Van Harmelen F., Lifschitz V., Porter B. Handbook of Knowledge Representation

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882 23. Cognitive Robotics

A fundamental question in the area of cognitive robotics (that Reiter had begun

to examine) is the relationship between pure logical representations of incomplete

knowledge and the more numerical measures of uncertainty. A start in this direction is

the work on the stochastic situation calculus [62] as well as that on noisy sensors and

effectors and decision-theoretic Golog, noted above.

On an even broader scale, a much tighter coupling of the high-level control pro-

gram and other parts of a robot’s software, like mapping and localization, or even

vision, is called for. For example, when localization fails and a robot gets lost, it

should be possible to use high-level control to do a reasoned failure recovery. Making

progress along these lines requires a deep understanding of both cognitive and more

traditional robotics, and should help to reduce the gap that currently exists between

the two research communities.

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Handbook of Knowledge Representation

Edited by F. van Harmelen, V. Lifschitz and B. Porter

DOI: 10.1016/S1574-6526(07)03024-6

887

Chapter 24

Multi-Agent Systems

Wiebe van der Hoek and Michael Wooldridge

We review the state of the art in knowledge representation formalisms for multi-agent

systems. We divide work in this area into two categories. In the ﬁrst category are

approaches that attempt to represent the cognitive state of rational agents, and to char-

acterize logically how such a state leads a rational agent to act. We begin by motivating

this approach. We then describe four of the best-known such logical frameworks, and

discuss the possible roles that such logics can play in helping us to engineer artiﬁ-

cial agents. In the second category are approaches based on representing the strategic

structure of a multi-agent environment, and in particular, the powers that agents have,

either individually or in coalitions. Here, we describe Coalition Logic, Alternating-

time Temporal Logic (

ATL), and epistemic extensions.

24.1 Introduction

The discipline of knowledge representation focuses on how to represent and reason

about environments with various different properties, usually with the goal of mak-

ing decisions, for example about how best to act in this environment. But what are the

things that are actually doing this representation and reasoning? The now-conventional

terminology is to refer to these entities as agents. The agents may be computer pro-

grams (in which case they are called software agents) or they may be people like you

or I. The case where there is only assumed to be one agent in the environment (for

example, a single autonomous robot operating in a warehouse) is usually the simplest

scenario for knowledge representation, and often does not require techniques beyond

those described elsewhere in this book. However, where there are multiple agents in

the environment, things get much more interesting—and challenging. This is because

it becomes necessary for an agent to represent and reason about the other agents in

the environment. Again there are two possibilities. The ﬁrst is that all the agents in

the environment can be assumed to share a common purpose. This might be the case,

for example, if we are designing a multi-robot system to operate in a warehouse en-

vironment. Here, we can assume the robots share a common purpose because we can

design them that way. However, the second case is again much more interesting, and

888 24. Multi-Agent Systems

presents many more challenges for knowledge representation. This is where the agents

comprising the system do not share the same purpose. This might be the case, for ex-

ample, in e-commerce systems, where a software agent is attempting to buy some

particular item for as low a price as possible, while a seller agent tries to sell it for as

high a price as possible. While in one sense the agents share a common goal of en-

gaging in trade, there is obviously a fundamental difference with respect to their more

speciﬁc goals.

How should we go about representing and reasoning about environments con-

taining multiple agents? That is, what aspects of them should we be attempting to

represent? Within the multi-agent systems community, one can distinguish two dis-

tinct trends:

Cognitive models of rational action: The ﬁrst main strand of research in repre-

senting multi-agent systems focuses on the issue of representing the attitudes

of agents within the system: their beliefs, aspirations, intentions, and the like.

The aim of such formalisms is to derive a model that predicts how a rational

agent would go from its beliefs and desires to actions. Work in this area builds

largely on research in the philosophy of mind.

Models of the strategic structure of the system: The second main strand of re-

search focuses not on the internal states or attitudes of agents, but on the

strategic structure of the environment: what agents can accomplish in the en-

vironment, either together or alone. Work in this area builds on models of

effectivity from the game theory community, and the models underpinning such

logics are closely related to formal games.

Inevitably, the actual divisions between these two categories are more blurred than our

rather crisp categorization suggests.

24.2 Representing Rational Cognitive States

In attempting to understand the behavior of agents in the everyday world, we fre-

quently make use of folk psychology:

Many philosophers and cognitive scientists claim that our everyday or “folk”

understanding of mental states constitutes a theory of mind. That theory is

widely called “folk psychology” (sometimes “commonsense” psychology). The

terms in which folk psychology is couched are the familiar ones of “belief” and

“desire”, “hunger”, “pain” and so forth. According to many theorists, folk psy-

chology plays a central role in our capacity to predict and explain the behavior of

ourselves and others. However, the nature and status of folk psychology remains

controversial. [117]

For example, we use statements such as Michael intends to write a paper in order

to explain Michael’s behavior. Once told this statement, we expect to ﬁnd Michael

shelving other commitments and developing a plan to write the paper; we would expect

him to spend a lot of time at his computer; we would not be surprised to ﬁnd him in

a grumpy mood; but we would be surprised to ﬁnd him at a late night party. The

philosopher Dennett coined the phrase intentional system to refer to an entity that is

W. van der Hoek, M. Wooldridge 889

best understood in terms of folk-psychology notions such as beliefs, desires, and the

like [25]. This was also what Hofstadter was referring to already in 1981, when he

sketched “coffee house conversation on the Turing test to determine if a machine can

think” [55], in which several students discuss AI and in which one of them states

that “you AI advocates have far underestimated the human mind, and that there are

things a computer will never, ever be able to do”. Sandy, a philosophy student puts the

following forward:

But eventually, when you put enough feelingless calculations together in a

huge coordinated organization, you’ll get something that has properties on an-

other level. You can see it—in fact you have to see it—not as a bunch of little

calculations, but as a system of tendencies and desires and beliefs and so on.

When things get complicated enough, you’re forced to change your level of de-

scription. To some extend that’s already happening, which is why we use words

such as “want”, “think”, “try”, and “hope”, to describe chess programs and other

attempts at mechanical thought.

The intentional stance is essentially nothing more than an abstraction tool. It is

a convenient shorthand for talking about certain complex systems (such as people),

which allows us to succinctly predict and explain their behavior without having to

understand or make claims about their internal structure or operation. Note that the

intentional stance has been widely discussed in the literature—let us just remark here

that Sandy of the Coffeeshop Conversation claims that the really interesting things in

AI will only begin to happen, ‘when the program itself adopts the intentional stance

towards itself’—and it is not our intention to add to this debate; see [112] for a discus-

sion and references.

If we accept the usefulness of the intentional stance for characterizing the proper-

ties of rational agents, then the next step in developing a formal theory of such agents

is to identify the components of an agent’s state. There are many possible mental

states that we might choose to characterize an agent: beliefs, goals, desires, intentions,

commitments, fears, hopes, and obligations are just a few. We can identify several

important categories of such attitudes, for example:

Information attitudes: those attitudes an agent has towards information about its

environment. The most obvious members of this category are knowledge and

belief.

Pro attitudes: those attitudes an agent has that tend to lead it to perform actions.

The most obvious members of this category are goals, desires, and intentions.

Normative attitudes: including obligations, permissions and authorization.

Much of the literature on developing formal theories of agency has been taken up with

the relative merits of choosing one attitude over another, and investigating the possible

relationships between these attitudes. While there is no consensus on which attitudes

should be chosen as primitive, most formalisms choose knowledge or belief together

with at least goals or desires.

890 24. Multi-Agent Systems

24.2.1 A Logical Toolkit

In attempting to axiomatize the properties of a rational agent in terms of (say) its

beliefs and desires, we will ﬁnd ourselves attempting to formalize statements such as

the following

(24.1)Wiebe believes Ajax are great.

(24.2)Wiebe desires that Ajax will win.

This suggests that a logical characterization of these statements must include construc-

tions of the form



believes

desires



where i is a term denoting an agent, and ϕ is a sentence. We immediately encounter

difﬁculties if we attempt to represent such statements in ﬁrst-order logic. First of all,

the constructs mentioned above should deﬁnitely not be extensional—even if “it rains

in Utrecht” and “it rains in Liverpool” may accidentally both be true, one can believe

one without the other, desire the second but not the ﬁrst, even try to achieve one while

hindering the other. Apart from this, representing such statements in ﬁrst-order logic—

as binary predicates of the form Bel(i, ϕ) and Desire(i, ϕ)—will not work, because

the second term is a sentence, and not a term. By ﬁxing the domain of the ﬁrst-order

language to be itself a language, we can get around this problem, thereby obtaining a

ﬁrst-order meta-language. The meta-language approach has been successfully adopted

by a number of researchers, for example, [106]. However, meta-language approaches

have also been criticized for representing mental states (see, e.g., [63] for a detailed

critique). Instead of choosing a meta-language approach, most researchers opt for a

modal approach, whereby an agent’s beliefs, desires, and the like are represented by

an indexed collection of modal operators. The semantics of these operators are gener-

ally given in terms or Kripke structures, in the by-now familiar way [19, 86, 13].The

use of Kripke structures and their associated mathematics of correspondence theory

makes it possible to quickly generate a number of soundness results for axiomati-

zations of these logics. However, the combination of many modalities into a single

framework presents asigniﬁcant challenge from a logical pointof view. Completeness,

expressivity and complexity results for logics that incorporate multiple modalities into

a single framework are typically complex, and this area of research is much at the

leading edge of contemporary modal logic research [34]. Moreover, reasoning in such

enriched systems is typically computationally very hard [39]. Despite these problems,

modal approaches dominate in the literature, and in this article, we focus exclusively

on such approaches.

In addition to representing an agent’s attitudes, logics of rational agency also typ-

ically incorporate some way of representing the actions that agents perform, and the

effects of these actions. Many researchers adapt techniques from dynamic logic in

order to represent actions and their effects [42], whereas others conﬁne themselves

to a temporal set-up. Although there is some work in establishing the exact relation

between the two approaches, this issue still deserves a better investigation.

In the next four sections, we review some of the best-known formalisms for rea-

soning about the cognitive states of rational agents:

W. van der Hoek, M. Wooldridge 891

• Dynamic Epistemic Logic (

DEL);

• Cohen and Levesque’s seminal intention logic [22];

• Rao and Georgeff’s

BDI framework [91]; and

• the

KARO framework of Linder et al. [70].

24.2.2 Dynamic Epistemic Logic

The ﬁrst formalism we deal with, dynamic epistemic logic, is intended to capture the

interaction between the actions that an agent performs and its knowledge. Elsewhere

in this handbook is a full treatment of logics for knowledge, and we pre-suppose

some familiarity with this subject. The idea is simply to take the logical machinery

of epistemic logic [30] and augment it with a dynamic component [43], for referring

to actions. The origins of such logics for knowledge representation lie in the work

of Robert Moore [77]. Moore’s chief concern was to study the ways that knowledge

and action interact, and he identiﬁed two main issues. The ﬁrst is that some actions

produce knowledge, and therefore their effects must be formulated in terms of the epis-

temic states of participants. The second is that of knowledge preconditions: what an

agent needs to know in order to be able to perform an action. A simple example is that

in order to unlock a safe, one must know the combination for the lock. Using these

ideas, Moore formalized a notion of ability. He suggested that in order for an agent to

be able to achieve some state of affairs ϕ, the agent must either:

• know the identity of an action α (i.e., have an “executable description” of an

action α) such that after α is performed, ϕ holds; or else

• know the identity of an action α such that after α is performed, the agent will

know the identity of an action α



such that after α



is performed, ϕ holds.

The point about “knowing the identity” of an action is that, in order for me to be able

to become rich, it is not sufﬁcient for me simply to know that there exists some action

I could perform which would make me rich; I must either know what that action is

(the ﬁrst clause above), or else to be able to perform some action which would furnish

me with the information about which action to perform in order to make myself rich.

This apparently subtle distinction is rather important, and it is known as the distinction

between knowledge de re (which involves knowing the identity of a thing) and de dicto

(which involves knowing that something exists) [30, p. 101]. We will see later, when

we review more recent work on temporal logics of ability, that this distinction also

plays an important role there.

Nowadays, the term Dynamic Epistemic Logic (

DEL) [11, 108] is used to refer

to formalisms that add a special class of actions—epistemic actions—to the standard

logic S5 for knowledge. The term “epistemic action” is used to refer to an action with

an epistemic component, such as learning or announcing something. Thus, in

DEL,

actions themselves have an epistemic ﬂavor: they denote an announcement, a private

message, or even the act of “suspecting” something.

There are several variants of dynamic epistemic logic in the literature. In the lan-

guage of [108], apart from the static formulas involving knowledge, there is also the

construct [α]ϕ, meaning that after execution of the epistemic action α, statement ϕ is