services relates an OU with the services that

contains; Goals describe the objectives that are

necessary to be reached inside an OU; and

Workspaces details the workspaces (see Deﬁ-

nition 4) where an OU can be located.

Properties of the Relations. The social relation inf

is symmetrical, since a role can provide informa-

tion to a second role, and viceversa; transitive, since

agents can build an information chain, and reﬂexive

as an agent can send information to himself. The re-

lations col and sup are both asymmetrical, since an

agent cannot monitor or supervise the agent which is

monitoring or supervising him; reﬂexive, because an

agent can collaborate or supervise himself; and tran-

sitive, allowing to create a command chain inside the

organization.

The compatibility relation (comp) has reﬂexive

and transitive properties, because a role is compati-

ble with itself and a role is compatible with the roles

that have a compatibility relation with its compati-

ble roles. It is interesting to notice that the comp

relation is not symmetrical (e.g. comp(r

, r

) not al-

ways implies comp(r

, r

)). For example, the relation

comp(Professor, Teacher) is correct, because a pro-

fessor can work as a teacher in every moment, but a

teacher might not be capable of playing the role of

professor. Finally, the relations RoleHier and comp

are related, since an agent playing a specialized role

is capable of playing its generalized role. Formally:

∀r

, r

∈ R : RoleHier(r

, r

) → comp(r

, r

) (1)

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

Let r

, r

∈ R be two roles belonging to OS. The

information, collaboration and supervision relations

deﬁne the following relations in an implicit way:

sup(r

, r

) → col(r

, r

) (2)

col(r

, r

) → inf(r

, r

) ∧ comp(r

, r

) (3)

This means that a supervision relation between

two agents implies that a supervised agent will collab-

orate with a supervisor agent to help him to reach his

objectives. Also, a collaboration relation between two

roles implies that an information link between them

exists and the second role of the relation is compati-

ble with the ﬁrst one.

The relation Contains from the StructRelations

set has the following properties: (i) asymmetrical,

since an OU cannot be contained in another OU that

contains it; (ii) transitive, because it is considered that

an OU contained inside another OU is also contained

inside the predecessors of the OU that contains it; and

(iii) irreﬂexive, since an OU cannot contain itself. In a

similar way, the RoleHier relation has the same prop-

erties of the Contains relation, because a role cannot

have an inheritance relation with itself, the relations

between roles are transitive to allow deﬁning a com-

plete role hierarchy and a subordinated role cannot be

the supervisor of its supervisor.

Properties of the Entities. Firstly, an organizational

unit is contained inside another OU, this implies that

the roles from this OU are compatible with those of

its predecessor OU. Formally:

∀OU

, OU

∈ OU : Contains(OU

, OU

)|∀r

∈ (4)

Roles(OU

) ∧ ∀r

∈ Roles(OU

) → comp(r

, r

)

It should be noted that the Roles relation is recur-

sive: the roles that an OU offers are not only its own

roles, but also these from its predecessor OUs. For-

mally:

∀o ∈ OU : ∀r ∈ Roles(o) → r ∈ Roles(o)∨ (5)

r ∈ Roles(o

) : o ∈ Contains(o

)

Properties of the OU. The relations between organi-

zational units allow deﬁning three different types of

structures of an organization:

• ’hierarchy’. A hierarchy implies that there is

a supervisor role, with supervision relations to

all the other members of its same organizational

unit (OU). Formally, ∃r ∈ Roles(OU) : ∀r

6= r ∈

Roles(OU) → sup(r, r). If a designer wants to

make his system tighter, he can also prohibit com-

munications between subordinated roles.

• ’team’. In this kind of structure, all roles have

coordination relations between them. Formally, it

is deﬁned as ∀r

, r

∈ Roles(OU) : col(r

, r

• ’plain’. This structure establishes information re-

lationships between roles. Formally, ∃r

, r

∈

Roles(OU) : inf(r

, r

4.1.2 Functional Dimension

The Functional Dimension details the speciﬁc func-

tionality of the system, based on services, tasks and

objectives, as well as the interactions of the system,

activated by means of objectives or service usage.

It allows deﬁning the functionality of organizational

units, roles and agents of the MAS, including services

and objectives that these entities offer or consume.

Deﬁnition 3. The Functional Dimension (FD) from

the Organizational Structure of a Virtual Organiza-

tion is deﬁned as FD = hG, S, Ta, FuncReli where:

• G represents the goals followed by the organiza-

tion.

• S is the set of services that the system offers or

requires.

• Ta are the tasks that compose the services.

• FuncRel = hGT,Client, Provider, Obtains,

Achieves, Task, Invoke, Plani is the set of rela-

tions of this dimension, where:

– GT : G → 2

is the Goal Tree of the organiza-

tion, describing the dependencies between dif-

ferent goals of the organization.

– Client : S → 2

relates a service with the set of

roles that use it.

– Provider : S → 2

relates a services with the set

of roles that offer it.

– Obtains : S → 2

describes the set of goals that

can be achieved by a service, thus deﬁning the

functionality of the system.

– Achieves: Ta → 2

deﬁnes the set of goals that

are reached when a task is executed.

– Task : S → 2

shows how services are split in

different tasks.

– Invoke : S → 2

describes the dependencies be-

tween services, showing which services need to

be invoked by other services to complete their

functionality, thus allowing the composition of

services.

– Plan : G → 2

represents the sequence of ser-

vices that must be followed in order to achieve

a goal.

Properties of the Relations. The Goal Tree relation

is irreﬂexive, asymmetrical and transitive, since a goal

cannot be related with itself, neither with its prede-

cessor but it can be related with the successors of its

successors.

FORMALIZING VIRTUAL ORGANIZATIONS

It must be assured that the provider of a service

must be a role contained in the same OU as the ser-

vice. Formally:

∀o ∈ OU ∧∀s ∈ Services(o) → Provider(s) ⊆ Roles(o)

(6)

This restriction assures that the services of an OU

will be provided only inside it, but they can be ac-

cessed by agents from other OUs (e.g. using the

Invoke relation).

As pointed out in this section, the Invoke relation

allows services to invoke other services to reach their

goals. In order to execute this operation, it must be

assured that the provider of the invoker service must

be client of the invoked service. Formally:

∀s

, s

∈ S, s

∈ Invokes(s

) : ∀r

∈ Provider(s

) →

∃r

∈ Client(s

) ∧ r

= r

(7)

A key issue for the system designer is to assure

that the services located in an organizationalunit must

help to reach its goals. Formally, it is described as:

∀o ∈ OU, ∀s ∈ Services(o)∧∀g

∈ Pursues(s) : ∃g

∈

Goals(o) → g

∈ GT(g

) (8)

It is is possible that a speciﬁc goal of a service

could not be reached by any of the tasks that com-

pose it, so then this service must invoke another which

should include at least a task that achieves this desired

goal. Formally, it is expressed as:

∀g ∈ Obtains(s

) → (∃t ∈ Task(s

)∧g ∈ Achieves(t))

∨(∃s

∈ S∧ g ∈ Obtains(s

) ∧ s

∈ Invokes(s

)) (9)

4.1.3 Environment Dimension

The Environment Dimension describes the artifacts,

i.e. entities that populate the environment of a MAS.

This dimension uses the concept of artifact (Ricci

et al., 2007), an element introduced by the Agents &

Artifacts (A&A) conceptual framework. These ele-

ments are employed by agents in order to reach their

goals, since artifacts have no associated goals. Addi-

tionally, the A&A framework presents the concept of

workspace, used to deﬁne the topology of the envi-

ronment of a MAS.

Deﬁnition 4. The Environment Dimen-

sion of a Virtual Organization is deﬁned as

ED = hWS, AR, EnvFunci where:

• WS is the set of workspaces that build the envi-

ronment of a MAS, where ws ∈ WS is deﬁned as

ws = hLoci and Loc is referred to the location of

the workspace inside the environment.

• AR is the set of artifacts, where an artifact ar ∈ AR

is deﬁned as ar = hPR, OP, LO, Sti, where:

– PR are the observable properties of an artifact

that agents can check without executing any op-

eration on it.

– OP is the set of operations that agents can exe-

cute when interacting with the artifact.

– LO refers to the link operations, which allows

the composition and distribution of artifacts.

– St is the internal state of an artifact.

• EnvFunc = hLocated,Compositioni is the set of

functions that act on the environmental elements,

where:

– Located : AR → 2

describes the set of

workspaces where an artifact is located.

– Composition : WS → 2

allows deﬁning

intersection and nesting relations between

workspaces that build the environment.

Properties of the Relations. The Composition rela-

tion is reﬂexive and symmetrical, since a workspace

can intersect with itself. Additionally, it is necessary

for an artifact to be contained at least in a workspace.

Formally:

∀ar ∈ Ar : ∃ws ∈ WS → ws ⊆ Located(ar) (10)

4.1.4 Normative Dimension

The Normative Dimension describes normative re-

strictions on the behavior of the entities of the system,

including sanctions and rewards, based on the work in

(Criado et al., 2010).

Deﬁnition 5. The Normative Dimension of a Virtual

Organization is deﬁned as ND = hN, >

i where:

• N is the set of norms of the system.

• >

is an order relationship between norms, deﬁn-

ing the priority between them. This relation es-

tablishes a total relation order between the norms

governing the system, avoiding the priority confu-

sion when a norm is executed.

Formally, a norm is deﬁned as:

Deﬁnition 6. A norm n ∈ N is deﬁned as n =

hD,CO, AC, EX, SA, REi where:

• D = {O, F} is the deontic operator, i.e. obliga-

tions (O) and prohibitions (F) that impose restric-

tions in the behavior of the agents.

• CO is a logical formula that represents the action

that must be carried out in case of obligations, or

has to be avoided in case of prohibitions.

• AC, EX are well-formed formulas that determine

the conditions of norm activation and expiration,

respectively.

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

• SA, RE ∈ S are expressions that describe the ac-

tions (sanctions, SA; and rewards, RE) that will

be carried out in case of violation or fulﬁlment of

norms, respectively.

Properties of the Relations. The priority function

is asymmetrical and transitive, deﬁning an univo-

cal relation between the norms governing the system.

The topology of the system will also deﬁne new

order relationships between norms. If an OU called

is contained in an OU named ou

, its norms must

have higher priority than the norms of ou

. Formally,

∀ou

, ou

: n

∈ Norms(ou

) ∧ n

∈ Norms(ou

)

∧Contains(ou

, ou

) → n

(11)

4.2 Organizational Entity

The Organizational Entity of a Virtual Organization is

the set of active elements of the organization. These

elements can change through time. They are consid-

ered as the dynamic elements of the system.

Deﬁnition 7. The Organizational Entity of a Vir-

tual Organization is deﬁned as OE = hA, GR, AN, ASi

where:

• A is the set of agents that populate the VO.

• GR is the set of groups that are currently in the

system. A group is an instantiation of an organi-

zational unit.

• AN ⊆ N is the set of active norms of the system,

i.e. all those norms whose activation condition

is true but its expiration condition has not been

reached yet (AC∧ ¬EX).

• AS ⊆ S is the set of services that the agents of the

organization are currently providing.

The agents (A) populating the system are playing

roles, they are located into groups (GR) and provide

services (S), as described in the next subsection. An

OU deﬁnes an organizational pattern for the agents

that are inside it, but this does not deﬁne the concrete

agents that must populate it. On the contrary, a group

is a concrete instantiation of an OU, deﬁning a set of

agents that populate it. Thus, an OU can be instanti-

ated by different groups.

4.3 Organizational Dynamics

The Organizational Dynamics presents the relations

between the elements of the Organizational Structure

and the Organizational Entity.

Deﬁnition 8. The Organizational Dynam-

ics of a Virtual Organization is deﬁned as

φ = hplays, inUnit, provides, perceives, isUniti

where:

• plays : A → 2

is a function that relates an agent

with the set of roles that he is playing inside the

organization.

• inUnit : A → 2

is the function that describes the

groups where an agent is located.

• provides : A → 2

represents the set of services

that an agent provides.

• perceives : A → 2

represents the set of

workspaces that an agent is able to perceive.

• isUnit : GR → OU deﬁnes the type of organiza-

tional unit instantiated by a group.

Properties of the Relations. The plays, inUnit,

provides and perceives relations allow agents to play

different roles, be located in different groups, provide

different services and perceive different workspaces

in the organization, respectively. The isUnit relation-

ship allows knowing the type of organizational unit

that a concrete group is instantiating.

The situation where an agent plays a role inside a

unit and a scenario where an agent is inside an orga-

nizational unit playing a role can be checked in equa-

tions 12 and 13. It must be noted that the Roles func-

tion is recursive, as explained in section 4.1.1.

∀r ∈ plays(a) → ∃o ∈ OU ∧ ∃g ∈ inUnit(a) :

isUnit(g) = o∧ r ∈ Roles(o) (12)

∀g ∈ inUnit(a) → ∃o ∈ OU ∧isUnit(g) = o∧

∃r ∈ Roles(o) : r ∈ plays(a) (13)

The ﬁrst equation establishes that an agent can

only play the roles provided by the groups where he is

located. These roles are the ones provided by the or-

ganizational units instantiated by these groups. The

second equation deﬁnes that an agent must play at

least a role from each group where he is located.

In addition, using the provides relationship from

φ, it is possible to deﬁne the set of active services (AS)

from OE. Formally,

AS =

[

a∈A

s ∈ provides(a) (14)

4.4 Multiagent Systems based on

Virtual Organizations

In the previous sections, the different dimensions and

entities that compose the state of a Virtual Organiza-

tion at a given time were deﬁned in a formal way.

Nevertheless, a VO changes through time, passing

from one state of the organization to another. Thus, it

is necessary to deﬁne all the possible states of the or-

ganization as well as the allowed transitions between

these states. For this issue, we based our work in the

proposal from (da Rocha Costa and Dimuro, 2008).

FORMALIZING VIRTUAL ORGANIZATIONS

To model the states of a Virtual Organization and

their transitions, let VO be the universe of all the pos-

sible organizations O. A multiagent system based on

virtual organizations is a structure MAS = (VO, D)

where, for every time t ∈ T, D

⊆ VO × VO deﬁnes

transitions between different states of the system. In

every state of the organization O ∈ VO, in a giventime

t ∈ T, there is a set of possible next states of the or-

ganization, denoted by D

(O) ⊆ VO. Thus, for every

t ∈ T, it holds that O

t+1

∈ D

), so an organization

will only change to another state when it is allowed to

reach from the initial state.

Since the organization is composed by three ele-

ments (OS, OE and φ), before executing a change of

state it is necessary to check that these elements are

able to change from the initial state to the possible

destination state. Formally:

(OS

t+1

, OE

t+1

, φ

t+1

) ∈ D

((OS

, OE

, φ

)) ↔ OS

t+1

∈ D

(OS

) ∧ OE

t+1

∈ D

(OE

) ∧ φ

t+1

∈ D

(φ

)

(15)

However, in order to swap from one state to an-

other, it is not necessary to produce a change in all

three elements that compose the Virtual Organization.

A change ranges from a very small variation in one or

few of the elements building the organization to a big

amount of changes in a large amount of entities from

the VO. Formally, it is possible that:

t+1

= OS

∨ OE

t+1

= OE

∨ φ

t+1

= φ

(16)

5 DISCUSSION

In section 3 an analysis of the most relevant formal-

ization proposals was presented. The Virtual Orga-

nization Formalization (VOF) takes inspiration from

features taken from some of the analyzed proposals.

In this section, we depict a comparison between VOF

and these background proposals.

Firstly, the organizational temporal evolution pro-

posed by VOF is mainly based on PopOrg, which

models the dynamics of the population (similar to our

OE) and the organization (similar to our OS).

Regarding the structure of an organization, OperA

offers relations between roles that are similar to those

included in VOF. The supervision of VOF is similar

to the combination of the power and authorization re-

lations of OperA, expressing that an agent is able to

delegate its objectives to a subordinated agent, like

the power relation does (the authorization relation ex-

presses the power relation, but as a temporal situa-

tion). Also, in OperA, the objective that a subordi-

nated agent can take from a superior agent is deter-

mined by the type of existing relation between roles,

which establishes their hierarchy. However, VOF de-

ﬁnes this hierarchy using the RoleHier relation.

In MOISE

Inst

, the structural levels of the orga-

nization are split into: (i) individual level, built by

the organizational roles, and presents hierarchy rela-

tions between roles (similar to our RoleHier relation);

(ii) social level, which is built from link relationships

between roles, classiﬁed as acq (acquaintance), i.e.

having a representation of other agents, com (similar

to our in f relation), in which agents are able to com-

municate between them, and aut expressing authority

over other agents, thus combining col and sup rela-

tions from VOF; and (iii) collective level, which de-

ﬁnes groups of agents, establishing the compatibility

between roles and their cardinalities. VOF adds the

comp relation, in order to express whether an agent

can take a given role if he is taking another role.

LAO is the only analyzed proposal which explic-

itly models the topology of the system by means of

dependency chains (that are interaction possibilities)

between agents. The topology can be a hierarchy, if

there is a chain of command, or a network, if every

agent is responsible for an organizational goal and

has a delegation relationship to another agent. VOF

models the topology of the system using Contains re-

lations between OUs. These relations allow deﬁning

three types of organizations: hierarchy, similar to the

structure deﬁned by LAO; team, when all agents col-

laborate with each other; and plain, which assumes

information relationships between roles.

Regarding the Functional Dimension, although

PopOrg and POMF model concepts that are similar

to services (by means of exchange processes or work-

ﬂows, respectively), they are better described in VOF.

PopOrg focuses on the actions developed by the pro-

cess and the agents that are carrying them out, while

POMF is focused on describing the tasks that com-

pose a given workﬂow. VOF goes beyond, (as it fol-

lows a Service Oriented Approach) and formalizes a

service by means of the roles that it can provide and

consume, the goals that can be achieved with this ser-

vice, the invoke relationships between services, and

the tasks that compose each service (as well as the

goals that these tasks help to reach).

The environment used in VOF is based on the

Agents & Artifacts conceptual framework, which was

included in the SODA metamodel, but it has not been

included in any other formal approach yet.

VOF model norms in a very similar way to the

proposal of MOISE

Inst

, although they use different

languages to describe norms. VOF is able to relate

a norm to a set of OUs, using the Norms relationship

from DimRelations, limiting its effect only to this set.

The Organizational Entity from VOF can be also

ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence

compared with other proposals. For example, a spec-

iﬁed group is deﬁned in MOISE

Inst

as a ’group speci-

ﬁcation’, while VOF deﬁnes it as an Organizational

Unit. On the other hand, a group instantiation is

named ’group’ in both MOISE

Inst

and VOF. In ad-

dition, the OE from VOF deﬁnes the set of norms and

services that are currently active in the organization.

Finally, VOF clearly divides the static elements of

the system (i.e. elements that will produce a structural

change if they are modiﬁed) and the more dynamic

elements of the MAS, represented in the OE. Our

speciﬁcation gives agents the possibility to belong to

a speciﬁc group and provide or use a service.

6 CONCLUSIONS AND FUTURE

WORK

This work presents a formal speciﬁcation for Vir-

tual Organizations, named VOF (Virtual Organization

Formalization), which is composed by: (i) the Organi-

zational Speciﬁcation, which details the static compo-

nents of the system and divides them by means of the

organizationaldimensions; (ii) the Organizational En-

tity, which deﬁnes the active elements of the system;

and (iii) the Organizational Dynamics, which details

the relationships between elements from the Organi-

zational Speciﬁcation and the Organizational Entity.

Additionally, we have analyzed a set of differ-

ent formalizations, focusing on typical organizational

concepts taken from the Organizational Dimensions.

After this analysis, we noticed that the analyzed for-

malizations do not take into account all concepts from

Organizational Dimensions. Therefore, our proposal

is aimed to cover all these concepts and to provide a

formalization as much complete as possible.

As future work, this formalization will help us

when dealing with concepts related to adaptation

in Organization Centered Multiagent Systems, being

easier for us to identify the entities of the system

which would change through time. VOF will be inte-

grated into the reasoning process of BDI agents, in or-

der to develop agents that are able to know whether an

organization is working in a correct way, or he needs

to executean adaptationprocess. Moreover,using this

formalization we will be able to check the correctness

of a deﬁned OCMAS.

ACKNOWLEDGEMENTS

This work is supported by TIN2009-13839-C03-01

and PROMETEO/2008/051 projects of the Spanish

government and CONSOLIDER-INGENIO 2010 un-

der grant CSD2007-00022.

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FORMALIZING VIRTUAL ORGANIZATIONS