A Probabilistic Implementation of Emotional BDI Agents

ao Gluz and Patricia Jaques

PIPCA - UNISINOS, Av. Unisinos, 950, Bairro Cristo Rei, CEP 93.022-000, S

ao Leopoldo, Brazil

Keywords:

BDI, Emotions, Appraisal, OCC.

Abstract:

A very well known reasoning model in Artiﬁcial Intelligence is the BDI (Belief-Desire-Intention). A BDI

agent should be able to choose the more rational action to be done with bounded resources and incomplete

knowledge in an acceptable time. Although humans need emotions in order to make immediate decisions

with incomplete information, traditional BDI models do not take into account affective states of the agent.

In this paper we present an implementation of the appraisal process of emotions in BDI agents using a BDI

language that integrates logic and probabilistic reasoning. Speciﬁcally, we implement the event-generated

emotions with consequences for self based on the OCC cognitive psychological theory of emotions. We also

present an illustrative scenario and its implementation. One original aspect of this work is that we implement

the emotions intensity using a probabilistic extension of a BDI language. This intensity is deﬁned by the

desirability central value, as pointed by the OCC model. In this way, our implementation of an emotional BDI

allows to differentiate between emotions and affective reactions. This is an important aspect because emotions

tend to generate stronger response. Besides, the intensity of the emotion also determines the intensity of an

individual reaction.

1 INTRODUCTION

A very well known reasoning model in Artiﬁcial In-

telligence (AI) is the BDI (Belief-Desire-Intention).

It views the system as a rational agent having cer-

tain mental attitudes of belief, desire, intention, rep-

resenting, respectively, the informational, motiva-

tional and deliberative states of the agent (Rao and

Georgeff, 1995; Wooldridge, 2009). A rational agent

has bounded resources, limited understanding and in-

complete knowledge on what happens in the environ-

ment where it lives in. A BDI agent should be able

to choose the more rational action to be done with

bounded resources and incomplete knowledge in an

acceptable time.

Damasio (Damasio, 1994) showed that humans

need emotions in order to make immediate decisions

with incomplete information. BDI agents also need

to decide quickly and with incomplete data from the

environment. The BDI is a practical reasoning ar-

chitecture, that is reasoning directed towards action,

employed in the cases when the environment is not

fully observable (Russell and Norvig, 2010). How-

ever, most BDI models do not take into account the

agent’s emotional mental states in its process of deci-

sion making.

Among the several approaches of emotions - for

example, basic emotions (Ekman, 1992), dimensional

models (Plutchik, 1980), etc, the appraisal theory

(Scherer, 2000; Scherer, 1999; Moors et al., 2013)

appears to be the most appropriate to implement emo-

tions into BDI agents. According to this theory, emo-

tions are elicited by a cognitive process of evaluation

called appraisal. The appraisal depends of one’s goals

and values. These goals and values can be represented

as the BDI agents’ goals and beliefs. In this way, it is

possible to make a direct relation between BDI agents

goals and beliefs and appraisals.

When addressing emotional mental states in BDI

agents, several research questions should be ad-

dressed. An important issue is how to represent and

implement the emotional appraisal, the emotions and

its properties, such as, intensity. This is a ﬁrst step

before representing how emotions can interfere back

in the cognitive processes of the agent, such as deci-

sion making. When addressing emotions, we should

take into account the emotions intensity, since it de-

ﬁnes when an emotion will occur or not. When an af-

fective reaction does not achieve a sufﬁcient intensity

threshold, it will not be experienced as an emotion.

The formal logical BDI approach is not appropri-

ate to represent the emotions intensity because it does

not allow to represent imprecise data. This is the rea-

son because most emotional BDI models do not take

121

Gluz J. and Jaques P..

A Probabilistic Implementation of Emotional BDI Agents.

DOI: 10.5220/0004815501210129

In Proceedings of the 6th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2014), pages 121-129

ISBN: 978-989-758-015-4

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

into account the notion of emotion intensity (Jiang

et al., 2007; Van Dyke Parunak et al., 2006; Adam

et al., 2009). In order to represent the emotions in-

tensity, we use AgentSpeak(PL) BDI language (Silva

and Gluz, 2011). AgentSpeak(PL) is a new agent pro-

gramming language, which integrates BDI and prob-

abilistic reasoning, i. e., bayesian networks.

This article presents an implementation of the

emotional appraisal into BDI agents. We are inter-

ested in the implementation of emotions and their

intensity using a language that integrates BDI and

Bayesian reasoning. Unlike other works, as we use a

probabilistic extension of the BDI model that is able

to represent the intensity of the affective reactions,

our work is able to differentiate between emotions and

other affective states with low intensity. Besides, the

intensity of the emotion also determines how strong

is the response of an individual (Scherer, 2000).

In this paper, we focus on the event-generated

emotions, i. e., emotions that are elicited by the eval-

uation of the consequences of an event for the accom-

plishment of a person’s goals. We do not formalize

emotions in which their appraisal evaluate the con-

sequences for others, such as resentment, pity, gloat-

ing and happy-for. We chose to implement the event-

generated emotions with consequences for self, since

these emotions seems to be the most important in the

decision making process (Bagozzi et al., 2003; Isen

and Patrick, 1983; Raghunathan and Pham, 1999).

This paper is organized as follow. Section 2

presents the OCC model, the psychological emotional

model that grounds our work. In Section 3, we de-

scribe the AgentSpeak(PL), a language that integrates

BDI and Bayesian Decision Network to reason about

imprecise data. Section 4 compares the proposed

work with related works and highlights its main con-

tribution. In Section 5, we cite a scenario and its im-

plementation with AgentSpeak (PL) to illustrate how

it can be used to implement emotional probabilistic

BDI agents. Finally, in Section 6, we present some

conclusions.

2 THE OCC MODEL

This work proposes an extension of the BDI model

to integrate emotions. We intend to implement the

appraisal process of emotions into BDI agents. We

implemented the appraisal process according to the

OCC model (Ortony et al., 1990) and using proba-

bilistic reasoning to represent emotions intensity.

According to the cognitive view of emotions

(Scherer, 1999), emotions appear as a result of an

evaluation process called appraisal. The central idea

of the appraisal theory is that “the emotions are

elicited and differentiated on the basis of a person’s

subjective evaluation (or appraisal) of the personal

signiﬁcance of a situation, event or object on a num-

ber of dimensions or criteria” (Scherer, 1999).

Ortony, Clore and Collins (Ortony et al., 1990)

constructed a cognitive model of emotion, called

OCC, which explains the origins of 22 emotions by

describing the appraisal of each one. For example,

hope appears when a person develops an expectation

that some good event will happen in the future.

The OCC model assumes that emotions can arise

by the evaluation of three aspects of the world: events,

agents, or objects. Events are the way that people

perceive things that happen. Agents can be people,

biological animals, inanimate objects or abstractions

such as institutions. Objects are objects viewed qua

objects. There are three kinds of value structures un-

derlying perceptions of goodness and badness: goals,

standards, and attitudes. The events are evaluated in

terms of their desirability, if they promote or thwart

one’s goals and preferences. Standards are used to

evaluate actions of an agent according to their obe-

dience to social, moral, or behavioural standards or

norms. Finally, the objects are evaluated as appeal-

ing depending on the compatibility of their attributes

with one’s tastes and attitudes. In this paper we refer

to the emotions that are generated from the evaluation

of an event consequences according to one’s goals as

event-generated emotions.

The elicitation of an emotion depends on a per-

son’s perception of the world – his construal. If an

emotion such as distress is a reaction to some unde-

sirable event, the event must be construed as unde-

sirable. For example, when one observes the reac-

tions of players at the outcome of an important game,

it is clear that those on the winning team are elated

while those on the losing team are devastated. In a

real sense, both the winners and losers are reacting to

the same objective event. It is their construal of the

event that is different. The winners construe it as de-

sirable, while the others construe it as undesirable. It

is this construal that drives the emotion system.

A central idea of the model is the type of an emo-

tion. An emotion type is a distinct kind of emotion

that can be realized in a variety of recognizably re-

lated forms and which are differentiated by their in-

tensity. For example, fear is an emotion type that can

be manifested in varying degrees of intensity, such as

“concern” (less afraid), “frightened”, and “petriﬁed”

(more afraid). The use of emotion type has the goal of

being language-neutral so that the theory is universal,

independent of culture. Instead of deﬁning an emo-

tion by using English words (the author’s language),

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the emotions are characterized by their eliciting con-

ditions.

In the OCC model, the emotions are also grouped

according to their eliciting conditions. For example,

the “attribution group” contains four emotion types,

each of which depends on whether the attribution of

responsibility to some agent for some action is posi-

tive or negative, and on whether the agent is the self

or another person.

The OCC model is illustrated in Figure 1. When

goals are the source, one may feel pleased if the event

is desirable, or displeased if it is not. Which spe-

ciﬁc emotion arises depends on whether the conse-

quences are for other or for oneself. When concerned

for oneself (label as CONSEQUENCES FOR SELF),

the evaluation depends on whether the outcomes are

past (label as PROSPECTS IRRELEVANT), like joy

and distress, or prospective (label as PROSPECTS

RELEVANT), such as hope and fear. If the prospect

is conﬁrmed or not, other four emotions may arise,

such as satisfaction, disappointment, fear-conﬁrmed

and relief. When concern for other (label as CON-

SEQUENCES FOR OTHER), the outcomes are eval-

uated according to when they are undesirable (label

as UNDESIRABLE FOR OTHER), such as gloating

and pity, or desirable for other (label as DESIRABLE

FOR OTHER), such as happy-for, resentment.

When the actions of agents are evaluated accord-

ing to standards, affective reactions of approval or

disapproval arise. The speciﬁc emotions depend on

whether the action is one’s own (labelled as SELF

AGENT), such as pride and shame; or someone else’s

(labelled as OTHER AGENT), such as admiration and

reproach.

The aspects of an object are evaluated according to

one’s tastes, if one likes or dislikes. In this case, emo-

tions such as love and hate may arise. Finally, emo-

tions like anger and gratitude involve a joint focus on

both goals and standards at the same time. For exam-

ple, one’s level of anger depends on how undesirable

the outcomes of events are and how blameworthy the

related actions are.

According to the OCC model, affective reactions

are effectively experienced as emotions only if they

achieve a minimum intensity degree. Before this,

these affective reactions have only a potential for the

emotion. But, after this potential surpasses the mini-

mum threshold necessary for an emotion, the emotion

starts to be felt.

The OCC authors believe that this model when

implemented in a machine can help to understand

what emotions people experience under what condi-

tions. According to them, it is not the objective of

the OCC model to implement machine with emotions,

Figure 1: Global Structure of Emotion Types - OCC Model

(Ortony et al., 1990).

but to be able to predict and explain human cogni-

tions related to emotions. However, Picard (Picard,

2000) disagrees and believes that the OCC model can

be used for emotion synthesis in machines. In fact, in

computing science research, there already are several

works that use OCC in order to implement emotions

in machine (Gebhard, 2005; Dias and Paiva, 2013;

Jaques et al., 2011; Signoretti et al., 2011).

The OCC authors also agree that this model is

a highly oversimpliﬁed vision of human’s emotions,

since in reality a person is likely to experience a mix-

ture of emotions (Ortony et al., 1990). Otherwise, in

order to understand which set of emotions is a per-

son or agent experiencing, we must ﬁrst try to iden-

tify each emotion separately. This is the case of the

approach adopted in the proposed work and in great

part of the emotion synthesis research.

3 A HYBRID BDN+BDI MODEL

The BDI model was based on the works of Searle

and Dennet, posteriorly generalized by the philoso-

pher Michael Bratman (Bratman, 1990), which gave

particular attention to the role of intentions in reason-

ing (Wooldridge, 1999). The BDI approach views the

system as a rational agent having certain mental atti-

tudes of belief, desire, intention, representing, respec-

tively, the information, motivational and deliberative

states of the agent (Rao and Georgeff, 1995). A ratio-

nal agent has bounded resources, limited understand-

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123

ing and incomplete knowledge on what happens in the

environment it lives in.

The beliefs represent the information about the

state of the environment that is updated appropriately

after each sensing action. Desires are the motivational

state of the system. They have information about the

objectives to be accomplished, i. e. what priorities or

pay-offs are associated with the various current objec-

tives. They represent a situation that the agent wants

to achieve. The fact that the agent has a desire does

not mean that the agent will do it. The agent carries

out a deliberative process in which it confronts its de-

sires and beliefs and chooses a set of desires that can

be satisﬁed. An intention is a desire that was chosen

to be executed by a plan, because it can be carried out

according to the agents beliefs (it is not rational an

agent carries out something that it does not believe).

Plans are pre-compiled procedures that depend on a

set of conditions for being applicable. The desires

can be contradictory to each other, but the intentions

cannot (Wooldridge, 1999). Intentions represent the

goals of the agent, deﬁning the chosen course of ac-

tion. An agent will not give up on its intentions – they

will persist, until the agent believes it has success-

fully achieved them, it believes it cannot achieve them

or because the purpose of the intention is no longer

present.

In the BDI model, a belief is deﬁned as a two-

state logical proposition: or the agent believes that

a certain event is true or it believes that the event is

false. Today, programming languages and tools avail-

able for development BDI agents do not work with the

concept of probabilistic beliefs (Bordini et al., 2005),

i.e. they do not allow agents to understand, infer or

represent degrees of belief (or degrees of uncertainty)

about a given proposition. A degree of belief is de-

ﬁned by the subjective probability assigned to a par-

ticular belief.

The concept of Bayesian Networks (BN) (Pearl,

1988) ﬁts in this scenario, allowing to model the prob-

abilistic beliefs of some agent. BN alone are excellent

tools to represent probabilistic models of agents, but,

with the addition of utility, and decision nodes, it is

possible to use the full spectrum of Decision Theory

to model agent’s behaviour. BN extended with util-

ity, and decision nodes, are called Bayesian Decision

Networks (BDN) (Russell and Norvig, 2010).

The integration between the current agent pro-

gramming languages and the concept of belief prob-

abilities can be approached in several ways and at

different levels of abstraction. In practical terms, it

is possible to make an ad-hoc junction of both kind

of models in the actual programming code of the

agents. Both BDI and BDN agent programming en-

vironments rely on libraries and development frame-

works, with a standard Application Programming In-

terface (API). Thus, a hybrid agent can be designed

and implemented by combining calls from different

sets of APIs, each one from distinct programming en-

vironments. The more abstract level to address this

issue of integration is usually treated by Probabilistic

Logics (Korb and Nicholson, 2003). Although Prob-

abilistic Logics have the ability to represent both log-

ical beliefs and probabilistic beliefs, there are notori-

ous problems related to the tractability of the result-

ing models (Korb and Nicholson, 2003). Another ap-

proach is to extend logic programming languages (es-

sentially Prolog) to handle probabilistic concepts. P-

Log (Baral and Hunsaker, 2007) and PEL (Milch and

Koller, 2000) ﬁt in this category. They offer interest-

ing ideas, but they lack the full integration with BDI

programming languages, like AgentSpeak(L) (Bor-

dini et al., 2007).

In the present work we consider a programming

approach that fully integrates the theoretical and prac-

tical aspects of BDN and BDI models. We use

AgentSpeak(PL) (Silva and Gluz, 2011) to imple-

ment a probabilistic process, for the appraisal of

(some of) the OCC’s emotions. AgentSpeak(PL) is

a new agent programming language, which is able to

support BDN representation and inference in a seam-

less integrated model of beliefs and plans of an agent.

AgentSpeak(PL) is based on the language AgentS-

peak(L) (Bordini et al., 2007), inheriting from it all

BDI programming concepts. AgentSpeak(PL) is sup-

ported by JasonBayes (Silva and Gluz, 2011), an ex-

tension of the Jason (Bordini et al., 2007) agent devel-

opment environment. The main changes of AgentS-

peak(PL), in respect to AgentSpeak(L), were:

• Inclusion of a probabilistic decision model of the

agent, consisting of the speciﬁcation of a BDN.

• Inclusion of events/triggers based on probabilistic

beliefs.

• Inclusion of achievement and test goals, based on

probabilistic beliefs.

• Inclusion of actions, which are able to update the

probabilistic model.

4 RELATED WORK

There are other researchers that have also been work-

ing in the extension of the BDI architecture in or-

der to incorporate emotions. (Jiang et al., 2007) de-

ﬁnes an extension of the generic architecture of BDI

agents that introduces emotions. However, this work

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124

explores the possible inﬂuences of emotions to de-

termine agents’ beliefs and intentions. (Van Dyke

Parunak et al., 2006) propose an extension of the BDI

model to integrate emotions, which is based on the

OCC model. In this model, the agent’s beliefs inter-

fere in its appraisal, which will determine its emo-

tions. The emotions, on the other hand, interfere in

the choice of intentions. This work is focussed on the

impact of the emotions in agent’s choice of intentions

from desires. Other related works are the ones pro-

posed by (Adam et al., 2009) and (Steunebrink et al.,

2012; Steunebrink et al., 2008). Both works present a

purely logical formalization of the OCC model. They

are theoretical works that use a BDI modal logic to

describe the OCC’s appraisal. They do not show how

to create an operational computing model based on

the logical formalization.

All the above cited related works do not use a

probabilistic model to represent the intensity of the

emotions. Their model is not able to represent if the

potential of an affective reaction in the appraisal pro-

cess achieved the necessary threshold to elicit an emo-

tion. In these works, when the appraisal process oc-

curs, an agent always has an emotion. This is not

the case, because an emotion only occurs when the

intensity achieves a speciﬁc threshold (Ortony et al.,

1990). To differentiate emotions from other affective

reactions is important because emotions tend to gen-

erate stronger response. Besides, the intensity of the

emotion also determines how strong is the response

of an individual (Scherer, 2000).

5 A SCENARIO

Let us present a scenario in order to illustrate the pro-

cess of appraisal that happens with an agent, which

has an emotional BDI+BDN architecture. Let us con-

sider a vacuum cleaner robot example, with its envi-

ronment of a grid with two cells. Besides the desires

to work and clean the environment, our agent, whose

name is Vicky, also has the desire of protecting its

own existence with a stronger priority.

While Vicky is cleaning Cell B, Nick, a clumsy re-

searcher who also works at the same laboratory, goes

towards Vicky without noticing it. When Vicky per-

ceives that Nick is going to stomp on itself, the de-

sire of self-protection becomes an intention and Vicky

feels fear of being damaged.

In order to alert the awkward scientist, Vicky

emits an audible alarm. Nick perceives Vicky (almost

behind his feet) and step on the other cell, avoiding

trample over Vicky. When Vicky perceives that it is

not in danger any more, ﬁnally, it feels relief. It can

continue to do its work; at least while Nick does not

decide to come back to his ofﬁce.

In the next section we present how the pro-

cess of emotion appraisal, with the correspond-

ing behaviour consequences, can be implemented in

AgentSpeak(PL), and how this process will evolve in

the the ﬁrst reasoning cycles of the agent.

5.1 AgentSpeak(PL) Implementation

Emotions in the OCC model depend on several cog-

nitive variables, related to the mental state of the

agent. These variables are instrumental in the pro-

cess of emotion’s arousal, because they determine the

intensity of the emotions. Not all affective reactions

(evaluation of an event as un/desirable) are necessar-

ily emotions: “Whether or not these affective reac-

tions are experienced as emotions depends upon how

intense they are” (Ortony et al., 1990, p. 20).

The OCC model divides these variables in central

variables, like desirability, and local variables, like ef-

fort. For our formal model, we need to deﬁne the de-

sirability and undesirability central variables because

these variables are important to event-generated emo-

tions.

Desirabilities are not utilities. From an ontologi-

cal perspective they are based on distinct things: the

prospective gains of some event in respect to the sub-

jective value of agent goals versus the functional rep-

resentation of rational preferences for states of the

world. However, from a purely formal point of view,

it is possible to use utilities to estimate the value of

the desirability. If we consider a subjective model for

the state of the world, then it is possible to assume

that utilities (as a kind of evaluation) could enter in

the formation of the desirability. The desirability of

some event could be calculated as the difference be-

tween the utility of the state of the world previous to

the occurrence of the event, and the utility after this

event happens, as hypothesized by the agent.

Using this interpretation, it is possible to apply a

tool like a Bayesian Decision Network (BDN) (Rus-

sell and Norvig, 2010) to make subjective (bayesian)

probabilistic model of the states of the world, and to

associate utilities to these states to estimate the desir-

ability. The BDN diagram shown in Figure 2 repre-

sents Vicky’s probabilistic model about the desirabil-

ity of smashed and dirty events.

The tables presented in Table 1 deﬁne the prior

and conditional probabilities, as well as the utility of

this probabilistic model. These tables provide esti-

mations of how good is to work and to continue to

exist. They can also be used to estimate how much

the fact of ﬁnding dirt will advance cleaning and self-

AProbabilisticImplementationofEmotionalBDIAgents

125

Figure 2: A BDN representing Vicky’s probabilistic model

about desirability of events.

Table 1: Probability tables for Vicky’s BDN model.

smash P(smash) dirty P(dirty)

true 0.5 true 0.5

false 0.5 false 0.5

cleaning smash dirty P(cleaning |

dirty & smash)

true true true 0.0

true true false 0.0

true false true 0.9

true false false 0.2

false true true 1.0

false true false 1.0

false false true 0.1

false false false 0.8

selfpreserv smash dirty P(selfpreserv

| dirty & smash )

true true true 0.1

true true false 0.1

true false true 1.0

true false false 1.0

false true true 0.9

false true false 0.9

false false true 0.0

false false false 0.0

cleaning U(clean val)

true 80

false 0

selfpreserv U(selfpres val)

true 100

false 0

preservation goals. Together with the knowledge that

any smashing will severely hinder the agent’s goals,

this model will allow Vicky to estimate the desirabil-

ity of cleaning and if it feels joy or fear.

Now, using an appropriate agent programming

language, it is a relatively straightforward task to pro-

gram Vicky’s beliefs, emotions, intentions, and plans.

To do so, we will use AgentSpeak(PL) (Silva and

Gluz, 2011), which generalizes AgentSpeak(L), al-

lowing a seamless integration of bayesian decision

model in the BDI planning process.

An AgentSpeak(PL) source code contains a BDN

model, the non-probabilistic beliefs, the agent’s goals,

and its corresponding plans. Figure 3 shows the

source code

for the BDN presented in Figure 2.

This code can be programmed by hand, or it can be

automatically generated from a graphical model similar to

// Probabilistic model

// Prior probabilities - standard syntax

%dirty(true) = 0.5.

%dirty(false) = 0.5.

// Prior probabilities - compact syntax

%smash(true,false) = [0.5, 0.5].

// Conditional probabilities - standard syntax

%cleaning(true) | smash(true) & dirty(true) = 0.0 .

%cleaning(true) | smash(true) & dirty(false) = 0.0 .

%cleaning(true) | smash(false) & dirty(true) = 0.9 .

%cleaning(true) | smash(false) & dirty(false) = 0.2.

%cleaning(false) | smash(true) & dirty(true) = 1.0.

%cleaning(false) | smash(true) & dirty(false) = 1.0.

%cleaning(false) | smash(false) & dirty(true) = 0.1.

%cleaning(false) | smash(false) & dirty(false)= 0.8.

// Conditional probabilities - compact syntax

%selfpreserving(true,false) | smash & dirty =

[0.1, 0.1, 1.0, 1.0, 0.9, 0.9, 0.0, 0.0].

// Utility function - standard syntax

$clean_val | cleaning(true) = 80.0 .

$clean_val | cleaning(false) = 0.0 .

// Utility function - compact syntax

$selfpres_val | selfpreserv = [100.0, 0.0].

Figure 3: Vicky’s BDN model programmed in AgentS-

peak(PL).

min_joy(50). min_distress(-100).

located(cell_b).

!cleaning.

!selfpreserv.

+dirty <-

+perceived(dirty); +!cleaning.

+human_fast_approx <-

+prospect(smash); +selfpreserv.

+human_fast_depart <-

-prospect(smash).

Figure 4: Vicky’s initial beliefs, goals, and perception plans.

Vicky’s initial non-probabilistic beliefs, its pri-

mary goals, and the plans to handle its perceptions

are deﬁned in Figure 4. Initially, as the battery energy

level of Vicky is high and it is located in a dirty cell

(cell B), Vicky selects the goal “clean the cell” as an

intention. We can also expect that Vicky has also a ba-

sic self-preservation instinct, i. e., it has the intention

of preserving its own existence. The perception plans

start intentions about what to do if some event is per-

ceived, incorporating the common sense knowledge

of Vicky about what happens when dirt is detected or

when some human is approximating fast.

The planning knowledge of Vicky, in respect to

what to do in its operation cycles, is relatively simple

and can be speciﬁed by the set of AgeentSpeak(PL)

plans deﬁned in Figure 5. The only small issue is that

in AgentSpeak(PL) it is necessary to start goals and

plans to calculate the desirability of events. This is

the BDN presented in Figure 2 (see (Silva and Gluz, 2011)

for details).

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126

+!cleaning : perceived(dirty) ->

+dirty(true);

!joy_inten(dirty,JI); JI > 0;

!fear_inten(smash,FI); FI = 0;

.cleaning_action.

+!selfpreserv : expect(smash) <-

!fear_inten(smash,FI);FI > 0;

.alarm_action.

Figure 5: Vicky’s plans for cleaning, and self preservation

intentions.

due to how the marginal probabilities and the utility

values of the BDN model are calculated: whenever

some evidence is added to the beliefs of the agent, the

bayesian inference engine is activated and all proba-

bilities and utilities are recalculated. An evidence is

simply a non-probabilistic belief, like dirty(true)

or smashed(false), that are identical in name to

some variable (node) of the BDN model.

Vicky’s code is completed by the plans to detect

if it feels some joy, or fear, presented in the Fig-

ure 6. These plans implement the rule-based com-

putational model for these emotions, as presented in

(Ortony et al., 1990, p. 182-186), deﬁning operational

functions to estimate the potential and the intensity of

these emotions.

5.2 First Reasoning Cycle

Initially, as the battery energy level of Vicky is high

and it is located in a dirty cell (cell B), Vicky selects

the goal “clean the cell” as an intention. We can also

expect that Vicky has also a basic self-preservation

instinct, i. e., it has the intention of preserving its own

existence.

In the ﬁrst cycle, when dirt is found, but not

smashing event expected, then the variable U1 in

joy poten(dirty,JP) plan will give the utility if

it is assumed that dirt is found. The value of

U1 will be 172, with the utility function returning:

$(clean val) = 72, and $(selfpres val)=100.

The variable U2 will give the utility, if we assume that

dirt is not found. Its value is 116, with $(clean val)

= 16, and $(selfpres val)=100. The difference JP

will be 56. With this value for the potential of joy,

then joy inten(dirty,JI) plan will return JI=6,

indicating that Vicky is feeling joy.

5.3 Second Reasoning Cycle

In the second cycle, while it is cleaning, Vicky re-

ceives from its vision sensor the perception “Human

fast approximation”. Vicky also knows that human

approximation can damage a robot, because the hu-

+!joy_poten(dirty,JP): not dirty(true) <-

J = 0.

+!joy_poten(dirty,JP): dirty(true) <-

U1 = $(clean_val) + $(selfpres_val);

-+dirty(true);

U2 = $(clean_val) + $(selfpres_val);

-+dirty(true);

JP = U1 - U2.

+!joy_inten(dirty,JI) <-

!joy_poten(dirty,JP); ?min_joy(MJ);

if (JP>MJ) {JI = JP - MJ} else {JI = 0}.

+!fear_poten(smash,J): not expected(smash) <-

J = 0.

+!fear_poten(smash,J): prospect(smash) <-

+smash(true),

U1 = $(clean_val) + $(selfpres_val);

-+smash(false);

U2 = $(clean_val) + $(selfpres_val);

-smash(false);

F = U2 - U1.

+!fear_inten(dirty,FI) <-

!fear_poten(smash,FP); ?min_fear(MF);

if (FP>MF) {FI = FP - MF} else {FI = 0}.

Figure 6: Vicky’s plans to estimate its joy, and fear emo-

tions.

man can trample the robot. It learned that from a pre-

vious bad-succeed experience with Nick.

In the second cycle, a similar situation

occurs, but this time the variable U1 in the

fear poten(smash,FP) plan, which estimates

the utility of some smashing occurs, will be 10, with

$(clean val) = 0, and $(selfpres val)=10. The

value of U2 in the same plan will be 172, giving an

estimation of 162 for FP, the undesirability of being

smashed. Then, fear inten(dirty,FI) plan will

return FI=62, indicating that Vicky has fear.

6 CONCLUSIONS

In this paper we presented an implementation of the

appraisal process of emotions in BDI agents using a

BDI language that integrates logic and probabilistic

reasoning. Speciﬁcally, we implemented the event-

generated emotions with consequences for self based

on the OCC cognitive psychological theory of emo-

tions. We also presented an illustrative scenario and

its implementation.

One original aspect of this work is that we im-

plemented the emotions intensity using a probabilistic

extension of a BDI language, called AgentSpeak(PL).

This intensity is deﬁned by the desirability central

value, as pointed by the OCC model. In this way, our

implementation of emotional BDI allows to differen-

tiate between emotions and affective reactions. This

AProbabilisticImplementationofEmotionalBDIAgents

127

is an important aspect because emotions tend to gen-

erate stronger response. Besides, the intensity of the

emotion also determines how strong is the response

of an individual (Scherer, 2000).

We are aware that the implementation of the ap-

praisal of emotions is only a ﬁrst step. An emotional

BDI implementation should address other important

dynamic processes between emotions and the mental

states of desires, intentions and beliefs in the BDI ar-

chitecture. As the BDI is a practical reasoning archi-

tecture, that is reasoning towards action (Wooldridge,

1999), it is important to discuss how the use of emo-

tions can help the agent to choose the most rational ac-

tion to be done and how the emotions can improve the

way that an agent reasons or decides or acts. These

are open questions that we intend to address in a fu-

ture work. However, we believe that the implementa-

tion of the appraisal and the arousal of an emotion de-

pending on the intensity of the affective reaction, pre-

sented in this paper, is an important and initial point

since the appraisal evaluation explains the origin of an

emotion and also differentiates them (Scherer, 1999).

ACKNOWLEDGEMENTS

This work is supported by the following re-

search funding agencies of Brazil: CAPES, CNPq,

FAPERGS and CTIC/RNP.

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