B2DI

A Bayesian BDI Agent Model with Causal Belief Updating based on MSBN

Alvaro Carrera and Carlos A. Iglesias

Departamento de Ingenier

ıa de Sistemas Telem

aticos, Universidad Polit

ecnica de Madrid, Madrid, Spain

Keywords:

Distributed, Agents, Bayesian, BDI, MSBN, Belief, Sharing.

Abstract:

In this paper, we introduce B2DI model that extends BDI model to perform Bayesian inference under uncer-

tainty. For scalability and ﬂexibility purposes, Multiply Sectioned Bayesian Network (MSBN) technology has

been selected and adapted to BDI agent reasoning. A belief update mechanism has been deﬁned for agents,

whose belief models are connected by public shared beliefs, and the certainty of these beliefs is updated

based on MSBN. The classical BDI agent architecture has been extended in order to manage uncertainty using

Bayesian reasoning. The resulting extended model, so-called B2DI, proposes a new control loop. The pro-

posed B2DI model has been evaluated in a network fault diagnosis scenario. The evaluation has compared this

model with two previously developed agent models. The evaluation has been carried out with a real testbed

diagnosis scenario using JADEX. As a result, the proposed model exhibits signiﬁcant improvements in the

cost and time required to carry out a reliable diagnosis.

1 INTRODUCTION

Many problems of our everyday life are connected in

huge information networks both computer and human

networks. Some of these problems are too complex to

be completely modelled and described. Thus, these

problems have been solved through distributed sys-

tems. Multi-agent systems (MAS) provide a suitable

abstraction level for dealing with the complexity of

large scale, open, heterogeneous, and evolving sce-

narios.

In recent past, several works have studied differ-

ent approaches (Fagundes et al., 2009; Casali et al.,

2011) to reason with uncertainty in a single agent. In

this work, an approach to deal with uncertainty in a

distributed way to achieve collaborative goal delib-

eration based on a BDI MAS is presented. Multi-

ply Sectioned Bayesian Network (Xiang et al., 1993)

(MSBN) approach is proposed to handle uncertainty

in a distributed way, to keep coherence in the infer-

ence process and to allow ﬂexibility in the multi-agent

system. We adopt the terminology by Xiang (Xiang

et al., 1993; Xiang, 2002; Xiang et al., 2006) in his

work.

The reminder of this paper is structured as fol-

lows. Sect. 2 presents the proposed Bayesian agent

model to perform distributed causal inference of be-

liefs. Sect. 3 presents the evaluation of the model on

the basis of a real testbed diagnosis scenario. Finally,

Sect. 4 presents several important related works and

Sect. 5 presents the reached conclusions and possible

future research areas.

2 B2DI: BAYESIAN BDI AGENT

MODEL

This section presents the extended BDI model to per-

form distributed causal inference using MSBNs.

Deﬁnition 1. Causal Model CM is a Bayesian Net-

work used by an agent to perform distributed causal

inference. CM is a subnet that is part of a MSBN.

The agent uses this CM to perform belief updating

depending on the current available data.

The proposed model is based on sharing a dis-

tributed causal model, that is partitioned among the

agents. In this partitioning, beliefs can be private or

shared with other agents.

Fig. 1 shows the block diagram of a B2DI Agent.

A B2DI agent works with a modiﬁed BDI architec-

ture. This model updates beliefs based on a dis-

tributed causal inference through MSBN.

A B2DI agent starts its behaviour with initial be-

liefs and intentions (Alg. 1). These beliefs are added

to the CM and synchronized (Algs. 2 and 3) with other

343

Carrera Á. and A. Iglesias C..

B2DI - A Bayesian BDI Agent Model with Causal Belief Updating based on MSBN.

DOI: 10.5220/0003746003430346

In Proceedings of the 4th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2012), pages 343-346

ISBN: 978-989-8425-96-6

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: B2DI Agent Model.

agents through MSBN. After deliberation process, a

plan is selected and executed. Any data obtained after

the execution of a plan is added to the CM.

Alg. 1 shows the agent control loop proposed in

this work. Several functions are used in this algo-

rithm. This control loop is similar to the previous

classic BDI model, but it has been extended with the

following functions: connect function (Alg. 2), be-

lief initialization function (Alg. 3), update notiﬁcation

function (Alg. 4), belief update function (Alg. 5) and

communicate belief function (Alg. 6).

One new variable is added in this proposed con-

trol loop algorithm (Alg. 1). Mod CM represents the

Causal Model (Def. 1) of the agent.

Algorithm 1: B2DI Agent Control Loop.

1: B := B

;

2: I := I

;

3: CM := connect(CM);

4: B := belie f initialization(B, CM)

5: while true do

6: if update noti f ication(CM) then

7: B := belie f update(B, CM);

8: else

9: get next percept ρ;

10: B := br f (B, ρ);

11: end if

12: CM := communicate belie f (B, CM);

13: D := options(B, I);

14: I := f ilter(B, D, I);

15: π := plan(B, I);

16: execute(π);

17: end while

Alg. 2 presents connect function to set-up the

agent CM (a subnet) with the distributed inference en-

gine. This function consists of two steps: moraliza-

tion and triangulation to achieve coherence.

Once the subnet is ready, the belief initialization

function is called to synchronize the shared know-

ledge. First of all, the agent receives a notiﬁcation of

Algorithm 2: B2DI Connect Function.

1: connect : (CM) → Mod;

3: MCM := null; {Moralized Causal Model}

4: TCM := null; {Triangulated Causal Model}

5: MCM := moralization(CM);

6: TCM := triangulation(MCM);

7: connect := TCM;

9: end − connect;

belief updating and it updates its own beliefs through

local inference process. After this, the agent propa-

gates its beliefs to other agents.

Algorithm 3: B2DI Belief Initialization Function.

1: belie f initialization : (B, CM) → Bel;

3: UB := null; {Updated Beliefs}

4: UB := belie f update(B, CM);

5: B := communicate belie f (U B);

6: belie f initialization := B;

8: end − belie f initialization;

Alg. 4 shows the update notiﬁcation function.

This function simply notiﬁes when it exists a change

in the set of shared beliefs.

Algorithm 4: B2DI Update Notiﬁcation Function.

1: update noti f ication : (CM) → boolean;

3: boolean result := f alse;

4: result := changedAnySharedBelie f ();

5: update noti f ication := result;

7: end − update noti f ication;

Alg. 5 shows the process required to receive be-

lieves. First of all, new beliefs are received through

linkages. Then, this beliefs are locally propagated in

the subnet CM (Def. 1) of the agent.

When local beliefs are modiﬁed or external be-

liefs are received, the agent must communicate this

updates to the rest of the MSBN. This process is com-

posed of two steps: collect beliefs and distribute be-

liefs.

3 EVALUATION

The evaluation has been carried out based on a bench-

ICAART 2012 - International Conference on Agents and Artificial Intelligence

344

mark for a real diagnosis scenario of the R&D project

“Magneto” (Arozarena et al., 2010). This scenario

consists of a P2P streaming scenario where a user

provides multimedia content and another user con-

sumes this content. Many faults may occur both in

connection and in services. The system is designed

to provide, to an end-user or an operator, the result

of the diagnosis made upon receipt of a notiﬁcation

of a symptom of failure. We have clustered all possi-

ble diagnoses of this scenario in 13 diagnosis cases to

simplify comparison and shown results.

The evaluation consists of the comparison of three

models that use Bayesian networks to perform causal

inference to diagnose faults:

Algorithm 5: B2DI Belief Update Function.

1: belie f update : (B, CM) → Bel;

3: AB := null; {Absorbed Beliefs}

4: AB := absorb through linkage(CM);

5: B := uni f y belie f (B, AB);

6: belie f update := B;

8: end − belie f update;

Algorithm 6: B2DI Communicate Belief Function.

1: communicate belie f : (B, CM) → Mod;

3: CB := null; {Collected Beliefs}

4: CB := collect belie f (B);

5: CM := distribute belie f (CB, CM);

6: communicate belie f := CM;

8: end − communicate belie f ;

• Model 1 (Belief Flooding): All agents have

Bayesian Networks with duplicated part of their

causal model CM to keep coherence in the process

inference. Agents share beliefs about the available

information of the current environment. When

new information is received from other agents, it

is propagated to the rest of the agents to assure

the coherence of the distributed reasoning pro-

cess. After this propagation, each agent continues

with its own behaviour and shares its beliefs if it

is required.

• Model 2 (Filtered Belief Flooding): Same than

Model 1 but this time when new information is

received from other agents, it is processed and ﬁl-

tered. Then, the agent takes its own decision and

execute a selected plan. Finally, only ﬁltered in-

formation is propagated to its neighbours.

• Model 3 (B2DI, Belief Sharing based on Causal

Dependencies): This model represents the pro-

posed B2DI model. These agents share their be-

liefs only with other agents which are interested

in them. When new information is available, it is

automatically propagated through MSBN mecha-

nism.

Table 1 shows the evaluation results in several

columns. MTTD (FitzGerald and Dennis, 2008)

(Mean Time to Diagnose) usually is the average num-

ber of minutes until the root cause of the failure is

correctly diagnosed; but, in this table, we show this

time rounded in seconds.

Model 3 presents a reduction of 48% in time and

37% in number of executed tests comparing with

Model 1 and a reduction of 40% in time and 60% in

number of executed tests comparing with Model 2.

4 RELATED WORK

Although uncertain belief representation in BDI-like

systems have been studied in AI over recent past (Fa-

gundes et al., 2009; Casali et al., 2011), this work

is novel in several respects. It proposes transpar-

ently sharing beliefs methods through MSBNs (Xi-

ang, 2002), i.e. an agent do not have to send its be-

liefs through a message. MSBN model assures con-

sistency and coherence during the inference process.

This MSBN model is embedded in the proposed B2DI

model (Sect. 2).

Furthermore, MSBN offers dynamically reconﬁg-

uration (Xiang et al., 2006) if any agent is born or dies

in the environment. Thus, all agents that share any set

of beliefs can reconﬁgure its causal model to link to

the global inference mechanism (MSBN) even if an

intermediate agent disappears.

The use of distributed causal models to fault di-

agnosis has been previously studied (Bocaniala and

da Costa, 2004) and the proposed methodology to par-

tition the global causal model in causally indepen-

dent (d-separated) regions. But, that methodology

only exposes how to fragment the causal model in

smaller pieces. It does not deal with how the inference

should be performed in a distributed way. Our pro-

posed approach (B2DI agent model) uses distributed

causal models and presents a framework to perform

distributed inference.

B2DI - A Bayesian BDI Agent Model with Causal Belief Updating based on MSBN

345

Table 1: MTTD and number of test comparison.

Diagnosis case MTTD (in seconds) Number of executed tests

Model 1 Model 2 Model 3 Model 1 Model 2 Model 3

Case 1 22 19 6 6 7 4

Case 2 9 8 4 5 2 2

Case 3 12 9 5 4 6 2

Case 4 15 10 9 6 9 4

Case 5 3 4 3 1 1 1

Case 6 16 15 5 4 8 2

Case 7 13 10 6 3 6 2

Case 8 15 14 7 3 9 2

Case 9 18 24 13 7 12 5

Case 10 15 19 13 5 8 3

Case 11 9 6 6 2 2 2

Case 12 13 9 7 3 5 2

Case 13 21 14 10 5 9 3

Average 14.4 12.5 7.4 4.2 6.9 2.6

5 CONCLUSIONS AND FUTURE

WORK

This paper proposes a Bayesian BDI agent model

with causal belief updating based on MSBN. This

process implies a modiﬁcation in the BDI control

loop. In B2DI model, there are several additional

operations to keep coherence and consistency in the

sharing process. These additional operations in the

control loop (see Alg. 1) allow to decrease the com-

plexity of the belief sharing process. This sharing pro-

cess is performed transparently through MSBN mech-

anisms and it has not to be implemented explicitly in

the agent behaviour. MSBN mechanisms offer ﬂexi-

bility (reconﬁguration capabilities) and robustness to

allow new agents to join the belief sharing group and

keep coherence in the reasoning process without any

modiﬁcation of the agent behaviour.

As future work, several paths can be explored.

One interesting option is the extension of MSBN use

for distributed goal deliberation. The sharing process

offered by MSBN can be used to achieve common

or private goals knowing intentions of other agents in

a transparent way. Further, another option to work

is a formal methodology to apply this model during

the development of multi-agent systems. Based on

graph theory, agents causal models (see Def. 1) could

be dynamically generated from a global knowledge

base, i.e. from a global causal model that deals with

the domain knowledge. For future scenario, sensor

networks will be applied. B2DI model meets the re-

quirements of sensor networks, such as distributed

data processing, robustness or reconﬁguration capa-

bilities during the inference process.

REFERENCES

Arozarena, P., Toribio, R., Kielthy, J., Quinn, K., and Zach,

M. (2010). Probabilistic Fault Diagnosis in the MAG-

NETO Autonomic Control Loop. In 4th International

Conference on Autonomous Infrastructure, Manage-

ment and Security, pages 102–105. Springer.

Bocaniala, C. D. and da Costa, J. (2004). Novel framework

for using causal models in distributed fault diagnosis.

In Proceedings of Workshop on Advances in Control

and Diagnosis, Karlsruhe, Germany, pages 142–147.

Citeseer.

Casali, A., Godo, L., and Sierra, C. (2011). A graded

BDI agent model to represent and reason about pref-

erences. Artiﬁcial Intelligence, 175(7-8):1468–1478.

Fagundes, M., Vicari, R., and Coelho, H. (2009). Delib-

eration process in a BDI model with Bayesian net-

works. Agent Computing and Multi-Agent Systems,

pages 207–218.

FitzGerald, J. and Dennis, A. (2008). Business Data Com-

munications and Networking. John Wiley and Sons.

Xiang, Y. (2002). Probabilistic reasoning in multiagent sys-

tems: a graphical models approach. Cambridge Uni-

versity Press.

Xiang, Y., Jensen, F. V., and Chen, X. (2006). Inference

in multiply sectioned Bayesian networks: methods

and performance comparison. IEEE Transactions on

Systems, Man and Cybernetics, Part B (Cybernetics),

36(3):546–558.

Xiang, Y., Poole, D., and Beddoes, M. P. (1993). Multi-

ply sectioned bayesian networks and junction forests

for large knowledge-based systems. Computational

Intelligence, 9(2):171–220.

ICAART 2012 - International Conference on Agents and Artificial Intelligence

346