To Maksymilian To Nicole

About the Authors

Barbara Dunin-Kęplicz

Barbara Dunin-Kęplicz is a Professor of computer science at the Institute of Informatics of Warsaw University and at the Institute of Computer Science of the Polish Academy of Sciences. She obtained her Ph.D. in 1990 on computational linguistics from the Jagiellonian University, and in 2004 she was awarded her habilitation on formal methods in multi-agent systems from the Polish Academy of Sciences.

She is a recognized expert in multi-agent systems. She was one of the pioneers of modeling BDI systems, recently introducing approximate reasoning to the agent-based approach.

Rineke Verbrugge

Rineke Verbrugge is a Professor of logic and cognition at the Institute of Artificial Intelligence of the University of Groningen.She obtained her Ph.D. in 1993 on the logical foundations of arithmetic from the University of Amsterdam, but shortly thereafter moved to the research area of multi-agent systems.

She is a recognized expert in multi-agent systems and one of the leading bridge builders between logic and cognitive science.


The ability to cooperate with others is one of the defining characteristics of our species, although of course humans are by no means the only species capable of teamwork. Social insects, such as ants and termites, are perhaps the best-known teamworkers in the animal kingdom and there are many other examples. However, where the human race differs from all other known species is in their ability to apply their teamwork skills to a variety of different domains and to explicitly communicate and reason about teamwork. Human society only exists by virtue of our ability to work together in dynamic and flexible ways. Plus of course, human society exists and functions despite the fact that we all have our own goals, our own beliefs and our own abilities, and in complete contrast to social insects, we are free agents, given fundamental and important control over how we choose to live our lives.

This book investigates teamwork from the point of view of logic. The aim is to develop a formal logical theory that gives an insight into the processes underpinning collaborative effort. The approach is distinguished from related work in for example game theory by the fact that the focus is on the mental states of cooperation participants: their beliefs, desires, and intentions. To be able to express the theory in such terms requires in itself new logical languages, for characterizing the mental state of participants engaged in teamwork. As well as developing the basic model of teamwork, this book explores many surrounding issues, such as the essential link between cooperative action and dialogue.

Michael Wooldridge
University of Liverpool, UK


The journey of a thousand miles startsfrom beneath yourfeet.

Tao Te Ching (Lao-Tzu, Verse 64)

Teamwork Counts from Two

Barbara and Rineke met at the Vrije UniversiteitAmsterdam in the Winter of 1995. The cooperation started blooming as the spring started, mostly during long lasting research sessions in Amsterdam's famous cafe "De Jaren". Soon Rineke moved to Groningen. Then, on her autumn visits, Barbara survived two floods in Groningen, while Rineke was freezing on her winter trips to Warsaw. Over these years ("de jaren"…) they started to dream not only about some detachment from their everyday university environment, but especially about a more human-friendly climate when working together. In 2001 Barbara recalled that a place of their dreams exists in reality! Certosa di Pontignano, a meeting place of scholars, situated in the old Carthusian monastery near Siena, Italy, hosted them out of the courtesy of Cristiano Castelfranchi.

Indeed, everything helped them there. A typical Tuscan landscape, commonly considered by visitors as a paradise, the simple, ancient but lively architecture, the amazing beauty of nature, and not to forget: people! Andrea Machetti, Marzia Mazzeschi and their colleagues turned their working visits into fruitful and wonderful experiences. As Barbara and Rineke see it now, the book wouldn't have become real, if Pontignano hadn't been there for them. If one could thank this wonderful place, then they would.

Teamwork Rules

What is contemporary computer science about? Distributed, interactive, autonomous systems are surely in the mainstream, and so are planning and reasoning. These tasks are complex by their very nature, so it is not surprising that in multi-agent environments their complexity tends to explode. Moreover, communication patterns appear to be complex as well. That is where logical modeling is of great help. In this book logic helps us to build minimal, but still workable formal models of teamwork in multi-agent systems. It also lends support when trying to clarify the nature of the phenomena involved, based on the principles of teamwork and other forms of working together, as discovered in the social sciences, management science and psychology. The resulting model TEAMLoo is designed to be lively: to grow or to shrink, but especially to adjust to circumstances when needed. In this logical context, the book is not intended to guide the reader through all possible teamwork-related subjects and the vast multi-disciplinary literature on the subject. It rather presents our personal view on the merits and pitfalls of teamwork in multi-agent settings.

As prerequisites, this book assumes some initial literacy in computer science that students would gain in the first years of a computer science, cognitive science or artificial intelligence curriculum. An introductory course on propositional logic suffices to get a sense of most of the formulas. Some knowledge of modal logic would be helpful to understand the more technical parts, but this is not essential for following the main conceptual line.

As computational agents are the main citizens of this book, we usually refer to a single agent by way of 'it'. If in some example it is clear, on the other hand, that a human agent is meant, we use the conventional reference 'he/she'.

Teamwork Support Matters

First of all, we are grateful to our colleagues who joined our team in cooperative research, leading to articles which later influenced some parts of this book. In particular, we would like to thank Frank Dignum for inspiring collaboration on dialogue - we remember in particular a scientifically fruitful family skiing-and-science trip to Zawoja, Poland. We would also like to thank Alina Strachocka, whose Master's research project under Barbara's wings extended our view on dialogues during collaborative planning. Michal Slizak, one of Barbara's Ph.D. students, wrote a paper with us on an environmental disaster case study. Finally, Marcin Dziubinski's Ph.D. research under Barbara's supervision led to a number of papers on complexity of teamwork logics.

Discussions with colleagues have found various ways to influence our work. Sometimes a clever member of the audience would point out a counter-example to an early version of our theory. Other times, our interlocutors inspired us with their ideas about dialogue or teamwork. In particular, we would like to thank Alexandru Baltag, Cristiano Castelfranchi, Keith Clark, Rosaria Conte, Frank Dignum, Marcin Dziubinski, Rino Falcone, Wiebe van der Hoek, Erik Krabbe, Theo Kuipers, Emiliano Lorini, Mike Luck, and Andrzej Szalas. Still, there have been many others, unnamed here, to whom we are also indebted.

We gratefully received specially designed illustrations of possible worlds models, team structures and the overarching architecture behind TEAMLoo from Kim Does, Harmen Wassenaar, Alina Strachocka and Andrzej Szalas. In addition, Kim, Michal and Alina also offered a great support by bringing numerous technical tasks to a successful end.

A number of colleagues have generously read and commented various portions of this book. First and foremost, we are very grateful to Andrzej Szalas, who read and suggested improvements on every single chapter! We thank Alina Strachocka, Marcin Dziubiriski, Elske van der Vaart, Michal Slizak and Liliana Pechal for their useful comments on parts of the book. Our students in Groningen and Warsaw, on whom we tried out material in our courses on multi-agent systems, also provided us with inspiring feedback. We would like to thank all of them for their useful suggestions. Any remaining errors are, of course, our own responsibility. Special mention among the students is deserved for

Filip Grzadkowski, Michal Modzelewski, and Joanna Zych who inspired some examples of organizational structures in Chapter 4. Violeta Koseska deserves the credit for urging us to write a book together.

From September 2006 through January 2007, Barbara and Rineke worked as Fellows at the Netherlands Institute of Advanced Studies in the Humanities and Social Sciences (NIAS) in Wassenaar. This joint book on teamwork was to be one of the -many!- deliverables of the theme group on Games, Action and Social Software, but as is often the case with such projects, the real work of writing and rewriting takes flight afterwards. We would like to thank group co-leader Jan van Eijck for his support. Furthermore, we are grateful to the NIAS staff, in particular to NIAS rector Wim Blockmans and to NIAS head of research planning and support Jos Hooghuis, for their open-mindedness in welcoming our rather unusual project team at NIAS, and for making us feel genuinely at home.

We also highly appreciate the work of our editors at Wiley, Birgit Gruber and Sarah Tilley, for supporting us in the writing process. During the final production process, the book became a real geographically distributed team effort at Wiley, and we would like to thank Anna Smart, Alistair Smith, Shruti Duarah, Jasmine Chang, and David Ando for their contributions.

A number of grants have helped us to work on this book. Both of us would like to acknowledge a NIAS Fellowship. In addition, Barbara would like to acknowlegde the support of the Polish KBN grant7T11C 006 20, the Polish MNiSW grant N N206 399334, and the EC grant ALFEBIITE++ (A Logical Framework for Ethical Behaviour between Infohabitants in the Information Trading Economy of the Information Ecosystem, IST- 1999-1029). Moreover, Rineke would like to acknowledge the Netherlands Organisation for Scientific Research for three grants, namely NWO ASI 051-04-120 (Cognition Programme Advanced Studies Grant), NWO 400-05-710 (Replacement Grant), and NWO 016-094-603 (Vici Grant).

Finally, we would like to express our immense gratitude to our partners for their steadfast support. Also, we thank them for bearing large part of the sacrifice that goes with such a huge project as writing a book, including having to do without us for long stretches of time.

Barbara Dunin-Kęplicz

Rineke Verbrugge


Teamwork in Multi-Agent Environments

The Master doesn’t talk, he acts.
When his work is done,
the people say, ‘Amazing:
we did it, all by ourselves!’

Tao Te Ching (Lao-Tzu, Verse 17)

1.1 Autonomous Agents

What is an autonomous agent? Many different definitions have been making the rounds, and the understanding of agency has changed over the years. Finally, the following definition from Jennings et al. (1998) has become commonly accepted:

An agent is a computer system, situated in some environment, that is capable of flexible autonomous action in order to meet its design objectives.

The environment in which agents operate and interact is usually dynamic and unpredictable.

Multi-agent systems (MASs) are computational systems in which a collection of loosely-coupled autonomous agents interact in order to solve a given problem. As this problem is usually beyond the agents’ individual capabilities, agents exploit their ability to communicate, cooperate, coordinate and negotiate with one another. Apparently, these complex social interactions depend on the circumstances and may vary from altruistic cooperation through to open conflict. Therefore, in multi-agent systems one of the central issues is the study of how groups work, and how the technology enhancing complex interactions can be implemented. A paradigmatic example of joint activity is teamwork, in which a group of autonomous agents choose to work together, both in advancement of their own individual goals as well as for the good of the system as a whole. In the first phase of designing multi-agent systems in the 1980s and 1990s, the emphasis was put on cooperating teams of software agents. Nowadays there is a growing need for teams consisting of computational agents working hand in hand with humans in multi-agent environments. Rescue teams are a good example of combined teams consisting of robots, software agents and people (Sycara and Lewis, 2004).

1.2 Multi-Agent Environments as a Pinnacle of Interdisciplinarity

Variety is the core of multi-agent systems. This simple statement expresses the many dimensions immanent in agency. Apparently, the driving force underlying multi-agent systems is to relax the constraints of the previous generation of complex (distributed) intelligent systems in the field of knowledge-based engineering, which started from expert systems, through various types of knowledge-based systems, up to blackboard systems (Engelmore and Morgan, 1988; Gonzalez and Dankel, 1993; Stefik, 1995). Flexibility is essential for ensuring goal-directed behavior in a dynamic and unpredictable environment. Complex and adaptive patterns of interaction in multi-agent systems, together with agents' autonomy and the social structure of cooperative groups, determine the novelty and strength of the agent-based approach.

Variety is the core of multi-agent systems also because of important links with other disciplines, as witnessed by the following quote from Luck et al. (2003):

A number of areas of philosophy have been influential in agent theory and design. The philosophy of beliefs and intentions, for example, led directly to the BDI model of rational agency, used to represent the internal states of an autonomous agent. Speech act theory, a branch of the philosophy of language, has been used to give semantics to the agent communication language of FIPA. Similarly, argumentation theory – the philosophy of argument and debate, which dates from the work of Aristotle – is now being used by the designers of agent interaction protocols for the design of richer languages, able to support argument and non-deductive reasoning. Issues of trust and obligations in multiagent systems have drawn on philosophical theories of delegation and norms.

 Social sciences: Although perhaps less developed than for economics, various links between agent technologies and the social sciences have emerged. Because multiagent systems are comprised of interacting, autonomous entities, issues of organisational design and political theory become important in their design and evaluation. Because prediction of other agents’ actions may be important to an agent, sociological and legal theories of norms and group behavior are relevant, along with psychological theories of trust and persuasion. Moreover for agents acting on behalf of others (whether human or not), preference elicitation is an important issue, and so there are emerging links with marketing theory where this subject has been studied for several decades.

1.3 Why Teams of Agents?

Why cooperation?

Cooperation matters. Many everyday tasks cannot be done at all by a single agent, and many others are done more effectively by multiple agents. Moving a very heavy object is an example of the first sort, and moving a very long (but not heavy) object can be of the second (Grant et al., 2005a).

Teams of agents are defined as follows (Gilbert, 2005):

The term ‘team’tends to evoke, for me, the idea of a social group dedicated to the pursuit of a particular, persisting goal: the sports team to winning, perhaps with some proviso as to how this comes about, the terrorist cell to carrying out terrorist acts, the workgroup to achieving a particular target.

Teamwork may be organized in many different ways. Bratman characterizes shared cooperative activity by the criteria of mutual responsiveness, commitment to joint activity, commitment to mutual support and formation of subplans that mesh with one another (Bratman, 1992). Along with his characteristics, the following essential aspects underlie our approach to teamwork:

Teamwork is a highly complex matter, that can be characterized along different lines. One distinction is that teamwork can be primarily defined:

1. In terms of achieving a certain outcome, where the roles of agents are of prime importance.

2. In terms of the motivations of agents, where agents’ commitments are first-class citizens.

In this book, the second point of view is taken.

1.4 The Many Flavors of Cooperation

It is useful to ask initially: what makes teamwork tick? A fair part of this book will be devoted to answering this question.

Coordinated group activity can be investigated from many different perspectives:

We take the practical reasoning perspective.

1.5 Agents with Beliefs, Goals and Intentions

Some multi-agent systems are intentional systems implementing practical reasoning – the everyday process of deciding, step by step, which action to perform next (Anscombe, 1957; Velleman, 2000). The intentional model of agency originates from Michael Brat-man’s theory of human rational choice and action (Bratman, 1987). He posits a complex interplay of informational and motivational aspects, constituting together a belief-desire-intention (BDI) model of rational agency.

Intuitively, an agent’s beliefs correspond to information it has about the environment, including other agents. An agent’s desires represent states of affairs (options) that it would choose. We usually use the term goal for this concept, but for historical reasons we use the abbreviation BDI. In human practical reasoning, intentions are first class citizens, as they are not reducible to beliefs and desires (Bratman, 1987). They form a rather special consistent subset of an agent’s goals, that it chooses to focus on for the time being. In this way they create a screen of admissibility for the agent’s further, possibly long-term, decision process called deliberation.

During deliberation, agents decide what state of affairs they want to achieve, based on the interaction of their beliefs, goals and intentions. The next substantial part of practical reasoning is means-ends analysis (or planning), an investigation of actions or complex plans that may best realize agents’intentions. This phase culminates in the construction of the agent’s commitment, leading directly to action.

In this book, we view software agents from the intentional stance introduced by Dennett (1987) as the third level of abstraction (the first two being the physical stance and the design stance, respectively). This means that agents’behavior is explained and predicted by means of mental states such as beliefs, desires, goals, intentions and commitments. The intentional stance, although possibly less accurate in its predictions than the two more concrete stances, allows us to look closer on essential aspects of multi-agent systems. According to Dennett, it does not necessarily presuppose that the agents actually have explicit representations of mental states. In contrast, taking the computer science perspective, we will make agents’mental state representations explicit in our logical framework.

1.6 From Individuals to Groups

A logical model of an agent as an individual, autonomous entity has been successfully created, starting from the early 1990s (Cohen and Levesque, 1990; Rao and Georgeff, 1991; Wooldridge, 2000). These systems have been proved to be successful in real-life situations, such as Rao and Georgeff’s system OASIS for air traffic control and Jennings and Bussmann’s contribution to making Daimler–Chrysler production lines more efficient (Jennings and Bussmann, 2003; Rao and Georgeff, 1995a).

More recently the question how to organize agents’cooperation to allow them to achieve their common goal while striving to preserve their individual autonomy, has been extensively debated. Bacharach notes the following about individual motivations in a team setting (Gold, 2005):

First, there are questions about motivations. Even if the very concept of a team involves a common goal, in real teams individual members often have private interests as well. Some individuals may be better motivated than others to‘play for the team’rather than for themselves. So questions arise for members about whether other members can be trusted to try to do what is best for the team. Here team theory meets trust theory, and the currently hot topic of when and why it is rational to trust. Organizational psychology studies how motivations in teams are determined in part by aspects of personality, such as leadership qualities, and by phenomena belonging to the affective dimension, such as mood and‘emotional contagion’.

The intentional stance towards agents has been best reflected in the BDI model of agency. However, even though the BDI model naturally comprises agents’individual beliefs, goals and intentions, these do not suffice for teamwork. When a team is supposed to work together in a planned and coherent way, it needs to present a collective attitude over and above individual ones. Without this, sensible cooperation is impossible, as agents are not properly motivated and organized to act together as a team. Therefore, the existence of collective (or joint) motivational attitudes is a necessary condition for a loosely coupled group of agents to become a strictly cooperative team. As in this book, we focus on cooperation within strictly cooperative teams, cases of competition are explicitly excluded. Strangely enough, many attempts to define coordinated team action and associated group attitudes have neglected the aspect of ruling out competition.

1.7 Group Attitudes

The formalization of informational attitudes derives from a long tradition in philosophy and theoretical computer science. As a result of inspiring discussions in philosophical logic, different axiom systems were introduced to express various properties of the notions of knowledge and belief. The corresponding semantics naturally reflected these properties (Fagin et al., 1995; Hintikka, 1962; Lenzen, 1978). Informational attitudes of groups have been formalized in terms of epistemic logic (Faginet al., 1995; Meyer and van der Hoek, 1995; Parikh, 2002). Along this line such advanced concepts as general, common and distributed knowledge and belief were thoroughly discussed and precisely defined in terms of agents’individual knowledge or, respectively, belief.

The situation is much more complex in case of motivational attitudes. Creating a conceptually coherent theory is challenging, since bilateral and collective notions cannot be viewed as a straightforward extension or a sort of sum total of individual ones. In order to characterize their collective flavor, additional subtle and diverse aspects of teamwork need to be isolated and then appropriately defined. While this process is far from being trivial, the research presented in this book brings new results in this respect. The complex interplay between environmental and social aspects resulting from the increasing complexity of multi-agent systems significantly contributes to this material. For example, in an attempt to answer what it means for a group of agents to be collectively committed to do something, both the circumstances in which the group is acting and properties of the organization it is part of, have to be taken into account. This implies the importance of differentiating the scope and strength of team-related notions. The resulting characteristics may differ significantly, and even become logically incomparable.

1.8 A Logical View on Teamwork:TEAMLOG

Research on a methodology of teamwork for BDI systems led us first to a static, descriptive theory of collective motivational attitudes, called TEAMLOG It builds on individual goals, beliefs and intentions of cooperating agents, addressing the question what it means for a group of agents to have a collective intention, and then a collective commitment to achieve a common goal.

While investigating this issue we realized the fundamental role of collective intention in consolidating a group to a strictly cooperating team. In fact, a team is glued together by collective intention, and exists as long as this attitude holds, after which the team may disintegrate. Plan-based collective commitment leads to team action. This plan can be constructed from first principles, or, on the other extreme of a spectrum of possibilities, it may be chosen from a depository of pre-constructed plans. Both notions of collective intentions and collective commitments allow us to express the potential of strictly cooperative teams.

When building a logical model of teamwork, agents’ awareness about the situation is essential. This notion is understood here as the state of an agent’s beliefs about itself, about other agents and about the environment. When constructing collective concepts, we would like to take into account all the circumstances the agents are involved in. Various versions of group notions, based on different levels of awareness, fit different situations, depending on organizational structure, communicative and observational abilities, and so on.

Various epistemic logics and various notions of group information (from distributed belief to common knowledge) are adequate to formalize agents’awareness (Dunin-Kęplicz and Verbrugge, 2004, 2006; Fagin et al., 1995; Parikh, 2002). The (rather strong) notion of common belief reflects ideal circumstances, where the communication media operate without failure and delay. Often, though, the environment is less than ideal, allowing only the establishment of weaker notions of group information.

1.9 Teamwork in Times of Change

Multi-agent environments by their very nature are constantly changing:

As the computing landscape moves from a focus on the individual standalone computer system to a situation in which the real power of computers is realised through distributed, open and dynamic systems, we are faced with new technological challenges and new opportunities. The characteristics of dynamic and open environments in which, for example, heterogeneous systems must interact, span organisational boundaries, and operate effectively within rapidly changing circumstances and with dramatically increasing quantities of available information, suggest that improvements on the traditional computing models and paradigms are required. In particular, the need for some degree of autonomy, to enable components to respond dynamically to changing circumstances while trying to achieve over-arching objectives, is seen by many as fundamental (Luck et al., 2003).

Regardless of the complexity of teamwork, its ultimate goal is always team action. Team attitudes underpin this activity, as without them proper cooperation and coordination wouldn’t be possible. In TEAMLOG, intentions are viewed as an inspiration for goal-directed activity, reflected in the strongest motivational attitudes, that is in social (or bilateral) and collective commitments. While social commitments are related to individual actions, collective commitments pertain to plan-based team actions.

Basically, team action is nothing more than a coordinated execution of actions from the social plan by agents that have socially committed to do them. The kind of actions is not prescribed: they may vary from basic individual actions like picking up a violin, to more compound ones like carrying a piano, requiring strict coordination of the agents performing them together. In order to start team action, the underlying collective commitment should first be properly constructed in the course of teamwork. Indeed, different individual, social and collective attitudes that constitute the essential components of collective commitment have to be built carefully in a proper sequence. Our approach is based on the four-stage model of Wooldridge and Jennings (1999).

First, during potential recognition, an initiator recognizes potential teams that could actually realize the main goal. Then, the proper group is to be selected by him/her and constituted by establishing a collective intention between team members. This takes place during team formation. Finally, in the course of plan formation, a social plan realizing the goal is devised or chosen, and all agents agree to their shares in it, leading ultimately to collective commitment. At this point the group is ready to start team action. When defining these stages we abstract from particular methods and algorithms meant to realize them. Instead, the resulting team attitudes are given.

The explicit model of teamwork provided by TEAMLOG helps the team to monitor its performance and especially to re-plan based on the present situation. The dynamic and unpredictable environment poses the problem that team members may fail to realize their actions or that new favorable opportunities may appear. This leads to the reconfiguration problem: how to re-plan properly and efficiently when the situation changes during plan execution? A generic solution of this problem in BDI systems is provided by us in the reconfiguration algorithm, showing the phases of construction, maintenance and realization of collective commitment. In fact, the algorithm, formulated in terms of the four stages of teamwork and their complex interplay, is devised to efficiently handle the necessary re-planning, reflected in an evolution of collective commitment. Next to the algorithm, the dynamic logic component of TEAMLOG dyn addresses issues pertaining to adjustments in collective commitment during reconfiguration.

The static definitions from TEAMLOG and dynamic properties given in TEAMLOG dyn express solely vital aspects of teamwork, leaving room for case-specific extensions. Under this restriction both parts can be viewed as a set of teamwork axioms within a BDI framework. Thus,TEAMLOGformulates postulates to be fulfilled while designing the system. However, one has to realize that any multi-agent system has to be tailored to the application in question.

1.10 Our Agents are Planners

“Variety is the core of multi-agent systems.” This saying holds also for agents’planning. In early research on multi-agent systems, successful systems such as DMARS, Touring-Machines, PRS and InteRRaP were based on agents with access to plan depositories, from which they only needed to select a plan fitting the current circumstances (d’Invernoet al., 1998; Ferguson, 1992; Georgeff and Lansky, 1987; Müller, 1997). The idea behind this approach was that all possible situations had to be foreseen, and procedures to tackle each of them had to be prepared in advance. These solutions appear to be quite effective in some practical situations. However, over the last few years the time has become ripe for more refined and more flexible solutions.

Taking reconfiguration seriously, agents should be equipped with planning abilities. Therefore our book focuses on the next generation of software agents, who are capable to plan from first principles. They may use contemporary planning techniques such as continual distributed planning (desJardins et al., 1999; Durfee, 2008). Planning capabilities are vital when dealing with real-life complex situations, such as evacuation after ecological disasters. Usually core procedures are pre-defined to handle many similar situations as a matter of routine. However, the environment may change in unpredictable ways that call for time-critical planning as addition to these pre-defined procedures. In such dynamic circumstances, a serious methodological approach to (re-)planning from first principles is necessary. Even so, ubiquitous access to complex planning techniques is still a‘song of the future’.

In this book, we aim to provide the vital methodological underpinnings for teamwork in dynamic environments.

1.11 Temporal or Dynamic?

TEAMLOG has been built incrementally starting from individual intentions, which we view as primitive notions, through social (bilateral) commitments, leading ultimately to collective motivational attitudes. These notions play a crucial role in practical reasoning. As they are formalized in multi-modal logics, their semantics is clear and well defined; this enables us to express many subtle aspects of teamwork like various interactions between agents and their attitudes. The static theory TEAMLOG has been proved sound and complete with respect to its semantics (see Chapter 3 for the proof).

Multi-agent systems only come into their own when viewed in the context of a dynamic environment. Thus, the static logic TEAMLOG is embedded in a richer context reflecting these dynamics. When formally modeling dynamics in logic, the choice is between dynamic logic and temporal logic. Shortly stated, in dynamic logic actions (or programs) are first-class citizens, while in temporal logic the flow of time is the basic notion (Barringer et al, 1986; Benthem, 1995; Benthemet al., 2006; Doherty and Kvarnström, 2008; Fischer and Ladner, 1979; Fisher, 1994; Harel et al., 2000; Mirkowska and Salwicki, 1987; Salwicki, 1970; Szalas, 1995). Both approaches have their own advantages and disadvantages, as well as proponents and detractors. Lately, the two approaches are starting to be combined and their interrelations are extensively studied, including translations from dynamic presentations into temporal ones (Benthem and Pacuit, 2006). However, the action-related flavor so typical for dynamic logic is hidden in the complex formulas resulting from the translation. Even though the solution is technically satisfying, for modeling applicable multi-agent systems it is appropriate to choose a more recognizable and explicit representation.

We choose agents, actions and plans as the prime movers of our theory, especially in the context of reconfiguration in a dynamic environment. Dynamic logic is eminently suited to represent agents, actions and plans. Thus, we choose dynamic logic on the grounds of clarity and coherence of presentation. Some aspects, such as an agent’s commitment strategies, specifying in which circumstances the agent drops its commitments, can be much more naturally formalized in a temporal framework than in a dynamic one. As commitment strategies have been extensively discussed elsewhere (see, for example Dunin-Kęplicz and Verbrugge (1996); Rao and Georgeff (1991)), we shall only informally discuss them in Chapter 4. In addition, the interested reader will find a temporal framework in which our teamwork theory could be embedded in the appendix.

We are agnostic as to which of the two approaches, dynamic or temporal, is better. As Rao and Georgeff did in their version of BDI logic, one can view the semantics of the whole system as based on discrete temporal trees, branching towards the future, where the step to a consecutive node on a branch corresponds to the (successful or failing) execution of an atomic action (Rao and Georgeff, 1991, 1995b). In this view, the states are worlds at a point on a time-branch within a time-tree, so in particular, accessibility relations for individual beliefs, goals and intentions point from such a state to worlds at a (corresponding) point in time.

1.12 From Real-World Data to Teamwork

Formal approaches to multi-agent systems are concerned with equipping software agents with functionalities for reasoning and acting. The starting point of most of the existing approaches is the layer of beliefs, in the case of BDI systems extended by goals and intentions. These attitudes are usually represented in a symbolic, qualitative way. However, one should view this as an idealization. After all, agent attitudes originate from real-world data, gathered by a variety of sources at the object level of the system. Mostly, the data is derived from sensors responsible for perception, but also from hardware, different software platforms and last, but not least, from people observing their environment. The point is that this information is inherently quantitative. Therefore one deals with a meta-level duality: sensors provide quantitative characteristics, while reasoning tasks performed at the meta-level require the use of symbolic representations and inference mechanisms.

Research in this book is structured along the lines depicted in The object-level information is assumed to be summarized in queries returning Boolean values. In this way we will be able to abstract from a variety of formalisms and techniques applicable in the course of reasoning about real-world data. This abstraction is essential, since the

The object- and meta-level views on teamwork.


focus of this book is on the meta-level, including formal specification and reasoning about teamwork, as exemplified by the static and dynamic parts of TEAMLOG.

1.13 How Complex are Models of Teamwork?

Having a complete static logic TEAMLOG at hand, a natural next step is to investigate the complexity of the satisfiability problem of TEAMLOG, with the focus on individual and collective attitudes up to collective intention. (The addition of collective commitment does not add to the complexity of the satisfiability problem.) Our logics for teamwork are squarely multi-modal, in the sense that different operators are combined and may interfere. One might expect that such a combination is much more complex than the basic multi-agent logic with one operator, but in fact we show that this is not the case. The individual part ofTEAMLOG is PSPACE-complete, just like the single modality case. The full system, modeling a subtle interplay between individual and group attitudes, turns out to be EXPTIME-complete, and remains so even when propositional dynamic logic is added to it.

Additionally we make a first step towards restricting the language of TEAMLOG in order to reduce its computational complexity. We study formulas with bounded modal depth and show that in case of the individual part of our logics, we obtain a reduction of the complexity to NPTIME-completeness. We also show that for group attitudes in TEAMLOGthe satisfiability problem remains EXPTIME-hard, even when modal depth is bounded by 2. We also study the combination of reducing modal depth and the number of propositional atoms. We show that in both cases this allows for checking the satisfiability of the formulas in linear time.