Strategies for Resolving Normative Conflict That Depends on

Execution Order of Runtime Events in Multi-Agent Systems

Mairon Belchior

, Jéssica Soares dos Santos

and Viviane Torres da Silva

Computer Science Department, Fluminense Federal University, Niterói, Brazil

IBM Research (on leave from Fluminense Federal University), Rio de Janeiro, Brazil

Keywords: Norms, Runtime Normative Conflict, Conflict Detection, Conflict Resolution, Multi-Agent Systems.

Abstract: Norms are being used in multi-agent systems to control the behavior of software agents and maintain social

order. They define which actions each agent can or not perform in different circumstances. Systems regulated

by multiple norms must be able to detect and resolve normative conflicts to guarantee the expected behavior

of the system. A normative conflict arises when a given agent is prohibited and obliged to perform the same

action at the same time. Our work aims to resolve normative conflict that occurs at runtime and where its

detection depends on the execution order of runtime events in multi-agent systems. This paper presents two

independent approaches to resolve the conflicts. The first approach resolves the conflict at design time by

eliminating the overlaps between two norms in conflict. The second approach resolves the normative conflict

at runtime by extending an existing automated planning algorithm in order to get plans that do not produce

sequence of conflicting actions.

1 INTRODUCTION

Open multi-agent systems (MAS) require a

mechanism to regulate the behavior of autonomous

and heterogeneous agents of the system. Norms can

be used as a powerful mechanism to maintain social

order, by establishing system-level constraints to be

followed by the agents. Those constraints define

obligations, permissions and prohibitions and do not

depend from the particular implementation of the

agents (Aphale et al., 2013).

It is important taking into account the possible

existence of normative conflicts in MAS regulated by

multiple norms. A normative conflict is a situation in

which the fulfillment of one norm causes a violation

of another one. Two norms are said to be in conflict

if (i) they are active at the same time, (ii) have

contradictory deontic concepts (i.e., prohibition

versus permission or prohibition versus obligation),

(iii) are associated with the same entity, (iv) regulate

the same behavior, and (v) are defined in the same

context. The detection of conflicts among norms is

not a trivial task to the system designer since a MAS

can be regulated by a big set of norms.

There are many approaches in the literature that

deal with normative conflicts in MAS. Some of them

deals with the detection of direct conflict, which are

simple conflicts between a prohibition and an

obligation or permission regulating the same agent,

the same behavior and defined in the same context.

Other approaches can also detect indirect conflicts.

Indirect conflict involves two norms whose norm

elements (i.e., entity, behavior, context of the norm)

are not the same but are related. The detection of

indirect conflicts can be done only when the

relationships among elements of the norms are

known.

In addition, there are conflicts that occur at

runtime. The detection of this conflict depends on

execution order of runtime events in the Multi-agent

Systems. In Belchior and da Silva (2017a, 2017b), the

authors investigated two approaches, in the design

phase, based on execution scenarios to deal with the

detection of normative conflicts that depends on

information about the runtime execution of the

system. In the first approach, the system designer is

able to provide examples of execution scenarios and

evaluate the conflicts that may arise if those scenarios

would be executed in the system. The second

approach, reported in Belchior and da Silva (2017b),

detects potential normative conflicts and generates

the execution scenarios to the system designer. The

conflict checker identifies potential normative

216

Belchior, M., Santos, J. and Silva, V.

Strategies for Resolving Normative Conﬂict That Depends on Execution Order of Runtime Events in Multi-Agent Systems.

DOI: 10.5220/0006593202160223

In Proceedings of the 10th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2018) - Volume 1, pages 216-223

ISBN: 978-989-758-275-2

conflicts by switching the position order of runtime

events referred in the norm conditions. It is called

potential conflict because it can be arisen or not

depending on the execution order of those events. The

output is an ordered list of events that caused the

normative conflict.

In this paper, we proposed two independent

approaches to resolve this normative conflict given

the output provided by the second conflict detection

approach. The first approach resolves the conflict at

design time by eliminating the overlaps between two

norms in conflict. The central idea of the first

approach is to eliminate the overlaps between two

norms by changing the after and before conditions of

one of the norms in conflict. Our mechanism chooses

to change the norm where the result does not

eliminate the entire norm. The result is a set of norms

free of conflict. The second resolution approach

resolves the normative conflict at runtime by

extending an existing automated planning algorithm

(Ghallab et al., 2004) in order to get plans that do not

produce sequence of conflicting actions.

This paper is organized as follows. Section 2

summarizes the norm representation and the potential

conflict detection approach. Section 3 describes the

two approaches to solve the normative conflict.

Section 4 presents related work and Section 5

concludes the paper and presents further research.

2 NORM REPRESENTATION

AND CONFLICT DETECTION

In Belchior and da Silva (2017a, 2017b), we have

proposed to use OWL DL and Semantic Web Rule

Language (SWRL) and reasoning tools to represent

the main concepts of a norm in MAS and to detect

norm violations and norm conflict. The main

concepts related to a nom are deontic concept, entity,

action, and context. The deontic concept describes

behavior restrictions for agents in the form of

obligations, permissions and prohibitions. Norms are

applied to a given entity whose behavior is being

controlled. The entities represented here are single

agents. Actions represent the behavior being

controlled by the norm and are executed by an entity.

Contexts determine the area of application of a norm.

Norms can be defined usually in two different

contexts, which are environment or organization. A

norm defined in a context should be fulfilled only by

agents executing in that context.

A norm is also related with a condition, which

determines the period during which a norm is active.

The conditions in Belchior and da Silva (2017a,

2017b) are runtime events, such as, execution of an

action by an agent, a fact that become true for an

agent, the fulfillment or violation of a norm and the

activation or deactivation of a norm. We have

considered two kinds of conditions: after condition,

and before condition. A norm can have one before

condition, one after condition, both of them or no

condition. Therefore, a norm can have one of the five

types of activation intervals illustrated in Figure 1.

Figure 1: Five types of activation intervals.

The first type is when a norm has no condition and

is always active. Its activation interval starts at time

zero and lasts until +infinite, i.e., the norm is always

active until the ending of the system execution. The

second type refers to a norm associated with only one

before condition. This interval starts from zero and

lasts until whenever that condition happens in the

system. The third type represents a norm with only

one after condition and the interval starts whenever

that condition happens and lasts until +infinite. The

fourth and fifth types refer to a norm associated with

both before and after conditions. They differ each

other by the moment the conditions happen in the

system. If the before condition happens first, then the

norm activation period is characterized by the fourth

interval type. Otherwise, the norm activation period

is represented by the fifth interval type.

The detection mechanism proposed in Belchior

and da Silva (2017b) identifies potential conflicts that

can be arisen depending on the execution order of

runtime events referred in the norm conditions. The

detection mechanism calculates all possible

combinations of those events by permuting the

positions of each event referred in the norms. The

output is potential normative conflicts along with

execution scenarios where the conflict may exist if

those scenarios would be executed in the system.

These execution scenarios are composed by an

ordered list of events, referred in the norm conditions,

which caused the conflict.

Strategies for Resolving Normative Conﬂict That Depends on Execution Order of Runtime Events in Multi-Agent Systems

217

For example, let us consider that there are three

norms n1, n2 and n3, defined as follows. Norm n1

obligates agent ag to perform action ac after an event

X, norm n2 prohibits the same agent from performing

the same action after an event Y and norm n3 is a

permission that authorizes the same agent to perform

the same action, but before an event Z. The detection

mechanism produces the following potential conflicts

followed by their execution scenarios, which are

graphically illustrated in Figure 2.

• Conflict between n2 and n3 if execution

order is: Y happens before Z, as shown in (a);

• Conflict between n1 and n2 if execution

order is: X happens after Y, as shown in (b);

• Conflict between n1 and n2 if execution

order is: X happens before Y, as shown in (c);

(a)

(b)

(c)

Figure 2: Scenarios of potential conflicts.

As can be seen, independently of the execution

order of X and Y, there is going to be a conflict

between norms n1 and n2. In addition, the conflict

detection identified a normative conflict between

norms n2 and n3 when the execution order in the

system is event Y happening before Z.

3 CONFLICT RESOLUTION

We proposed two approaches to resolve the

normative conflicts described in section 2. The first

approach resolves the conflict in design time by

eliminating the overlaps between two norms in

conflict. The second approach extends an existing

automated planning algorithm (Ghallab et al., 2004)

in order to get plans that do not produce sequences of

conflicting actions. The second approach resolves the

conflict at runtime and it can be used when the events

related in the norms are only actions. These

approaches are detailed in the following sections.

3.1 Eliminating Conflicting Activation

Intervals

The first approach resolves the normative conflicts at

design time. The resolution mechanism resolves all

normative conflicts by eliminating the overlap of

pairs of norms in conflict based on four strategies,

described later in this section. The resolution

mechanism receives, as input, a set of norms and one

pair of norms in conflict along with an ordered list of

events that caused the conflict, returned by detection

approach. The resolution mechanism chooses one

norm of the pair and applies one or more strategies,

depending on the types of activation intervals of the

pair of norms in conflict. Unless the activation

interval of the conflicting norms are identical, our

mechanism chooses to change the norm where the

result does not eliminate the entire norm. After

applying the strategies, the result are new norms that

are created to replace one of the original conflicting

norms in order to eliminate the conflict. The new

norms are added to the set of norms and the old one

is removed. The detection mechanism is called again

and the resolution mechanism receives the new set of

norms and another pair of norms in conflict along

with an ordered list of events that caused the conflict.

These steps are repeated until the detection

mechanism does not return any conflict.

Figures 3-11 illustrate different kinds of conflict

and resolution strategies. The parts with “X” in the

figures represent conflicting activation intervals,

which are removed during the resolution process. The

circled parts in the figures indicate the new norms that

are added after the resolution process.

We defined four strategies to eliminate the

conflict, which are used by the resolution algorithm.

Let n1 and n2 be a pair of norms in conflict. Each

strategy, except the first one, changes somehow the

after and before conditions of the norms. The four

strategies are defined as follow.

• Strategy 0: One of the norms in conflict are

removed by taking into account its modality

and the modality of the other norm. There

are several lines of research that also choose

to curtail/remove a conflicting norm

according to its modality, such as Kagal and

Finin (2007), Gaertner et al. (2007) and Oren

et al. (2008). We assume that when a conflict

involves a prohibition and a permission, the

permission is removed; and when a conflict

involves a prohibition and an obligation, the

prohibition is removed. However, the

decision to remove a norm according to its

modality is dependent on the requirements

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

218

of the system addressed and the order of

relevance of the modalities of the norms

could be easily changed by the system

designer (Gaertner et al., 2007).

• Strategy 1: Norm n1 is removed and a new

norm n1' is included in the set of norms. The

norm n1’ is a copy of n1, but whose after

condition is the before condition of n2 and

before condition is the after condition of n2.

• Strategy 2: Norm n1 is removed and a new

norm n1' is added in the set of norms, which

is a copy of n1, but its before condition is

changed to be the after condition of n2.

• Strategy 3: Norm n1 is removed and a new

norm n1’ is included in the set of norms,

which is a copy of n1, but its after condition

is changed to be the before condition of n2.

The resolution mechanism applies one or more

strategies, depending on the types of activation

intervals of the pair of norms in conflict, detailed as

follow. We consider a combination of all possible

types of activation intervals to decide how to change

the after and before conditions of the norms. When

both conflicting norms are active exactly in the same

intervals, the resolution mechanism apply Strategy 0

in order to remove the overlap. This specific case

occurs when the conflict involves norms whose

activation intervals are type 1 (norms without before

and after conditions) or when after/before conditions

of the conflicting norms are the same, i.e., norms

whose activation intervals are exactly the same.

When a conflict involves a norm n1 whose

activation interval is type 1 and a norm n2 whose

activation interval is types 2, 3, 4 or 5, the strategy 1

can be used to solve the conflict. It is also the case

when n1 has activation interval type 2 and n2 has

activation interval type 3. Figure 3 illustrates those

cases. As mentioned above, the resolution mechanism

chooses to change the norm where the result does not

eliminate the entire norm. Thus, norm n1 is selected

in Figures 3.a, 3.b, 3.c and 3.d. In Figure 3.e, the

resolution mechanism could choose either norm,

since it does not eliminate neither one. In this case,

the first norm was selected.

(a)

(b)

(c)

(d)

(e)

Figure 3: Conflict resolution involving activation interval

type 1 and type 2 (a), type 1 and type 3 (b), type 1 and type

4 (c), type 1 and type 5 (d), and type 2 and type 3 (e), all

using Strategy 1.

When both conflicting norms n1 and n2 have

activation intervals type 2, assuming that the after

condition of n1 occurs before the after condition of

n2, a new norm n1' is created by using Strategy 2. The

norm n1' is a copy of n1, but its before condition (an

empty condition) is changed to be the after condition

of n2 (see Figure 4.a). After that, the new norm n1' is

included in the set of norms and n1 is removed. When

both conflicting norms have activation intervals type

3, assuming that before condition of n1 occurs after

the before condition of n2, the resolution mechanism

uses Strategy 3 for solving the conflict (Figure 4.b).

(a)

(b)

Figure 4: Conflict resolution involving activation intervals

type 2 (a) by using Strategy 2 and (b) activation intervals

type 3 by using Strategy 3.

When the conflict involves a norm n1 whose

activation interval is type 2 and a norm n2 whose

activation interval is type 4, the resolution mechanism

uses Strategy 2 and Strategy 3 for solving the conflict.

By using Strategy 3, a copy of n1, called n1', is

created but its after condition is changed to be the

before condition of n2 (see Figure 5.a). If the after

condition of n1 occurs before the after condition of

n2, in addition of creating n1', a new norm n1'' is also

created by using Strategy 2. The norm n1'' is a copy

of n1, but its before condition (an empty condition) is

changed to be the after condition of n2 (see Figure

5.b). After that, the new norms n1' and n1'' are

included in the set of norms and n1 is removed.

(a)

(b)

Figure 5: Conflict resolution involving activation interval

type 2 and type 4 (a) by using Strategy 3 and (b) by using

Strategy 2 and 3.

When the conflict involves a norm n1 whose

activation interval is type 2 and a norm n2 whose

activation interval is type 5, the resolution mechanism

uses Strategy 1, Strategy 2 or Strategy 3 for resolving

the conflict. If n1 has an after condition that occurs

after the after condition of n2, Strategy 3 is adopted.

In the Strategy 3, a copy of n2, called n2', is created

and its after condition is changed to be the before

condition of n1 (an empty condition). In addition of

creating n2', a new norm n2'' is created by using

Strategy 2. The norm n2'' is a copy of n2, but its

before condition is changed to be the after condition

of n1 (see Figure 6.a). Note that, the activation

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219

interval of the norm n1 is contained within the

activation interval of the norm n2 and, for this reason,

we chose to modify the activation interval of n2,

avoiding n1 to be completely removed.

If the after condition of n1 is the same of n2, only

n2' is created. The new norms n2' and n2'' are

included in the set of norms and n2 is removed. On

the other hand, if the after condition of n1 occurs

before the before condition of n2, only a new norm

n1' is created by using Strategy 1 (see Figure 6.b). The

norm n1' is included in the set of norms and n1 is

removed. However, if the after condition of n1 occurs

after the before condition of n2 and before the after

condition of n2, a new norm n1' is created by using

Strategy 2 (see Figure 6.c).

(a)

(b)

(c)

Figure 6: Conflict resolution involving activation interval

type 2 and type 5 by using (a) Strategy 2 and Strategy 3, (b)

Strategy (1), and (c) Strategy 2.

When the conflict involves a norm n1 whose

activation interval is type 3 and a norm n2 whose

activation interval is type 4, the resolution mechanism

uses Strategy 2 and Strategy 3 for resolving the

conflict. A new norm n1' is created by using Strategy

2, i.e., n1' is a copy of n1, but its before condition is

changed to be the after condition of n2 (see Figure

7.a). If the before condition of n1 occurs after the

before condition of n2, in addition of creating n1', a

new norm n1'' is created by using Strategy 3. Norm

n1'' is a copy of n1, but its after condition (an empty

condition) is changed to be the before condition of n2

(see Figure 7.b).

(a)

(b)

Figure 7: Conflict resolution involving activation intervals

type 3 and type 4 by using Strategy 2 (a), and by using

Strategy 2 and Strategy 3 (b).

When the conflict involves a norm n1 whose

activation interval is type 3 and a norm n2 whose

activation interval is type 5, the resolution mechanism

uses Strategy 1, Strategy 2 and Strategy 3. If the

before condition of n1 occurs before the before

condition of n2, two new norms n2' and n2'' are

created, where both norms are copies of n2, but the

after condition of n2'' is changed to be the before

condition of n1 (Strategy 3) and the before condition

of n2' is changed to be the after condition of n1 (an

empty condition) (Strategy 2) (see Figure 8.a). On the

other hand, if the before condition of n1 occurs after

the before condition of n2 and before the after

condition of n2, a new norm n1' is created by using

Strategy 3 (see Figure 8.b). Otherwise, if the before

condition of n1 occurs after the after condition of n2

or if the before condition of n1 is the after condition

of n2, a new norm n1' is created by using Strategy 1

(see Figure 8.c). Otherwise, if the before condition of

n1 is the before condition of n2, a new norm n2' is

created by using Strategy 2 (see Figure 8.d).

(a)

(b)

(c)

(d)

Figure 8: Conflict resolution involving activation interval

type 3 and type 5 by using Strategy 2 and Strategy 3 (a), by

using Strategy 3 (b), by using Strategy 1 (c), and by using

Strategy 2 (d).

When both norms involved in the conflict have

activation intervals type 4, the resolution mechanism

uses Strategy 2 and Strategy 3 for resolving the

conflict. If the before condition of n1 occurs after the

before condition of n2 and the after condition of n1

occurs after the after condition of n2 or n1 and n2

have the same after condition, a new norm n1' is

created by using Strategy 3 (see Figure 9.a).

Otherwise, if the after condition of n2 occurs after the

after condition of n1 and the before condition of n2

occurs before the before condition of n1, in addition

of creating n1', a new norm n1'' is created by using

Strategy 2 (see Figure 9.b). On the other hand, if the

after condition of n2 occurs after the after condition

of n1 and the before condition of n2 occurs after the

before condition of n1 or n1 and n2 have the same

before condition, only n1' is created (see Figure 9.c).

(a)

(b)

(c)

Figure 9: Conflict resolution involving activation intervals

type 4 by using Strategy 3 (a), by using Strategy 3 and 2 (b),

and by using Strategy 2 (c).

When the conflict involves a norm n1 whose

activation interval is type 4 and a norm n2 whose

activation interval is type 5, the resolution mechanism

uses Strategy 1, Strategy 2 and Strategy 3 for

resolving the conflict. If the after condition of n1

occurs before the before condition of n2 and the

before condition of n1 occurs after the after condition

of n2, the Strategy 1 is adopted for creating a new

norm n1' (see Figure 10.a). Otherwise, if the after

ICAART 2018 - 10th International Conference on Agents and Artiﬁcial Intelligence

220

condition of n1 occurs before the before condition of

n2, and the before condition of n1 occurs before the

before condition of n2 or the before condition of both

norms are the same, a new norm n2' is created by

using Strategy 2. If the before conditions of n1 and n2

are not the same, in addition of creating n2', a new

norm n2'' is created by using Strategy 3 (see Figure

10.b). On the other hand, if the after condition of n1

occurs after the after condition of n2 or n1 and n2

have the same after condition, a new norm n2' is

created by using Strategy 3. If the after condition of

n1 and n2 are not the same, in addition of creating n2',

a new norm n2'' is created by using Strategy 2 (see

Figure 10.c).

(a)

(b)

(c)

Figure 10: Conflict resolution involving activation interval

type 4 and type 5 by using Strategy 1 (a), and by using

Strategy 2 and Strategy 3 (b) (c).

When both norms involved in the conflict have

activation intervals type 5, Strategies 1, 2 and 3 are

adopted for solving the conflict. If the before

condition of n1 occurs after the after condition of n2,

a new norm n1' is created by using Strategy 1 (see

Figure 11.a). However, if the before condition of n2

occurs after the after condition of n1, a new norm n1'

is created by using Strategy 1 (see Figure 11.b).

Otherwise, if the before condition of n2 occurs after

the before condition of n1 and the after condition of

n2 occurs before the after condition of n1, two new

norms n2' and n2'' are created, where both norms are

copies of n2, but the after condition of n2' is changed

to be the before condition of n1 (Strategy 3) and the

before condition of n2'' is changed to be the after

condition of n1 (Strategy 2) (see Figure 11.c).

(a)

(b)

(c)

(d)

(e)

Figure 11: Conflict resolution involving activation intervals

type 5 by using Strategy 1 (a) (b), by using Strategy 2 and

Strategy 3 (c), by using Strategy 2 (d), and by using Strategy

3 (e).

On the other hand, if the before conditions of n1

and n2 are the same, assuming that the after condition

of n1 occurs before the after condition of n2, a new

norm n1' is created by using Strategy 2 (see Figure

11.d). Otherwise, if the after conditions of n1 and n2

are the same, assuming that the before condition of n1

occurs before the before condition of n2, a new norm

n2' is created by using Strategy 3 (see Figure 11.e).

The main structure of the resolution algorithm is

described in Algorithm 1. It invokes the function

assignArbitraryTime (line 2) that assigns arbitrary

values to the events received as input according to a

conflicting order returned by the detection

mechanism and creates a copy of the original set of

norms (line 3). After that, it invokes the function

removeOverlapping that decides which resolution

strategy to choose. Note that, removeOverlapping is

invoked two times, when the first time does not

modify the set of norms. In the second time, n1 and

n2 are passed to the function removeOverlapping in

different orders (lines 4 to 6) to guarantee that all

possible combinations of kinds of conflict are

considered. Finally, Algorithm 1 returns the copy of

the original set of norms (setOfNorms') after

removing the normative conflict between n1 and n2.

Algorithm 1: Algorithm that solves conflicts between

two norms and returns the set of norms without the

given conflict.

Input: n1, n2: Norms in conflict, setOfNorms: Set of

norms, listOfConditions: Ordered list of conditions

Output: setOfNorms': Set of norms without the given

conflict

1. function solveConflicts(n1, n2, setOfNorms,

listOfConditions)

2. assignArbitraryTime(listOfConditions);

3. setOfNorms' ← setOfNorms;

4. removeOverlapping(n1, n2, setOfNorms');

5. if (setOfNorms'==setOfNorms) then

6. removeOverlapping(n2, n1, setOfNorms');

7. return setOfNorms';

3.2 Resolution based on Artificial

Intelligence Planning

The second approach resolves the normative conflict

described in Section 2 by avoiding them at runtime.

We propose to extend an existing automated planning

algorithm (Ghallab et al., 2004) in order to get plans

that do not produce sequence of conflicting actions.

The detection conflict approach outputs sequences of

actions that would cause a normative conflict.

Therefore, the planner must find a plan that does not

contain any of the sequence of actions returned by the

normative detection approach. That way, at runtime,

the agents would never perform actions that would

cause normative conflict. This second approach can

be used when the events related in the norms are

actions or can be represented as actions.

Artificial Intelligence Planning is the task of

coming up with a sequence of actions that will

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221

achieve a goal (Russel and Norvig, 2003). A planning

problem is represented by states, actions and goals.

Planners decompose the world into logical conditions

and represent a state as a conjunction of positive

literals. A goal is a partially specified state,

represented as a conjunction of positive ground

literals. A propositional state s satisfies a goal g if s

contains all the atoms in g (and possibly others). An

action is specified in terms of the preconditions that

must hold before it can be executed and the effects

that ensue when it is executed.

In order to demonstrate this second resolution

approach, we choose to extend the forward-search

planning algorithm (Ghallab et al., 2004), because it

is one of the simplest planning algorithms. The

forward-search planning algorithm searches forward

from the initial state of the world to try to find a state

that satisfies the goal formula. Algorithm 2 extends

the forward-search planning algorithm in lines 7 to

12. After choosing an action from applicable action

set (line 9), the algorithm checks if that action added

to the current plan p would cause any normative

conflict by calling isConflictingPlan function. If so,

that action is removed from applicable action set (line

11) and a new action are chosen. This repeats until it

finds a no conflicting plan or the applicable set of

actions is empty. Algorithm 3 checks if a plan p

would generate any normative conflict by verifying if

any sequence of conflicting actions returned by

detection conflict approach is in plan p (line 4). If that

is the case, the algorithm returns true. Otherwise, it

returns false.

Algorithm 2: Free conflict planning algorithm

Input: O: Actions, S

: Start State, G: Goal State

Output: p: No conflicting plan

1. function freeConflictPlan(O, S

, G)

2. S ← S

3. p ← the empty plan

4. loop

5. if S satisfies G then return p

6. applicable ← {a | a is a ground instance of an

operator in O, and precond(a) is true

in s}

7. do

8. if applicable = ∅ then return failure

9. nondeterministically choose an action a ∈

applicable

10. conflicting ← isConflictingPlan(p . a)

11. if conflicting then remove a from applicable

12. while conflicting

13. S ← 𝛾(S, a)

14. p ← p . a

15. return p

Algorithm 3: Checks if a plan contains conflicting

actions.

Input: p: Plan

Output: An boolean value stating if plan p would

generate any normative conflict or not

1. function isConflictingPlan(p)

2. SCA ← all sequences of conflicting actions

3. foreach sequence s ∈ SCA do

4. if s in p then return true

5. return false

4 RELATED WORK

In the literature, there are several strategies applied to

resolve conflicts among norms of a multi-agent

system, as described in (Santos et al., 2017).

In the work described in Vasconcelos et al.

(2009), norms can have variable terms in their

definition that relate actions to constraints. The

authors assume that a normative conflict occurs when

the variables of a prohibition overlap with the

variables of an obligation or permission. They present

an algorithm for conflict resolution that manipulates

the constraints of norms to avoid overlapping values

of variables, i.e., it adds constraints to restrict the

scope of influence of one of the conflicting norms,

eliminating the normative conflict.

Similarly, the resolution method described in

Gaertner et al. (2007) and Vasconcelos et al. (2012)

also curtails the scope of influence of the norms after

verifying which values the norms cannot assume to

avoid the conflict. The authors curtail prohibitions but

state that the same mechanism can be applied to

curtail obligations. Our strategy differs from those

approaches because we reduce the scope of influence

by modifying the before/after conditions of the norms

while them change variables associated with the

actions being regulated.

The work detailed in Aphale et al. (2013) presents

strategies to solve conflicts based on standard

techniques and norm refinement. The standard

techniques consist of determining an order of norm

overruling after determining norm precedence, based

on three classical principles to resolve deontic

conflicts: lex posterior (the most recent norm is

prioritized); lex specialis (the most specific norm is

prioritized); and lex superior (the norm imposed by

the most important authority is prioritized)

(Vasconcelos et al., 2009). The strategy of norm

refinement uses planning, as in Sensoy et al. (2012),

to expire the activation interval of one of the

conflicting norms. In this case, an automated planner

searches for a plan that implies a state of the world in

which the expiration condition of one of the

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conflicting norms holds. Our approach differs from

the one described in Aphale et al. (2013) because we

use a planner to avoid certain actions to be performed.

In the research described in Günay and Yolum

(2013), obligations and prohibitions are represented

through commitments and the conflicts are solved by

changing the activation condition of the

commitments.

Although the related approaches also reduce the

scope of influence of the norms or use a method based

on planning to solve the conflicts, none of them

focuses on conflicts that depends on execution order

of runtime events in multi-agent systems.

5 CONCLUSIONS

Norms are being used in multi-agent systems to

control the behavior of software agents, without

restricting their autonomy. It is important taking into

account the possible existence of normative conflicts

in MAS regulated by multiple norms. A normative

conflict arises when the fulfilment of one norm causes

the violation of another. This paper presented two

approaches to resolve normative conflicts that

depends on execution order of runtime events in

multi-agent systems. The first approach eliminates, at

design time, the overlaps between two norms in

conflict by changing the activation intervals of the

conflicting pair. The result is a set of norms free of

conflict. The second approach resolves the normative

conflict by extending an existing automated planning

algorithm in order to get plans that do not produce

sequence of conflicting actions. Therefore, the

planner would generate sequence of actions that are

free of normative conflict. As future work, we intend

to extend the proposed approach to support several

before and after conditions in the norm definition. In

this version, the norm definition only supports one

after and one before conditions. Moreover, we would

like to exploit our mechanisms in real world

scenarios.

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