=Paper=
{{Paper
|id=None
|storemode=property
|title=Towards a Normative BDI Architecture for Norm Compliance
|pdfUrl=https://ceur-ws.org/Vol-627/coin_5.pdf
|volume=Vol-627
|dblpUrl=https://dblp.org/rec/conf/mallow/CriadoANB10
}}
==Towards a Normative BDI Architecture for Norm Compliance==
https://ceur-ws.org/Vol-627/coin_5.pdf
Towards a Normative BDI Architecture for
Norm Compliance
N. Criado1 , E. Argente1 , P. Noriega2 , and V. Botti1
1
Departamento de Sistemas Informáticos y Computación
Universidad Politécnica de Valencia
Camino de Vera s/n. 46022 Valencia (Spain)
Email: {ncriado,eargente,vbotti}@dsic.upv.es
2
Institut d’Investigació en Intel.ligència Artificial
Consejo Superior de Investigaciones Cientı́ficas
Campus de la UAB, Bellaterra, Catalonia (Spain)
Email: pablo@iiia.csic.es
Abstract. Multi-Agent Systems require coordination mechanisms in or-
der to assemble the behaviour of autonomous and heterogeneous agents
and achieve the desired performance of the whole system. Norms are
deontic statements employed by these coordination mechanisms which
define constraints to the potential excesses of agents’ autonomous be-
haviour. However, norms are only effective if agents are capable of un-
derstanding and managing them pragmatically. In this paper, we propose
an extension of the BDI proposal in order to allow agents to take prag-
matic autonomous decisions considering the existence of norms. In par-
ticular, coherence and consistency theory will be employed as a criterion
for determining norm compliance.
1 Introduction
The development of network technologies and Internet has made it possible
to evolve from monolithic and centralized applications, in which problems are
solved by a single component, to distributed applications, in which problems are
solved by means of the interaction among autonomous agents. In these systems,
the autonomy and heterogeneity of agents make mandatory the definition of
coordination mechanisms for ensuring the whole performance of the system.
With this aim, social notions, such as organizations, institutions and norms,
have been introduced in the design and implementation of distributed systems.
Norms have been defined in distributed systems as regulations or patterns of
behaviour established in order to constrain the potential excesses of autonomous
agents. The definition of norms for controlling distributed systems requires the
development of normative agents. Normative agents [8] must be endowed with
capabilities for considering norms and deciding which norms to comply with and
how to comply with them. The multi-context Graded BDI architecture [7] allows
agents to reason in uncertain and dynamic environments.
65
The work presented in [9] is a first effort on the extension of the Graded BDI
architecture [7] in order to allow agents to accept norms autonomously. This
work focuses on the description of the architecture as a whole but it provides
few details about how agents acquire new norms and face with the norm compli-
ance dilemma. In addition, it lacks an elaborated definition of norm and norm
dynamics. According to these criticisms, in this paper we propose to revise this
architecture in order to allow agents to take norms into account in a more sophis-
ticated way. In particular, here we focus on the application of both Cognitive
Coherence Theory [26] and Consistency Theory [2] for reasoning about norm
compliance. Coherence is a cognitive theory whose main purpose is the study of
how pieces of information influence each other by imposing a positive or nega-
tive constraint over the rest of information. Consistency is a logic property which
analyses the relationship among a formula and its negation. Our proposal con-
sists on applying deliberative coherence theory for determining which norms are
more coherent with respect to the agent’s mental state. In addition, consistency
criterion is considered when determining how to comply with norms. Therefore,
this paper tries to overlap some of the main drawbacks of the original proposal
by means of adding coherence and consistency constraints to the architecture.
This paper is structured as follows: next section describes the background of
our proposal; Section 3 provides norm definitions; in Section 4 the normative BDI
architecture is explained; the two components in charge of norm management
are explained in Sections 5 and 6; Section 7 describes the norm internalization
process; and, Section 8 remarks the contributions and future work.
2 Background
Along this section all approaches considered for this work are explained. In
particular, the normative multi-context Graded BDI architecture (n-BDI for
short) refined in this paper is explained first. Next subsections introduce the
basis of consistency and coherence theories.
2.1 BDI architectures for normative agents
Usually, proposals on agent architectures which support normative reasoning do
not consider norms as dynamic objects which may be acquired and recognised by
agents. On the contrary, these proposals consider norms as static constraints that
are hard-wired on agent architectures. Regarding recent proposals on individual
norm reasoning, the BOID architecture [4] represents obligations as mental at-
tributes and analyses the relationship and influence of such obligations on agent
beliefs, desires and intentions. However, this proposal presents some drawbacks:
i) it only considers obligation norms; ii) it considers norms as static entities that
are off-line programmed in agents. In relation with this last feature, the EMIL
proposal [1] has developed a framework for autonomous norm recognition. Thus,
agents would be able to acquire new norms by observing the behaviour of other
agents which are situated in their environments. The main disadvantage of EMIL
66
is that agents obey all recognised norms blindly without considering their own
motivations. The multi-context graded BDI agent architecture [7] does not pro-
vide an explicit representation of norms. However, it is capable of representing
and reasoning with graded mental attitudes, which makes it suitable as a basis
for a norm aware agent architecture.
In order to overlap these drawbacks, in [9, 10], the multi-context graded BDI
agent architecture [7] has been extended with recognition and normative rea-
soning capabilities. According to the n-BDI proposal, an agent is defined by a
set of interconnected contexts, where each context has its own logic (i.e. its own
language, axioms and inference rules). In addition, bridge rules are inference
rules whose premises and conclusions belong to different contexts. In particular,
an n-BDI agent [9, 10] is formed by:
– Mental contexts [6] to characterize beliefs (BC), intentions (IC) and desires
(DC). These contexts contain logic propositions such as (Ψ γ, δ); where Ψ
is a modal operator in {B, D+ , D− , I} which express beliefs, positive and
negative desires and intentions, respectively; γ ∈ LDL is a dynamic logic
[19] proposition; and δ ∈ [0, 1] represents the certainty degree associated
to this mental proposition. For example (Bγ, δ) represents a belief about
proposition γ of an agent and δ represents the certainty degree associated
to this belief.
– Functional contexts [6] for planning (PC) and communication (CC).
– Normative contexts [9] for allowing agents to recognise new norms (RC) and
to consider norms in their decision making processes (NC).
– Bridge Rules for connecting mental, functional and normative contexts. A
detailed description of these bridge rules can be found in [7]. For a more
detailed description of normative bridge rules see [9].
Regarding the normative extension of the BDI architecture, the norm decision
process consists of the following steps:
1. It starts when the RC derives a new norm through analysing its environment.
2. These norms are translated into a set of inference rules which are included
into the NC. The NC is responsible for deriving new beliefs and desires
according to the current agent mental state and the inference rules which
have been obtained from norms.
3. After performing the inference process for creating new beliefs and desires
derived from norm application, the normative context must update the men-
tal contexts.
The original proposal [9, 10] is a preliminary work towards the definition of
autonomous norm aware agents capable of making a decision about norm com-
pliance. In this sense, this approach presents several problems and deficiencies.
Firstly, the notion of norm is vague and imprecise, in this sense there is not a
clear definition of what an abstract norm and a norm instance mean. Regarding
the norm recognition process, no details about how the set of abstract norms is
updated and maintained are provided. Thus, the RC is seen as a black box that
67
gives no analysis of how it deals with different types of norms (e.g. social norms,
explicit norms created by the institution). Finally, it lacks a more concrete de-
scription of how a BDI agent may decide about obeying or not a norm. In this
sense, the derivation of positive and negative desires from obligations and pro-
hibitions is too simple. In particular, norms that guide agent behaviours might
be in conflict, since they are aimed at defining the ideal behaviour of different
roles which may be played by one agent. Besides that, norm compliance deci-
sions should be consistent with the mental state of agents. Therefore, how agents
make consistent decisions about norm compliance is the main contribution of the
current paper with respect to the original proposal [9].
As a solution to this problem we will employ works on formalisms for ensuring
consistency [2] and coherence [26]. In particular, this paper describes how these
works are applied for reasoning about norm compliance. Next subsections briefly
describe both the proposal of Casali et al. [6] on consistency among graded
bipolar desires and the work of Joseph et al. [17] on the formalization of deductive
coherence for multi-context graded BDI agents.
2.2 Consistency for Graded BDI Agents
In [2] Benferhat et al. made a study of consistency among bipolar graded prefer-
ences. Taking this definition of consistency, Casali et al. in [6] proposed several
schemas for ensuring consistency among mental graded propositions. In particu-
lar, the maintenance of consistency among desires is achieved by means of three
different schemas (i.e. DC1 , DC2 and DC3 ) which impose some constraints be-
tween the positive and negative desires of a formula and its negation. Thus, DC2
schema (which will be employed in this paper) imposes a restriction over positive
and negative desires for the same goal ((D+ γ, δγ+ ) and (D− γ, δγ− ), respectively).
In particular, it claims that an agent cannot desire to be in world more than it
is tolerated (i.e. not rejected). Therefore, it determines that:
δγ+ + δγ− ≤ 1
where δγ+ and δγ− are the desirability and undesirability degrees (i.e. the certainty
of the positive and negative desire) of proposition γ, respectively.
2.3 Coherence for Graded BDI Agents
In [26] Thagard claims that coherence is a cognitive theory whose main purpose
is the study of associations; i.e. how pieces of information influence each other by
imposing a positive or negative constraint over the rest of information. According
to Thagard’s formalization, a coherence problem is modelled by a graph g =
�V, E, ζ�; where V is a finite set of nodes representing pieces of information, E are
the edges representing the positive or negative constraints among information;
each constraint has a weight (ζ : E → [−1, 1] \ {0}) expressing the constraint
strength. Maximizing the coherence [26] is the problem of partitioning nodes
68
into two sets (accepted A and rejected V \ A) which maximizes the strength of
the partition, which is the sum of the weights of the satisfied constraints.
Taking a proof-theoretic approach, Joseph et al. [17] provide a formalization
of deductive coherence for multi-context graded BDI agents. Thus, this work
proposes a formalization together with mechanisms for calculating the coher-
ence of a set of graded mental attitudes. The main idea beyond this formal-
ism is to consider the inference relationships among propositions belonging to
the same context for calculating the weight of coherence and incoherence rela-
tionships. Similarly, bridge rules are employed for setting the coherence degree
among propositions belonging to different contexts. Details concerning building
the coherence graph can be found in [17].
Regarding the relation of coherence with normative decision processes, in [18]
Joseph et al. employed coherence as a criterion for rejecting or accepting norms.
However, this work is based on a very simple notion of norm as an unconditional
obligation. Moreover, this proposal only considers coherence as the one rational
criterion for norm acceptance. In addition, the problem of norm conflict has not
been faced. Finally the process by which agents’ desires are updated according
to norms have also been defined in a simple way without considering the effect
of these normative desires on the previous existing desires.
3 Norm Notion
Norms have been studied from different fields such as philosophy, psychology,
law, etc. MAS research has given different meanings to the norm concept, been
employed as a synonym of obligation and authorization [14], social law [20], social
commitment [24] and other kinds of rules imposed by societies or authorities.
In this work, we take as a basis the formalization of norms made in [21]. In
this proposal a distinction among abstract norms and norm instances is made.
An abstract norm is a conditional rule that defines under which conditions obli-
gations, permissions and prohibitions should be created. In particular, the ac-
tivation condition of an abstract norm defines when an obligation, permission
or prohibition must be instantiated. The norm instances that are created out
of the abstract norms are a set of active unconditional expressions that bind a
particular agent to an obligation, permission or prohibition. Moreover, a norm
instance is accompanied by an expiration condition which defines the validity
period or deadline of the norm instance.
Following this proposal our definition of both abstract norms and norm in-
stances is provided.
Definition 1 (Abstract Norm). An abstract norm is defined as a tuple na =
�D, A, E, C, S, R� where:
– D ∈ {F, P, O} is the deontic type of the norm. In this work obligations
(O) and prohibitions (F) impose constraints on agent behaviours; whereas
permissions (P) are operators that define exceptions to the activation of obli-
gations or prohibitions;
69
– A is the norm activation condition. It defines under which circunstancies the
abstract norm is active and must be instantiated.
– E is the norm expiration condition, which determines when the norm no
longer affects agents.
– C is a logic formula that represents the state of affairs or actions that must
be carried out in case of obligations, or that must be avoided in case of
prohibition norms.
– S, R are expressions which describe the actions (sanctions S and rewards R)
that will be carried out in case of norm violation or fulfilment, respectively.
Since this work is focused on the norm compliance problem, only those norms
addressed to the agent will be taken into account.
Definition 2 (Norm Instance). Given belief theory ΓBC an abstract norm
na = �D, A, E, C, S, R� is instanciated into a norm instance
ni = �D, C � �where:
– ΓBC � σ(A), where σ is a substitution of variables in A such that A� = σ(A)
and σ(S), σ(R) and σ(E) are fully grounded.
– C � = σ(C).
Once the activation conditions of an abstract norm hold it becomes active
and several norm instances, according to the possible groundings of the activa-
tion condition, must be created. For simplicity, we assume that once a norm is
being instantiated then it is fully grounded. In our proposal, the instantiation
of activation and expiration conditions are considered by the Norm Instantia-
tion bridge rule (which will be explained in Section 6). Similarly, sanctions and
rewards are also considered by this bridge rule in order to decide about conve-
nience of norm compliance. Thus, for simplicity we omit the instantiation of the
norm expiration and activation conditions (σ(A) and σ(E)) and the sanction
and reward (σ(S) and σ(R)) in the representation of a norm instance.
4 Normative BDI Architecture (n-BDI)
As previously mentioned, the main contribution of this paper is to refine the
n-BDI architecture, which was originally proposed in [9, 10], with a more elabo-
rated notion of norm and norm reasoning. In order to design this second version
of the n-BDI, the work of Sripada et al. [25] has been considered as a reference.
It analyses the psychological architecture subserving norms. In particular, this
architecture is formed by two closely linked innate mechanisms: one responsible
for norm acquisition, which is responsible for identifying norm implicating be-
haviour and inferring the content of that norm; and the other in charge of norm
implementation, which maintains a database of norms, detects norm violations
and generates motivations to comply with norms and to punish rule violators.
The evolution of n-BDI is focused on reasoning about norm compliance and
acceptance, so issues related to the detection and reaction to norm violation
are beyond the scope of this paper. In this sense, norms affect n-BDI agents in
70
two ways: i) when a norm is recognised and accepted then it is considered to
define new plans; and ii) when accepted norms are active then their instances
are used for selecting the most suitable plan which complies with norms. This
paper tackles with this last effect of norms. In particular, this paper describes
how Deductive Coherence (described in Section 2.3) and Consistency Theory
(described in Section 2.2) are applied for reasoning about norm compliance.
The n-BDI refines the normative contexts (described in Section 2.1) according
to the norm notions introduced in Section 3. Therefore, Figure 1 shows a scheme
of the n-BDI proposed in this paper. In particular, the RC has been redefined as
the Norm Acquisition Context (NAC), whereas the NC has been redefined into
the Norm Compliance Context (NCC).
Fig. 1. Normative Extension of the Multi-Context BDI Architecture. Grey contexts
and dashed lines (bridge rules) correspond to the basic definition of a BDI agent. The
normative extensions are the white contexts and bold lines.
In this new version of the agent architecture not only the normative contexts
have been improved by considering more elaborated normative definitions, but
also the norm reasoning process has been extended with consistency and coher-
ence notions. Thus, the norm reasoning process can be described as follows:
1. It starts when the NAC receives information cues for inferring new abstract
norms through the Norm Acquisition bridge rule. The NAC carries out an
inference process for maintaining the set of abstract norms in force in a
specific moment.
2. Once the norm activation conditions hold, abstract norms are instantiated
and included into the NCC by means of the Norm Instantiation bridge rule.
Then, the NCC carries out an internal process for determining compliance
with which of the norm instances. In this sense, not all active norms should
be considered when updating the mental state. In this sense, our proposal
consists in employing coherence theory as a criterion for determining which
norms comply with. Therefore, the coherence maximization process is cal-
71
culated in order to determine which norm instances are consistent and must
be taken into account when updating the desire theory.
3. Then, Norm Internalization bridge rules derive new desires according to the
current agent mental state and the set of complied norms, also taking into
account consistency considerations. These new desires may help the agent to
select the most suitable plan to be intended and, as a consequence, normative
actions might be carried out by the agent.
Thus, the norm reasoning process is formed by four different phases: acquisition
of norms in force, decision about norm compliance and internalization of norms.
Next sections describe each one of these phases in detail.
5 Norm Acquisition (NAC)
The NAC context allows agents to maintain a norm base that contains those
norms which are in force in a specific moment (i.e. all norms which are currently
applicable). Thus it is responsible for acquiring new norms and deleting obsolete
norms; and updating the set of in force norms accordingly. This process can be
defined as objective since no motivation or goal is considered in the acquisition
process. Thus, agents only take into account their knowledge of the world in
order to determine the set of norms which is more likely to be in force.
NAC Language. The NAC is formed by expressions such as (n, ρ) where n is
an abstract norm according to Definition 1; and ρ ∈ [0, 1] is a real value which
assigns a degree to this abstract norm. This parameter ρ can have different
interpretations. It can be defined as the reputation of the informer agent in
case of leadership-based norm spreading. If norms are inferred by imitation, ρ
might represent the acceptance degree of the norm. In case of utility maximizing
approaches, as learning algorithms, it can be defined as the expected utility of
the norm.
Abstract Norm Recognition. Regarding how new and obsolete norms are
recognised, the NAC consists of a computational model of autonomous norm
recognition which receives the agent perceptions, both observed and communi-
cated facts, and identifies the set of norms which control the agent environment.
Perceptions which are relevant to the norm recognition may be classified into:
– Explicit normative perceptions. They correspond to those messages exchanged
by agents in which norms are explicitly communicated. Following this ap-
proach, several works have focused on analysing the role of leaders in the
norm spreading. In particular, these leaders provide normative advices to
follower agents when deciding about a norm [27, 22].
– Implicit normative perceptions. This type of perceptions includes the obser-
vation of actions performed by agents as a way of detecting norms. Since
norms are usually supported by enforcing mechanisms such as sanctions and
72
rewards, the detection of them has been considered as an alternative for ac-
quiring new norms [15]. Other works have proposed imitation mechanisms
as a criterion for acquiring new norms. These models are characterized by
agents mimicking the behaviour of what the majority of the agents do in a
given agent society [28, 5]. Moreover, in [23] researchers have experimented
with learning algorithms to identify a norm that maximizes an agent’s utility.
– Mixed normative perceptions. There are proposals which consider both ex-
plicit and implicit normative perceptions as cues for inferring norms [1].
Abstract Norm Dynamics. The set of norms which are in force may change
both explicitly, by means of the addition, deletion or modification of the existing
norms; and implicitly by introducing new norms which are not specifically meant
to modify previous norms, but which change in fact the system because they are
incompatible with such existing norms and prevail over them [16]. However, this
is a complex issue which is out of the scope of this paper. Works presented at the
Formal Models of Norm Change 3 are good examples of proposals which provide
a formal analysis of all kinds of dynamic aspects involved in systems of norms.
This paper does not focus on the norm acquisition problem and the dynamics
of abstract norms. In the following, the NAC will be considered as a black box
that receives cues for detecting norms as input and generates abstract norms as
output.
6 Norm Compliance (NCC)
The NCC is the component responsible for reasoning about the set of norms
which hold in a specific moment. In this sense the NAC recognises all norms
that are in force, whereas the NCC only contains those norms which are active
according to the current situation. The NCC should determine which and how
norms will be obeyed and support agents when facing with norm violations.
In this sense, the NCC detects norm violations and fulfilments and generates
punishing and rewarding reactions. This last issue is over the scope of this paper
and will be analysed in future works.
The functionalities carried out by the NCC which are covered by this work
are related to three main issues: the NCC is in charge of maintaining the set
of instantiated norms which are active; then it considers convenience of norm
compliance and determines which norms comply with; and, finally, it derives new
desires for fulfilling these norms.
NCC Language. The NCC is formed by expressions such as: (n, ρ) where n
is a norm instance according to Definition 2. ρ ∈ [0, 1] is a real value which
assigns a degree to this norm instance. This parameter can be interpreted as the
salience of the norm instance. Its value can be determined according to different
3
http://www.cs.uu.nl/events/normchange2/
73
criteria such as utility of norm compliance, emotional considerations, intrinsic
motivations, etc. In this paper, it is defined with regard to the certainty of norm
activation as well as the convenience of norm compliance.
Instantiated norms are inferred by applying instantiation bridge rules to
norms when their activation is detected. Next, these normative bridge rules are
described in detail.
Norm Instantiation Bridge Rule.
N AC : (�D, A, E, C, S, R�, ρ), BC : (B A, βA ), BC : (B¬E, βE )
(1)
N CC : (�D, C�, finstantiation (θactivation , θcompliance )))
If an agent considers that an abstract norm na = �D, A, E, C, S, R� is cur-
rently active ((B A, βA ) ∧ (B¬E, βE )) then a new norm instance ni = �D, C� is
generated. The degree assigned to the norm instance is defined by the finstantiation
function which combines the values obtained by the θactivation and θcompliance
functions.
On the one hand, θactivation combines the evidence about norm activation
(i.e. the certainty degrees βA , βE and ρ). It can be given a sophisticated definition
depending on the concrete application. In this work, it has been defined as the
weighed average among these three values, as follows:
wA × βA + wE × βE + wρ × ρ
θactivation =
wA + wE + wρ
If all values are equally weighed, then we obtain that θactivation = βA +β3 E +ρ
On the other hand, θcompliance considers both intrinsic and instrumental mo-
tivations for norm compliance. In [11] different strategies for norm compliance
from an instrumental perspective over this architecture are described. In par-
ticular, they consider the influence of norm compliance and violation on agent’s
goals for determining whether the agent accepts the norm. For example, an egoist
agent will accept only those norms which benefit its goals (i.e. whose condition
is positively desired). In this case:
�
1 if δC +
> 0, where (D+ C, δC
+
) ∈ ΓDC ;
θcompliance =
0 otherwise
Finally, values obtained by the θactivation and the θcompliance functions are
combined by the finstantiation :
wactivation × θactivation + wcompliance × θcompliance
finstantiation (θactivation , θcompliance ) =
wactivation + wcompliance
Again, if these two parameters are equally weighed, then we obtain that
θactivation + θcompliance
finstantiation (θactivation , θcompliance ) =
2
74
This approach relies upon various values such as wcompliance , wA and wactivation .
The definition of these values is beyond the scope of this paper. In previous works
[9, 11, 10], it has been considered that they are defined off-line by the agent de-
signer. However, this solution is static and it does not allow agents to adapt these
values according to a changing environment. Thus, this issue will be considered
in future works.
6.1 Coherence For Norm Instances
Once Norm Instantiation bridge rule has been applied, it is possible that there
is an incoherence between mental propositions. Because of this, a maximizing
coherency process is needed in order to determine which propositions are consis-
tent and must be taken into account; and which propositions belonging to the
rejection set will be ignored when deriving normative desires.
Since our proposal of agent architecture employs graded logics for repre-
senting mental propositions, this work takes as a basis the work described in
Section 2.3. As argued before, this work proposes a formalization together with
mechanisms for calculating the deductive coherence of a set of graded mental at-
titudes. Our proposal adapts this work by applying the coherence maximization
algorithm to the norm compliance problem. Figure 2 illustrates an overview of
the employment of coherence as a criterion for resolving the norm compliance
dilemma. As shown by this figure, the normative coherence process considers
propositions belonging to the BC, the NCC and NAC. Basically this process
takes into account: i) the beliefs that sustain the activation of norms and their
relationships among them and other beliefs of the BC; ii) the norm instances
and conflict relationships among them; and iii) the abstract norms which have
triggered the norm activation. Relationships among propositions belonging to
each context are defined by means of inference rules and axioms, whereas coher-
ence connections among propositions of different contexts are defined by means
of norm instantiation bridge rules.
By considering coherence we will address three different problems: i) deter-
mining norm deactivation; ii) determining active norms in incoherent states and
iii) normative conflict resolution. In order to formalize normative incoherence
the original proposal of [17] must be extended with extra constraints. Moreover,
since we apply the coherence calculation algorithms for improving the normative
reasoning, then only those propositions which are relevant to the norm compli-
ance process are taken into account. Next, both the definition of normative
coherence constraints for facing with each one of these three questions as well
as the determination of relevant propositions is detailed.
Detecting Norm Activation in Incomplete and Inconsistent States. As
illustrated in Figure 2, norm instantiation bridge rule (see equation 6) allows
norm instances (from NCC) to be connected to beliefs from BC related to their
activation and expiration conditions. Norm instantiation bridge rule has as pre-
conditions the belief about the occurrence of the activation condition A and the
75
Fig. 2. Usage of coherence as a criterion for resolving the norm compliance dilemma.
negation of the expiration condition E. Usually agents do not have an explicit
knowledge about the negation of E. However, it is possible to infer a certainty
degree about ¬E from the certainty degree of E. Following this idea, the first
step for computing coherence is to calculate the closure under negation of beliefs
as follows:
Definition 3 (Closure of Beliefs under Negation). Let Γ be a finite belief
theory presentation using graded formulas. We define the closure of Γ under
negation as:
Γ ¬ = Γ ∪ {(B¬ϕ, (1 − δ)) : (B¬ϕ, β) �∈ Γ and (Bϕ, δ) ∈ Γ }
Therefore, the closure of a set of beliefs under negation consists on extending this
theory by inferring new information from what is actually believed. In particular,
if an agent believes that proposition E is true with a certainty degree δ but it
does not have any belief concerning its negation, it is logic to assume that the
certainty degree assigned to ¬E should be lower than (1−δ). We need to calculate
the closure of beliefs under negation in order to detect norm deactivation. In this
sense, when the certainty about the expiration condition E increases it can be
inferred that the certainty of ¬E decreases even if the agent does not have
explicit evidence of it.
In addition we want to define an incoherence relationship among a belief
related to a general proposition and its negation. This relationship is defined by
means of the addition of an inference rule in the belief context:
(BC1 ) (Bγ, βγ ), (B¬γ, β¬γ ) � (0̄, 1 − (βγ + β¬γ ))
Basically this scheme means that to belief γ and ¬γ simultaneously is a con-
tradiction (0̄). The certainty degree of this contradiction is defined in [18] as
1 − (βγ + β¬γ ).
76
One of the main problems of the multi-context BDI architecture is the fact
that it does not allow the definition of bridge rules for deleting propositions. In
this sense, there is a bridge rule for inferring a new instance of a norm when
its activation condition holds. However, it is not possible to create a bridge rule
which deletes this instance when the expiration condition holds. In response to
this problem, coherence will be used as a criterion for detecting norm deacti-
vation. Moreover, an agent may have beliefs related to the occurrence of both
the norm activation and expiration conditions. Thus it should consider all those
evidences that sustain the occurrence of the expiration and activation conditions
in order to determine the set of norms which are active. In particular, coherence
will be used as a criterion for detecting norm activation/deactivation according
to the certainty of both the expiration and the activation conditions.
Resolving Normative Conflicts. As previously argued, the above process
of normative coherence is useful not only to determine which norms are active
but even to resolve a norm conflict. Usually, a norm conflict has been defined
in other works as a situation in which something is considered as forbidden
and obliged or forbidden and permitted. In our proposal, we define permissions
as a normative operator which allows defining an exception to the application
of a more general obligation or prohibition norm. Thus, we also consider that
norms which define something as forbidden and permitted are also in conflict.
However, there is no constraint that represents this type of incoherence. In order
to represent incoherence inferred from norm conflicts we add the next inference
rules to the NCC:
(N CC1 ) (�O, C�, ρO ), (�F, C�, ρF ) � (0̄, −min(ρO , ρF ))
(N CC2 ) (�O, C�, ρO ), (�P, ¬C�, ρP ) � (0̄, 1 − (ρO + ρP ))
(N CC3 ) (�F, C�, ρF ), (�P, C�, ρP ) � (0̄, 1 − (ρF + ρP ))
In case of a conflict between a permission and an obligation or a prohibition, the
degree of the falsity constant (0̄) is assigned value 1 − (ρO + ρP ) or 1 − (ρF + ρP ),
respectively, in a similar way as in BC1 . In case of a conflict among a prohibition
and an obligation we define a stronger incoherence by defining the degree of the
falsity constant as −min(ρO , ρF ).
Selecting Relevant Propositions. Once the coherence graph has been de-
fined and a maximising partition (A, V \ A) over this graph has been found
following [17], the set of propositions belonging to the NCC (i.e.ΓN CC ) is re-
vised in order to consider only the accepted norms:
ΓN� CC = ΓN CC ∩ A
where A is the accepted set of norm instances according to the maximizing
coherence process [17], i.e. ”the most coherent norm instances”.
77
7 Norm Internalization
Regarding works on norm internalization in the MAS community, maybe the
most relevant proposal are the works of Conte et al. [8]. According to them,
a characteristic feature of norm internalization is that norms become part of
the agent’s identity. The concept of identity implies that norms become part of
the cognitions of the individual agent. In particular, Conte et al. define norm
internalization as a multi-step process, leading from externally enforced norms
to norm-corresponding goals, intentions and actions with no more external en-
forcement. Thus they account for different types and levels of internalization.
In this paper a simplistic approximation to the norm internalization process
has been considered. However, it will be object of future work extensions. In
particular, we have only considered the internalization of norms as goals. In
this sense, the process of norm internalization has been described by the self-
determination theory [13] as a dynamic relation between norms and desires.
This shift would represent the assumption that internalised norms become part
of the agent’s sense of identity. Thus, after performing the coherence process for
creating new norm instances, the NCC must update the DC (Figure 1 Norm
Internalization Bridge Rules) with the new normative desires. The addition of
these propositions into this mental context may cause an inconsistency with
the current mental state. As explained in Section 2.2, in [6] three schemas for
ensuring consistency among mental graded propositions have been proposed.
According to schema DC2 , which imposes a restriction over positive and negative
desires for a same goal, we have implemented the following inference rule:
(DC2 ) (D+ γ, δγ+ ), (D− γ, δγ− ) � (0̄, 1 − (δγ+ + δγ− ))
Our proposal needs bipolar representation of desires since it is useful when
selecting plans to be intended for achieving the desires. In this sense, both neg-
ative and positive effects of actions will be taken into account when selecting
a plan to be intended. For example, the fact that a plan involves a forbidden
action may be considered as a negative effect. Therefore, obligation norms are
internalized as positive desires whereas prohibition norms are translated into
negative ones. Because of this, DC2 has been considered as a basis for the defi-
nition of bridge rules responsible for updating the DC in a consistent way. Next
these norm internalization bridge rules are described.
Norm Internalization Bridge Rules.
– Obligation Norm. According to DC2 schema, bridge rule for updating the
DC with the positive desires derived from obligation norms is defined as
follows:
N CC : (�O, C�, ρ), DC : (D− C, δ − ), DC : (D+ C, δ + )
(2)
DC : (D+ C, max(ρ, δ + )), DC : (D− C, min(δ − , 1 − max(ρ, δ + )))
78
If an agent considers that the obligation is currently active then a new pos-
itive desire will be inferred corresponding to the new norm condition. Thus,
the desire degree assigned to the new proposition C is defined as the max-
imum between the new desirability and the previous value (max(ρ, δ + )).
Moreover, the undesirability assigned to C is updated as the minimum be-
tween the previous value of undesirability assigned to γ (δ − ) and its maxi-
mum coherent undesirability, which is defined as 1 − max(ρ, δ + ).
– Prohibition Norm. Bridge rule for updating the DC with negative desires is
defined as follows:
N CC : (�F, C�, ρ), DC : (D− C, δ − ), DC : (D+ C, δ + )
(3)
DC : (D− C, max(ρ, δ − )), DC : (D+ C, min(δ + , 1 − max(ρ, δ − )))
Similarly to obligation norms, a prohibition related to a condition C is trans-
formed into a negative desire related to the norm condition (D− C, max(ρ, δ − )).
– Permission Norm. Finally, permission norms do not infer a positive or neg-
ative desire about the norm condition. Permission norms define exceptions
to the application of a more general obligation or prohibition norm. As a
consequence, they only are defined for creating an incoherence with these
more general norms.
8 Conclusion
In this work a previous proposal [9, 10] of a normative BDI architecture has been
revised. The first contribution of the current paper is the usage of coherence
theory in order to determine what means to follow or violate a norm according
to the agent’s cognitions and making a decision about norm compliance. The
second contribution of this paper is the employment of consistency notions for
updating agent cognitions in response to these normative decisions.
The impact of normative decisions on agent cognitions will be object of fu-
ture work. In this paper, the norm internalization problem has been faced in a
simplistic way by considering only the impact of obeyed norms on agent’s de-
sires. Therefore, in future works the role of both deliberative coherence [26] and
emotions on the norm compliance will be analysed. In particular, deliberative co-
herence, which deals with goal adoption in the context of decision making, will
be considered when building plans for obeying or violating norms. In addition,
we will work on extending our agent architecture with an explicit representa-
tion of emotions which will allow agents to consider phenomena such as shame,
honour, gratitude, etc. in their decision making processes.
Due to lack of space, no evaluation or case study has been included here
that might provide a more understanding perspective of our proposal. However,
works describing the original proposal [10, 11] (neither consistency nor coherence
are considered here) provide examples belonging to the m-Water case study. The
m-Water [3] is a water right market which is implemented as a regulated open
79
multi-agent system. It is a challenging problem, specially in countries like Spain,
since scarcity of water is a matter of public interest. The m-Water framework
[12] is a somewhat idealized version of current water-use regulations that articu-
late the interactions of those individual and collective entities that are involved
in the use of water in a closed basin. This is a regulated environment which
includes the expression and use of regulations of different sorts: from actual laws
and regulations issued by governments, to policies and local regulations issued
by basin managers, and to social norms that prevail in a given community of
users. For these reasons, we consider the m-Water problem as a suitable case
study for evaluating performance of the n-BDI agent architecture, since agents’
behaviour is affected by different sorts of norms which are controlled by different
mechanisms such as regimentation, enforcement and grievance and arbitration
processes.
Finally, we are working on the implementation of a prototype of the n-BDI
architecture. Our aim is to evaluate empirically our proposal through the design
and implementation of scenarios belonging to the m-Water case study. In future
works, we will make some experiments concerning the flexibility and performance
of the n-BDI agent model with respect to simple BDI agents, using the m-Water
case study. However, preliminary results of the experimental evaluation of the
n-BDI original proposal can be found in [10].
9 Acknowledgments
This work was partially supported by the Spanish government under grants
CONSOLIDER-INGENIO 2010 CSD2007-00022, TIN2009-13839-C03-01 and
TIN2008-04446 and by the FPU grant AP-2007-01256 awarded to N. Criado.
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