An Algorithm for Conflict Resolution in Regulated Compound Activities
Available from www.garcia-camino.es
Page 1
An Algorithm for Conflict Resolution in Regulated Compound Activities
An Algorithm for Conflict Resolution in
Regulated Compound Activities
Andre´s Garc´ıa-Camino, Pablo Noriega, and Juan-Antonio Rodr´ıguez-Aguilar
IIIA-CSIC, Campus UAB, 08193 Bellaterra, Spain
{andres, pablo, jar}@iiia.csic.es
Abstract. The use of norms is a well-known technique of co-ordination
in multi-agent systems (MAS) adopted from human societies. A norma-
tive position is the “social burden” associated with individual agents,
that is, their obligations, permissions and prohibitions. Compound ac-
tivities may be regulated by means of normative positions. However,
conflicts may appear among normative positions of activities and sub-
activities. Recently several computational approaches have appeared to
make norms operational in MAS but they do not cope with compound
activities. In this paper, we propose an algorithm to determine the set of
applicable normative positions, i.e., the largest set of normative positions
without conflicts in the state of an activity, and propagate them to the
sub-activities.
1 INTRODUCTION
Society has frequently come across the need of coordinating interactions among
individuals and one way of addressing that need has been to establish restric-
tive environments where the interactions are constrained to only those partici-
pants and those interactions that are meant to be. For analogous reasons, the
MAS community has proposed regulated environments where agents –human or
software– interact as [1,2,3].
The environments we will have in mind in this paper are regulated environ-
ments where agent interactions are structured as repetitive interactions –that
we shall call activities– and the whole environment is the result of the com-
position of many such activities. These activities are subject to explicit sets of
conventions that prescribe how the actions of agents that participate in a given
activity establish or fulfil commitments that affect the participants of that ac-
tivity and of subordinate activities. For lack of a better term we will refer to
such environments as regulated compound activities.
Many real world societies conform to this type of regulated environments
and virtual counterparts are easy to conceive. For instance, Figure 1 describes
the example of an on-line commodities trading market that has different price-
fixing conventions which may have different simultaneous enactments (different
auctions to buy, say, wholesale fruit and poultry; one-to-many negotiations for
supermarkets to stock their weekly supply, direct purchasing for scarce quality
Regulated Compound Activities
Andre´s Garc´ıa-Camino, Pablo Noriega, and Juan-Antonio Rodr´ıguez-Aguilar
IIIA-CSIC, Campus UAB, 08193 Bellaterra, Spain
{andres, pablo, jar}@iiia.csic.es
Abstract. The use of norms is a well-known technique of co-ordination
in multi-agent systems (MAS) adopted from human societies. A norma-
tive position is the “social burden” associated with individual agents,
that is, their obligations, permissions and prohibitions. Compound ac-
tivities may be regulated by means of normative positions. However,
conflicts may appear among normative positions of activities and sub-
activities. Recently several computational approaches have appeared to
make norms operational in MAS but they do not cope with compound
activities. In this paper, we propose an algorithm to determine the set of
applicable normative positions, i.e., the largest set of normative positions
without conflicts in the state of an activity, and propagate them to the
sub-activities.
1 INTRODUCTION
Society has frequently come across the need of coordinating interactions among
individuals and one way of addressing that need has been to establish restric-
tive environments where the interactions are constrained to only those partici-
pants and those interactions that are meant to be. For analogous reasons, the
MAS community has proposed regulated environments where agents –human or
software– interact as [1,2,3].
The environments we will have in mind in this paper are regulated environ-
ments where agent interactions are structured as repetitive interactions –that
we shall call activities– and the whole environment is the result of the com-
position of many such activities. These activities are subject to explicit sets of
conventions that prescribe how the actions of agents that participate in a given
activity establish or fulfil commitments that affect the participants of that ac-
tivity and of subordinate activities. For lack of a better term we will refer to
such environments as regulated compound activities.
Many real world societies conform to this type of regulated environments
and virtual counterparts are easy to conceive. For instance, Figure 1 describes
the example of an on-line commodities trading market that has different price-
fixing conventions which may have different simultaneous enactments (different
auctions to buy, say, wholesale fruit and poultry; one-to-many negotiations for
supermarkets to stock their weekly supply, direct purchasing for scarce quality
Page 2
2 A. Garc´ıa-Camino et al.
Fig. 1. Example of compound activities
goods like spices). These price-fixing activities are, on one hand, preceded by ac-
tivities whose purpose is to set the grounds for the day’s trading (e.g., activities
to introduce whatever is to be exchanged during the day, or the accreditation of
buyers and their credit lines, etc.) and, on the other hand, they may be followed
by other activities like delivery contracting, temporary warehousing or packag-
ing, which in-turn may be compound activities on their own, etc. Other examples
of compound activities that naturally come to mind are hospital operation, the
football world association (FIFA) activities, or the execution of everyday local
government activities.
The conventions that regulate activities, as the examples show, usually have
both a procedural component and a declarative one. The conventions may be
expressed in different ways although the most familiar ones are commitment-
based interaction protocols (e.g., [1,4,3]) and logical (and logic-based) systems
(e.g., [5,6]), or as a combination of both [7]. Some of these approaches have
elegant conceptual frameworks behind and a few have also an operationalisation
that is amenable to be implemented and still a few have been able to integrate
the three previous types of convention representation. This last family is what
we aim at in our proposal.
In advancing conceptual or implementation frameworks for compound activi-
ties, one of the main problems to address —from a social perspective— is to keep
track of the commitments that are being established and fulfilled dynamically
anywhere in the (compound) society while the society is active. This is a partic-
ularly significant problem in societies where truly autonomous entities intervene.
The actual problem, then, is to keep an appropriate record of the commitments
that are being made and their follow-up, to make sure that the commitments
are consistent. This entails the need to make the problem operational, state it
in such a way that formal and implementations are feasible and practical.
Fig. 1. Example of compound activities
goods like spices). These price-fixing activities are, on one hand, preceded by ac-
tivities whose purpose is to set the grounds for the day’s trading (e.g., activities
to introduce whatever is to be exchanged during the day, or the accreditation of
buyers and their credit lines, etc.) and, on the other hand, they may be followed
by other activities like delivery contracting, temporary warehousing or packag-
ing, which in-turn may be compound activities on their own, etc. Other examples
of compound activities that naturally come to mind are hospital operation, the
football world association (FIFA) activities, or the execution of everyday local
government activities.
The conventions that regulate activities, as the examples show, usually have
both a procedural component and a declarative one. The conventions may be
expressed in different ways although the most familiar ones are commitment-
based interaction protocols (e.g., [1,4,3]) and logical (and logic-based) systems
(e.g., [5,6]), or as a combination of both [7]. Some of these approaches have
elegant conceptual frameworks behind and a few have also an operationalisation
that is amenable to be implemented and still a few have been able to integrate
the three previous types of convention representation. This last family is what
we aim at in our proposal.
In advancing conceptual or implementation frameworks for compound activi-
ties, one of the main problems to address —from a social perspective— is to keep
track of the commitments that are being established and fulfilled dynamically
anywhere in the (compound) society while the society is active. This is a partic-
ularly significant problem in societies where truly autonomous entities intervene.
The actual problem, then, is to keep an appropriate record of the commitments
that are being made and their follow-up, to make sure that the commitments
are consistent. This entails the need to make the problem operational, state it
in such a way that formal and implementations are feasible and practical.
Page 3
An Algorithm for Conflict Resolution in Regulated Compound Activities 3
In this paper, consequently, we want to make headway towards a proposal
of a framework for commitment management in regulated environments formed
by compound activities. For this purpose we adopt a social perspective to the
problem and take a simplified and unconventional approach along the follow-
ing lines: We abstract the notion of commitment and commitment management
by focusing only on the prohibitions, permissions and obligations associated to
actions, what we will call the normative positions. We also abstract the way nor-
mative positions propagate in the society by having a directed graph linking the
activities that inherit normative positions and assuming that the graph is prede-
fined and to that extent independent of the way activities are actually connected
in formal and implementational ways. The management of commitments is also
abstracted in this paper by focusing only in the resolution of conflicts among
normative positions and using conventional priority criteria to choose between
conflicting positions and only then propagate normative positions to the subor-
dinate activities. Since we are interested in making our proposal operational we
also present an algorithm that implements these ideas and keeps track of the
evolution of normative positions in acyclic compound activities and maintains a
conflict-free normative positions base.
The rest of the paper is structured as follows. In section 2, normative posi-
tions, deontic conflicts and criteria for conflict resolution are introduced. Com-
pound activities and their deontic conflicts are defined in section 3. In this sec-
tion, properties of normative consistency in regulated compound activities, as
e.g. strong and weak conflict-freedom, are also introduced. In section 4, an algo-
rithm to resolve deontic conflicts in compound activities is proposed. In section
5 we present an example of how the algorithm works. Finally, conclusions and
future work are outlined in the last section.
2 NORMATIVE POSITIONS
A normative position is the “social burden” associated with individual agents,
that is, their obligations, permissions and prohibitions (cf. [5]). Depending on
what agents do, their normative positions may change – for instance, permis-
sions/prohibitions can be revoked or obligations, once fulfilled, may be removed.
In regulated actions, the change of normative positions maybe determined
by rules that, for example, are time-dependent. For instance, a permission to
lend a book is enabled every week day at 9:00a.m. and disabled every week day
at 9:00p.m. Action performances can enable normative positions that can be
subsequently fulfilled or cancelled. For example, an obligation to pay for a good
is enabled if that good is received (generation). This obligation can be disabled
either by paying for the good (fulfilment) or by returning it (cancellation).
Deontic conflicts may appear when norms enable new normative positions
that are incompatible with the normative positions already enabled. Tradition-
ally, three principles have been used to resolve deontic conflicts: legis posterior,
legis specialis and legis superior. These principles order the norms to avoid con-
flicts following three criteria: a chronological criterion (lex posterior), a speciality
In this paper, consequently, we want to make headway towards a proposal
of a framework for commitment management in regulated environments formed
by compound activities. For this purpose we adopt a social perspective to the
problem and take a simplified and unconventional approach along the follow-
ing lines: We abstract the notion of commitment and commitment management
by focusing only on the prohibitions, permissions and obligations associated to
actions, what we will call the normative positions. We also abstract the way nor-
mative positions propagate in the society by having a directed graph linking the
activities that inherit normative positions and assuming that the graph is prede-
fined and to that extent independent of the way activities are actually connected
in formal and implementational ways. The management of commitments is also
abstracted in this paper by focusing only in the resolution of conflicts among
normative positions and using conventional priority criteria to choose between
conflicting positions and only then propagate normative positions to the subor-
dinate activities. Since we are interested in making our proposal operational we
also present an algorithm that implements these ideas and keeps track of the
evolution of normative positions in acyclic compound activities and maintains a
conflict-free normative positions base.
The rest of the paper is structured as follows. In section 2, normative posi-
tions, deontic conflicts and criteria for conflict resolution are introduced. Com-
pound activities and their deontic conflicts are defined in section 3. In this sec-
tion, properties of normative consistency in regulated compound activities, as
e.g. strong and weak conflict-freedom, are also introduced. In section 4, an algo-
rithm to resolve deontic conflicts in compound activities is proposed. In section
5 we present an example of how the algorithm works. Finally, conclusions and
future work are outlined in the last section.
2 NORMATIVE POSITIONS
A normative position is the “social burden” associated with individual agents,
that is, their obligations, permissions and prohibitions (cf. [5]). Depending on
what agents do, their normative positions may change – for instance, permis-
sions/prohibitions can be revoked or obligations, once fulfilled, may be removed.
In regulated actions, the change of normative positions maybe determined
by rules that, for example, are time-dependent. For instance, a permission to
lend a book is enabled every week day at 9:00a.m. and disabled every week day
at 9:00p.m. Action performances can enable normative positions that can be
subsequently fulfilled or cancelled. For example, an obligation to pay for a good
is enabled if that good is received (generation). This obligation can be disabled
either by paying for the good (fulfilment) or by returning it (cancellation).
Deontic conflicts may appear when norms enable new normative positions
that are incompatible with the normative positions already enabled. Tradition-
ally, three principles have been used to resolve deontic conflicts: legis posterior,
legis specialis and legis superior. These principles order the norms to avoid con-
flicts following three criteria: a chronological criterion (lex posterior), a speciality
Page 4
4 A. Garc´ıa-Camino et al.
criterion (lex specialis) by which a specific law prevails over a general law and a
source criterion, where preference is linked to the rank of the issuing authority
(lex superior). We extend these criteria with an extra criterion, the salience cri-
terion where we may capture whatever other notions of pertinence or relevance
may be of use in a specific activity.
Although such criteria are used to resolve deontic conflicts, in some occasions
two or more criteria may need to be sequentially applied to achieve that goal. In
those circumstances the criteria involved need to be totally ordered. An exam-
ple of this meta-ordering is when the source criterion prevails over the speciality,
salience and the chronological ones, the salience criterion prevails over the spe-
ciality and the chronological ones, and the speciality criterion prevails over the
chronological one.
In this paper, the chronological and salience criteria will have a straightfor-
ward operationalisation. The speciality criterion will correspond to the hierar-
chical dependence of an activity and its subactivities. Establishing certain agents
as sources of law, defining the ordering of sources of law, and ordering norms
using the source criterion are left for future work.
We may now illustrate these ideas and state them in a more precise way.
We mentioned that a normative position is a permission, a prohibition or an
obligation to perform a specific action. Since we are concerned with resolving
conflicts between normative positions, we find useful to associate to every norma-
tive position a time stamp that corresponds to the moment it becomes effective
(enabled). For the same reason we find useful to associate to normative positions
an argument that stands for its salience, although it is beyond the scope of this
paper how values may be assigned to that parameter. More precisely:
Definition 1. Let δ ∈ {per, prh, obl} be a label for the “social burden” of per-
forming an action identified by a, a salience constant s ∈ N and a time-stamp
t ∈ N, the formula δ(a, s, t) stands for a normative position that states that at
time t, and with priority s, action a becomes permitted, obligatory or prohibited.
Examples of normative positions may be: per(bidag1 , 0, 0), prh(bidag1 , 2, 1),
etc. The former normative position intuitively states that agent ag1 is permitted
to bid since time 0 and this normative position has priority 0. The latter nor-
mative position intuitively means that agent ag1 is prohibited to bid since time
1 and this normative position has priority 2.
As mentioned above, deontic conflicts among normative positions can arise
as agent interactions progress. We will say that two normative positions are in
conflict if one is a permission or obligation and the other is a prohibition over
the same action than the former, regardless of their corresponding salience and
enabling times. That is:
Definition 2. Given two normative positions np, np′ such that np = δ(a, s, t)
and np′ = δ′(a′, s′, t′) ; np, np′ are in conflict, denoted np≫≪np′, iff:
1. {δ} ∪ {δ′} = {per, prh}, a = a′; or
2. {δ} ∪ {δ′} = {obl, prh}, a = a′.
criterion (lex specialis) by which a specific law prevails over a general law and a
source criterion, where preference is linked to the rank of the issuing authority
(lex superior). We extend these criteria with an extra criterion, the salience cri-
terion where we may capture whatever other notions of pertinence or relevance
may be of use in a specific activity.
Although such criteria are used to resolve deontic conflicts, in some occasions
two or more criteria may need to be sequentially applied to achieve that goal. In
those circumstances the criteria involved need to be totally ordered. An exam-
ple of this meta-ordering is when the source criterion prevails over the speciality,
salience and the chronological ones, the salience criterion prevails over the spe-
ciality and the chronological ones, and the speciality criterion prevails over the
chronological one.
In this paper, the chronological and salience criteria will have a straightfor-
ward operationalisation. The speciality criterion will correspond to the hierar-
chical dependence of an activity and its subactivities. Establishing certain agents
as sources of law, defining the ordering of sources of law, and ordering norms
using the source criterion are left for future work.
We may now illustrate these ideas and state them in a more precise way.
We mentioned that a normative position is a permission, a prohibition or an
obligation to perform a specific action. Since we are concerned with resolving
conflicts between normative positions, we find useful to associate to every norma-
tive position a time stamp that corresponds to the moment it becomes effective
(enabled). For the same reason we find useful to associate to normative positions
an argument that stands for its salience, although it is beyond the scope of this
paper how values may be assigned to that parameter. More precisely:
Definition 1. Let δ ∈ {per, prh, obl} be a label for the “social burden” of per-
forming an action identified by a, a salience constant s ∈ N and a time-stamp
t ∈ N, the formula δ(a, s, t) stands for a normative position that states that at
time t, and with priority s, action a becomes permitted, obligatory or prohibited.
Examples of normative positions may be: per(bidag1 , 0, 0), prh(bidag1 , 2, 1),
etc. The former normative position intuitively states that agent ag1 is permitted
to bid since time 0 and this normative position has priority 0. The latter nor-
mative position intuitively means that agent ag1 is prohibited to bid since time
1 and this normative position has priority 2.
As mentioned above, deontic conflicts among normative positions can arise
as agent interactions progress. We will say that two normative positions are in
conflict if one is a permission or obligation and the other is a prohibition over
the same action than the former, regardless of their corresponding salience and
enabling times. That is:
Definition 2. Given two normative positions np, np′ such that np = δ(a, s, t)
and np′ = δ′(a′, s′, t′) ; np, np′ are in conflict, denoted np≫≪np′, iff:
1. {δ} ∪ {δ′} = {per, prh}, a = a′; or
2. {δ} ∪ {δ′} = {obl, prh}, a = a′.
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An Algorithm for Conflict Resolution in Regulated Compound Activities 5
In the previous example, per(bidag1 , 0, 0) and prh(bidag1 , 2, 1) are in conflict
by the first condition of definition 2.
We take care of the other two parameters of normative positions with the
following definitions.
Definition 3. A normative position np = δ(e, s, t) is a chronological successor
of np′ = δ′(e′, s′, t′), written as np ≻T np′, iff t > t′.
Definition 4. A normative position np = δ(e, s, t) is more salient than np′ =
δ′(e′, s′, t′), written as np ≻P np′, iff s > s′.
In our example, prh(bidag1 , 2, 1) is more salient and a chronological successor
of per(bidag1 , 0, 0).
3 REGULATED COMPOUND ACTIVITIES
In this paper we have in mind that a performance of a set of actions —subject
to some regulation—constitute an activity and that an activity may be com-
posed of several sub-activities which in turn may also be decomposed into other
sub-activities. Take the example of a clearinghouse involving different activities
outlined in Figure 1. The main activity, trading, involves subactivities —like
auctioning, one-to-many negotiation or direct purchasing— that serve the pur-
pose of fixing the conditions for purchasing goods and other activities required
for payment and delivery of goods.
Several models and methodologies for MAS (e.g., [1,2,3]) have looked into
the notion of compound activity using different names such as performative
structure, missions or simply interaction. For our purposes we only need to look
into those aspects that relate to the evolution of normative positions within an
activity and how these are propagated in the hierarchy.
Each activity behaves like a transition system: it has a state, represented by
a set of grounded terms, that changes with the performance of the actions of
the agents in the activity. This transition function is partial since not all the
actions may occur in all the states of an activity. Norms establish what actions
are permitted, forbidden or obligatory (and their effects) in a given state of the
activity, defining the transition function of the activity. Normative positions are
part of the state of an activity and they also change by the performance of ac-
tions and the application of the transition function. Note also that since different
activities may be connected —in the sense that what happens in one has effect
on the other— when those normative positions in the first change, the normative
positions in the other may also change. We will say that the scope of a normative
position is the activity where it becomes enabled and all the sub-activities asso-
ciated with that activity. Finally, recall that conflicts among normative positions
could be avoided through the sequential use of criteria (chronological, salience,
speciality) that order normative positions. Once these conflicts are resolved, we
obtain the set of normative positions that will be applied and propagated to the
sub-activities.
All these elements are part of the following definition:
In the previous example, per(bidag1 , 0, 0) and prh(bidag1 , 2, 1) are in conflict
by the first condition of definition 2.
We take care of the other two parameters of normative positions with the
following definitions.
Definition 3. A normative position np = δ(e, s, t) is a chronological successor
of np′ = δ′(e′, s′, t′), written as np ≻T np′, iff t > t′.
Definition 4. A normative position np = δ(e, s, t) is more salient than np′ =
δ′(e′, s′, t′), written as np ≻P np′, iff s > s′.
In our example, prh(bidag1 , 2, 1) is more salient and a chronological successor
of per(bidag1 , 0, 0).
3 REGULATED COMPOUND ACTIVITIES
In this paper we have in mind that a performance of a set of actions —subject
to some regulation—constitute an activity and that an activity may be com-
posed of several sub-activities which in turn may also be decomposed into other
sub-activities. Take the example of a clearinghouse involving different activities
outlined in Figure 1. The main activity, trading, involves subactivities —like
auctioning, one-to-many negotiation or direct purchasing— that serve the pur-
pose of fixing the conditions for purchasing goods and other activities required
for payment and delivery of goods.
Several models and methodologies for MAS (e.g., [1,2,3]) have looked into
the notion of compound activity using different names such as performative
structure, missions or simply interaction. For our purposes we only need to look
into those aspects that relate to the evolution of normative positions within an
activity and how these are propagated in the hierarchy.
Each activity behaves like a transition system: it has a state, represented by
a set of grounded terms, that changes with the performance of the actions of
the agents in the activity. This transition function is partial since not all the
actions may occur in all the states of an activity. Norms establish what actions
are permitted, forbidden or obligatory (and their effects) in a given state of the
activity, defining the transition function of the activity. Normative positions are
part of the state of an activity and they also change by the performance of ac-
tions and the application of the transition function. Note also that since different
activities may be connected —in the sense that what happens in one has effect
on the other— when those normative positions in the first change, the normative
positions in the other may also change. We will say that the scope of a normative
position is the activity where it becomes enabled and all the sub-activities asso-
ciated with that activity. Finally, recall that conflicts among normative positions
could be avoided through the sequential use of criteria (chronological, salience,
speciality) that order normative positions. Once these conflicts are resolved, we
obtain the set of normative positions that will be applied and propagated to the
sub-activities.
All these elements are part of the following definition:
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6 A. Garc´ıa-Camino et al.
Definition 5. An activity state is a tuple q = 〈Ag,Ac, I,N,N in, Nout, τ, O,Ω〉
where
– Ag is a finite, non-empty set of agent identifiers;
– Ac is a finite, non-empty set of action labels;
– I is a finite subset of grounded terms that describe the current value of the
parameters involved in the activity;
– N is the set of normative positions of an activity state q;
– N in is the set of normative positions propagated from a state of a super-
activity to activity state q;
– Nout is the set of applicable normative positions propagated by activity state
q to the sub-activities;
– τ : Q×2Ac → Q is a partial transition function from the set of activity states
and sets of actions to the set of activity states Q, which defines the state
τ(q, ac) that would result by the performance of actions ac = {ac1, . . . , acn}
from state q – note that, as this function is partial, not all the set of actions
are possible in all the states;
– O is a finite, non-empty set of partial order relations i in the set of nor-
mative positions; and
– Ω is a total order relation over O.
Henceforth, we will respectively denote with a q subscript the components of
activity state q.
N inq is the set of normative positions propagated to a activity state q. Algo-
rithm 1, presented in section 4, calculates N in of the super-activities of q prior
to use Algorithm 2 to calculate Noutq . Intuitively, the set of inherited normative
positions is the union of applicable normative positions of the super-states.
Noutq is the set of applicable normative positions in an activity state q that will
be propagated to the sub-activities. It is obtained by removing conflicting nor-
mative positions from the union of those that are inherited from super-activities
and those that arise from the transition that produces state q. For the removal of
conflicting normative positions we use the ordering criteria in O in the sequence
established by Ω. To calculate Noutq , we use Algorithm 2 presented in section
4 that applies the meta-ordering Ω of activity state q in Nq ∪ N inq in order to
remove the less priority, conflicting normative positions.
Figure 2 shows an example of state of an auctioning activity with 3 agents:
an auctioneer, and two buyer agents. Auctioneer made an offer and the buyer
can bid for that offer. Buyers have a credit that is decreased when they win an
auction. If an agent performs an unsupported bid a sanction of 10 is applied.
The set of inherited normative positions (N in) is empty since we assume that
auctioning is not part of other activity. The set of applicable normative positions
is equal to the set of associated normative positions since there is no conflict.
Partial function τ is defined using ∪C and \C operators that respectively adds
and removes formulae from a set C of the tuple defining an activity state. For
instance, q∪N {obl(payag1 , 0, t)} intuitively means that the obligation is added to
the set of normative positions N of activity state q. Notice that τ checks the set
Definition 5. An activity state is a tuple q = 〈Ag,Ac, I,N,N in, Nout, τ, O,Ω〉
where
– Ag is a finite, non-empty set of agent identifiers;
– Ac is a finite, non-empty set of action labels;
– I is a finite subset of grounded terms that describe the current value of the
parameters involved in the activity;
– N is the set of normative positions of an activity state q;
– N in is the set of normative positions propagated from a state of a super-
activity to activity state q;
– Nout is the set of applicable normative positions propagated by activity state
q to the sub-activities;
– τ : Q×2Ac → Q is a partial transition function from the set of activity states
and sets of actions to the set of activity states Q, which defines the state
τ(q, ac) that would result by the performance of actions ac = {ac1, . . . , acn}
from state q – note that, as this function is partial, not all the set of actions
are possible in all the states;
– O is a finite, non-empty set of partial order relations i in the set of nor-
mative positions; and
– Ω is a total order relation over O.
Henceforth, we will respectively denote with a q subscript the components of
activity state q.
N inq is the set of normative positions propagated to a activity state q. Algo-
rithm 1, presented in section 4, calculates N in of the super-activities of q prior
to use Algorithm 2 to calculate Noutq . Intuitively, the set of inherited normative
positions is the union of applicable normative positions of the super-states.
Noutq is the set of applicable normative positions in an activity state q that will
be propagated to the sub-activities. It is obtained by removing conflicting nor-
mative positions from the union of those that are inherited from super-activities
and those that arise from the transition that produces state q. For the removal of
conflicting normative positions we use the ordering criteria in O in the sequence
established by Ω. To calculate Noutq , we use Algorithm 2 presented in section
4 that applies the meta-ordering Ω of activity state q in Nq ∪ N inq in order to
remove the less priority, conflicting normative positions.
Figure 2 shows an example of state of an auctioning activity with 3 agents:
an auctioneer, and two buyer agents. Auctioneer made an offer and the buyer
can bid for that offer. Buyers have a credit that is decreased when they win an
auction. If an agent performs an unsupported bid a sanction of 10 is applied.
The set of inherited normative positions (N in) is empty since we assume that
auctioning is not part of other activity. The set of applicable normative positions
is equal to the set of associated normative positions since there is no conflict.
Partial function τ is defined using ∪C and \C operators that respectively adds
and removes formulae from a set C of the tuple defining an activity state. For
instance, q∪N {obl(payag1 , 0, t)} intuitively means that the obligation is added to
the set of normative positions N of activity state q. Notice that τ checks the set
Page 7
An Algorithm for Conflict Resolution in Regulated Compound Activities 7
q = 〈Ag,Ac, I,N,N in, Nout, τ, O, Ω〉 where
– Ag = {auct, ag1, ag2};
– Ac = {offerauct, bidag1 , bidag2 , payag1 , payag2};
– I =
credit(ag1, 100), credit(ag2, 50), item(it1), price(it1, 100),
decrement(it1, 10), reserveprice(it1,30)
ff
;
– N = {per(bidag1 , 0, 0), per(bidag2 , 0, 0)};
– N in = ∅;
– Nout = {per(bidag1 , 0, 0), per(bidag2 , 0, 0)};
– τ (q, ac)
8
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q ∪N {obl(payag1 , 0, t)}
if ac = {bidag1} and
price(i, p), credit(ag1, x) ∈ Iq and
x ≥ p and time(t)
...
(q \I {credit(ag1, x)})∪I
{credit(ag1, x− 10)}
if ac = {bidag1} and
price(i, p), credit(ag1, x) ∈ Iq and
x < p and time(t)
...
((q \I {credit(ag1, x)})\N
{obl(payag1 , s, t)})∪I
{credit(ag1, x− p)}
if ac = {payag1} and
price(i, p), credit(ag1, x) ∈ Iq and
x ≥ p and obl(ac, s, t) ∈ Noutq
...
q ∪I {collision} if ac = {bidag1 , bidag2}
...
– O = {≻T ,≻P }; and
– Ω = {〈≻P ,≻T 〉}.
Fig. 2. Example of activity state.
of applicable normative positions, since Noutq is supposed to be conflict-free, but
changes the set of existing normative positions Nq. Furthermore, there are the
two order relations introduced in section 2, as mentioned above salience criterion
is preferred over the chronological one.
The scope of norms is established by the scope of the normative positions
that the norms enable (or disable). Their scope is the activity (and sub-activities)
where their normative positions are associated. When a compound activity has
a normative position associated, it is propagated to its sub-activities.
Definition 6. If an activity A is a sub-activity of activity B, denoted A ≪
B, then there exists at least one state q′ of activity B such that its applicable
normative positions are a subset of the normative positions propagated to each
state q of A. Formally, A ≪ B =⇒ ∀q ∈ A, ∃q′ ∈ B : Noutq′ ⊆ NP inq .
An activity structure defines which sub-activities compose it and which sub-
activities compose the former sub-activities by relating the states of activities.
q = 〈Ag,Ac, I,N,N in, Nout, τ, O, Ω〉 where
– Ag = {auct, ag1, ag2};
– Ac = {offerauct, bidag1 , bidag2 , payag1 , payag2};
– I =
credit(ag1, 100), credit(ag2, 50), item(it1), price(it1, 100),
decrement(it1, 10), reserveprice(it1,30)
ff
;
– N = {per(bidag1 , 0, 0), per(bidag2 , 0, 0)};
– N in = ∅;
– Nout = {per(bidag1 , 0, 0), per(bidag2 , 0, 0)};
– τ (q, ac)
8
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:
q ∪N {obl(payag1 , 0, t)}
if ac = {bidag1} and
price(i, p), credit(ag1, x) ∈ Iq and
x ≥ p and time(t)
...
(q \I {credit(ag1, x)})∪I
{credit(ag1, x− 10)}
if ac = {bidag1} and
price(i, p), credit(ag1, x) ∈ Iq and
x < p and time(t)
...
((q \I {credit(ag1, x)})\N
{obl(payag1 , s, t)})∪I
{credit(ag1, x− p)}
if ac = {payag1} and
price(i, p), credit(ag1, x) ∈ Iq and
x ≥ p and obl(ac, s, t) ∈ Noutq
...
q ∪I {collision} if ac = {bidag1 , bidag2}
...
– O = {≻T ,≻P }; and
– Ω = {〈≻P ,≻T 〉}.
Fig. 2. Example of activity state.
of applicable normative positions, since Noutq is supposed to be conflict-free, but
changes the set of existing normative positions Nq. Furthermore, there are the
two order relations introduced in section 2, as mentioned above salience criterion
is preferred over the chronological one.
The scope of norms is established by the scope of the normative positions
that the norms enable (or disable). Their scope is the activity (and sub-activities)
where their normative positions are associated. When a compound activity has
a normative position associated, it is propagated to its sub-activities.
Definition 6. If an activity A is a sub-activity of activity B, denoted A ≪
B, then there exists at least one state q′ of activity B such that its applicable
normative positions are a subset of the normative positions propagated to each
state q of A. Formally, A ≪ B =⇒ ∀q ∈ A, ∃q′ ∈ B : Noutq′ ⊆ NP inq .
An activity structure defines which sub-activities compose it and which sub-
activities compose the former sub-activities by relating the states of activities.
Page 8
8 A. Garc´ıa-Camino et al.
Definition 7. An activity structure is an acyclic directed graph H = 〈Q,E〉
where Q is the finite, non-empty set of activity states; and E is a finite, non-
empty set of edges 〈q, q′〉. If 〈q, q′〉 ∈ E we say that q is a sub-state of q′ and q′
is a super-state of q.
Henceforth, we will denote with a subscript H the components of activity
structure H .
Definition 8. Given two activities A and B, A is a sub-activity of B iff all the
states of A are a sub-state of, at least, one state of B. Formally, A ≪ B ⇐⇒
∀q ∈ A, ∃q′ ∈ B : 〈q, q′〉 ∈ E.
3.1 DEONTIC CONFLICTS IN COMPOUND ACTIVITIES
Deontic conflicts can appear either between the set N of normative positions
generated in an activity state by the transition function or the set N in of nor-
mative positions inherited from other activity states. As expressed in definition
2, two normative positions of the same activity state are in conflict if one is a
permission or obligation and the other is a prohibition over the same action than
the former. Two normative positions from different activity states are in conflict
if one is a permission or obligation and the other is a prohibition over the same
action than the former and one of them is associated to a sub-state of the other.
Definition 9. Given two normative positions np and np′, respectively pertaining
to activity states q and q′, such that np = δ(a, s, t), np′ = δ′(a′, s′, t′) and q, q′ ∈
QH ; np, np′ are in conflict in an activity structure H, denoted np
H≫≪np′, iff
np≫≪np′ and q = q′; or np≫≪np′ and exists a path between q and q′ in E.
By relating activity states in an activity structure, we can adapt the speciality
ordering criterion introduced in section 2 to our definition of activity state:
Definition 10. A normative position np is more specific than np′ in activity
state q, written as np ≻S np′, if np ∈ Nq and np′ ∈ N inq .
Given the example of a trading activity composed of two auctioning sub-
activities and the activity structure introduced above, we have:
– N intrading = ∅ since trading has no super-state.
– Ntrading = {prh(bidag1 , 1, 1)} if agent ag1 made an unsupported bid.
– Nouttrading = {prh(bidag1 , 1, 1)} since there is no conflict in Ntrading∪N intrading.
– N inauction1 = {prh(bidag1 , 1, 1)} since auction1 activity state has only trading
as super-state and Nouttrading = {prh(bidag1 , 1, 1)}.
– Nauction1 = {per(bidag1 , 0, 0)}, for example, as agents are permitted to bid
in auction houses.
Thus, there is a conflict between Nauction1 and N inauction1. Normative position
per(bidag1 , 0, 0) is more specific than prh(bidag1 , 1, 1) because the former belongs
to Nauction1 and the latter to N inauction1. In order to calculate the set of normative
Definition 7. An activity structure is an acyclic directed graph H = 〈Q,E〉
where Q is the finite, non-empty set of activity states; and E is a finite, non-
empty set of edges 〈q, q′〉. If 〈q, q′〉 ∈ E we say that q is a sub-state of q′ and q′
is a super-state of q.
Henceforth, we will denote with a subscript H the components of activity
structure H .
Definition 8. Given two activities A and B, A is a sub-activity of B iff all the
states of A are a sub-state of, at least, one state of B. Formally, A ≪ B ⇐⇒
∀q ∈ A, ∃q′ ∈ B : 〈q, q′〉 ∈ E.
3.1 DEONTIC CONFLICTS IN COMPOUND ACTIVITIES
Deontic conflicts can appear either between the set N of normative positions
generated in an activity state by the transition function or the set N in of nor-
mative positions inherited from other activity states. As expressed in definition
2, two normative positions of the same activity state are in conflict if one is a
permission or obligation and the other is a prohibition over the same action than
the former. Two normative positions from different activity states are in conflict
if one is a permission or obligation and the other is a prohibition over the same
action than the former and one of them is associated to a sub-state of the other.
Definition 9. Given two normative positions np and np′, respectively pertaining
to activity states q and q′, such that np = δ(a, s, t), np′ = δ′(a′, s′, t′) and q, q′ ∈
QH ; np, np′ are in conflict in an activity structure H, denoted np
H≫≪np′, iff
np≫≪np′ and q = q′; or np≫≪np′ and exists a path between q and q′ in E.
By relating activity states in an activity structure, we can adapt the speciality
ordering criterion introduced in section 2 to our definition of activity state:
Definition 10. A normative position np is more specific than np′ in activity
state q, written as np ≻S np′, if np ∈ Nq and np′ ∈ N inq .
Given the example of a trading activity composed of two auctioning sub-
activities and the activity structure introduced above, we have:
– N intrading = ∅ since trading has no super-state.
– Ntrading = {prh(bidag1 , 1, 1)} if agent ag1 made an unsupported bid.
– Nouttrading = {prh(bidag1 , 1, 1)} since there is no conflict in Ntrading∪N intrading.
– N inauction1 = {prh(bidag1 , 1, 1)} since auction1 activity state has only trading
as super-state and Nouttrading = {prh(bidag1 , 1, 1)}.
– Nauction1 = {per(bidag1 , 0, 0)}, for example, as agents are permitted to bid
in auction houses.
Thus, there is a conflict between Nauction1 and N inauction1. Normative position
per(bidag1 , 0, 0) is more specific than prh(bidag1 , 1, 1) because the former belongs
to Nauction1 and the latter to N inauction1. In order to calculate the set of normative
Page 9
An Algorithm for Conflict Resolution in Regulated Compound Activities 9
positions without conflict, we may use the speciality criterion to remove less
priority, conflicting normative positions resulting Noutauction1 = {per(bida, 0, 0)}.
When the normative positions in an activity state are not conflicting, we will
say that this activity state is conflict-free:
Definition 11. An activity state q is conflict-free if there is no conflict among
its normative positions (from N inq ∪Nq).
In the example above, the trading activity state is conflict-free sinceN intrading∪
Ntrading has no deontic conflict.
When the applicable normative positions in an activity state q (Noutq ) are
not conflicting, we will say that activity state q is Ω-conflict-free. Ω is the meta-
ordering of activity state q used to resolve any deontic conflict.
Definition 12. An activity state q is Ω-conflict-free if the set of applicable nor-
mative positions in the activity state (Noutq ) is the largest set of normative po-
sitions Noutq ⊆ N inq ∪Nq that is conflict-free after applying meta-ordering Ω of
activity state q to resolve deontic conflicts.
In the example above, auction1 activity state is Ω-conflict-free.
On the one hand, there are activity structures without conflicts before ap-
plying any method of conflict resolution, we call them strongly conflict-free. An
activity structure H is strongly conflict-free if there is no conflict in the norma-
tive positions of any activity state.
Definition 13. An activity structure H is strongly conflict-free if ∀q ∈ QH ,
∀np, np′ ∈ Nq ∪N inq : ¬(np
H≫≪np′).
On the other hand, there are activity structures without conflicts after ap-
plying a method of conflict resolution, we call them weakly conflict-free. This
property holds when the method of conflict resolution is effective. An activity
structure is weakly conflict-free if there is no conflict in the set of applicable
normative positions (Nout) of any activity state.
Definition 14. An activity structure H is weakly conflict-free if ∀q ∈ QH ,
∀np, np′ ∈ Noutq : ¬(np
H≫≪np′).
In the example above, the activity structure that constitutes the trading ac-
tivity composed of two auctioning activities is not strongly conflict-free because
there is a conflict between two normative positions in auction1 activity state (in
Nauction1 ∪N inauction1). However, it is weakly conflict-free because after applying
the Ω meta-ordering, the conflict is resolved and Noutauction1 includes no conflicting
normative positions.
positions without conflict, we may use the speciality criterion to remove less
priority, conflicting normative positions resulting Noutauction1 = {per(bida, 0, 0)}.
When the normative positions in an activity state are not conflicting, we will
say that this activity state is conflict-free:
Definition 11. An activity state q is conflict-free if there is no conflict among
its normative positions (from N inq ∪Nq).
In the example above, the trading activity state is conflict-free sinceN intrading∪
Ntrading has no deontic conflict.
When the applicable normative positions in an activity state q (Noutq ) are
not conflicting, we will say that activity state q is Ω-conflict-free. Ω is the meta-
ordering of activity state q used to resolve any deontic conflict.
Definition 12. An activity state q is Ω-conflict-free if the set of applicable nor-
mative positions in the activity state (Noutq ) is the largest set of normative po-
sitions Noutq ⊆ N inq ∪Nq that is conflict-free after applying meta-ordering Ω of
activity state q to resolve deontic conflicts.
In the example above, auction1 activity state is Ω-conflict-free.
On the one hand, there are activity structures without conflicts before ap-
plying any method of conflict resolution, we call them strongly conflict-free. An
activity structure H is strongly conflict-free if there is no conflict in the norma-
tive positions of any activity state.
Definition 13. An activity structure H is strongly conflict-free if ∀q ∈ QH ,
∀np, np′ ∈ Nq ∪N inq : ¬(np
H≫≪np′).
On the other hand, there are activity structures without conflicts after ap-
plying a method of conflict resolution, we call them weakly conflict-free. This
property holds when the method of conflict resolution is effective. An activity
structure is weakly conflict-free if there is no conflict in the set of applicable
normative positions (Nout) of any activity state.
Definition 14. An activity structure H is weakly conflict-free if ∀q ∈ QH ,
∀np, np′ ∈ Noutq : ¬(np
H≫≪np′).
In the example above, the activity structure that constitutes the trading ac-
tivity composed of two auctioning activities is not strongly conflict-free because
there is a conflict between two normative positions in auction1 activity state (in
Nauction1 ∪N inauction1). However, it is weakly conflict-free because after applying
the Ω meta-ordering, the conflict is resolved and Noutauction1 includes no conflicting
normative positions.
Page 10
10 A. Garc´ıa-Camino et al.
4 MAINTENANCE OF Ω-CONFLICT-FREEDOM
After the norms are applied in each activity state using τ , the set of norma-
tive positions associated in each activity state (N) changes. Since the scope of
normative positions also include the sub-states of the activity state where the
normative position is associated, the set of applicable normative positions should
be calculated and propagated to the sub-states.
For that purpose, we introduce in this section Propagate-NPs algorithm
that takes as input a list of the leaves of the trees defined by the activity structure
and ensures that each activity state in the activity structure is Ω-conflict-free.
Algorithm 1 Propagate-NPs(leaves, h)
Require: leaves is a list of the leaves of each tree of the activity structure h = 〈Q,E〉
Ensure: Every Nout is conflict-free
1: for all leaf ∈ leaves do
2: if Noutleaf = null then {First execution for activity state leaf}
3: parents← {q′ | 〈leaf, q′〉 ∈ E}
4: l← ∅
5: if parents 6= ∅ then
6: Propagate-NPs(parents, h)
7: for all parent ∈ parents do {Append Nout of parents}
8: l← l ∪Noutparent
9: end for
10: end if
11: N inleaf ← l
12: Noutleaf ← Get-ConflictFreeNPs(leaf)
13: end if
14: end for
15: return leaves
In algorithm 1, for each leaf of the activity structure, if Nout has not been
calculated yet (line 2), we apply recursively Propagate-NPs to the parents (if
they exist) (line 6) and we gather the list of all the normative positions inherited
by the current activity state and update N in (line 12). We set to Nout, the result
of the algorithm Get-ConflictFreeNPs applied to the updated activity state
(line 13).
When normative positions are propagated, the set of applicable normative
positions of an activity state should be calculated. For that purpose, Algorithm 2
returns this set ensuring that it is conflict-free. In algorithm 2, for each normative
position np, we gather in s, by calling Get-SetInConflict, a list of normative
positions including np and the ones in conflict with np (line 4). If there is at least
one normative position in conflict, then we call Get-PriorityNP to resolve the
conflict and get the highest priority normative position (line 6). This normative
position is added to the result list anp (line 8). Otherwise, np is added to the
result list in anp (line 11).
4 MAINTENANCE OF Ω-CONFLICT-FREEDOM
After the norms are applied in each activity state using τ , the set of norma-
tive positions associated in each activity state (N) changes. Since the scope of
normative positions also include the sub-states of the activity state where the
normative position is associated, the set of applicable normative positions should
be calculated and propagated to the sub-states.
For that purpose, we introduce in this section Propagate-NPs algorithm
that takes as input a list of the leaves of the trees defined by the activity structure
and ensures that each activity state in the activity structure is Ω-conflict-free.
Algorithm 1 Propagate-NPs(leaves, h)
Require: leaves is a list of the leaves of each tree of the activity structure h = 〈Q,E〉
Ensure: Every Nout is conflict-free
1: for all leaf ∈ leaves do
2: if Noutleaf = null then {First execution for activity state leaf}
3: parents← {q′ | 〈leaf, q′〉 ∈ E}
4: l← ∅
5: if parents 6= ∅ then
6: Propagate-NPs(parents, h)
7: for all parent ∈ parents do {Append Nout of parents}
8: l← l ∪Noutparent
9: end for
10: end if
11: N inleaf ← l
12: Noutleaf ← Get-ConflictFreeNPs(leaf)
13: end if
14: end for
15: return leaves
In algorithm 1, for each leaf of the activity structure, if Nout has not been
calculated yet (line 2), we apply recursively Propagate-NPs to the parents (if
they exist) (line 6) and we gather the list of all the normative positions inherited
by the current activity state and update N in (line 12). We set to Nout, the result
of the algorithm Get-ConflictFreeNPs applied to the updated activity state
(line 13).
When normative positions are propagated, the set of applicable normative
positions of an activity state should be calculated. For that purpose, Algorithm 2
returns this set ensuring that it is conflict-free. In algorithm 2, for each normative
position np, we gather in s, by calling Get-SetInConflict, a list of normative
positions including np and the ones in conflict with np (line 4). If there is at least
one normative position in conflict, then we call Get-PriorityNP to resolve the
conflict and get the highest priority normative position (line 6). This normative
position is added to the result list anp (line 8). Otherwise, np is added to the
result list in anp (line 11).
Page 11
An Algorithm for Conflict Resolution in Regulated Compound Activities 11
Algorithm 2 Get-ConflictFreeNPs(q)
Require: q = 〈Agq, Acq, Iq, Nq, N inq , Noutq , τq , Oq , Ωq〉
Ensure: anp is the list of applicable normative positions
1: anp← ∅
2: nps← Nq ∪N inq
3: for all np ∈ nps do
4: s← Get-SetInConflict(np,nps)
5: if Length(s) > 1 then
6: pnp← Get-PriorityNP(Ωq , s)
7: if pnp 6∈ anp then
8: anp← anp ∪ pnp
9: end if
10: else if Length(s) = 1 then
11: anp← anp ∪ np
12: end if
13: end for
14: return anp
Although different activity states can share super-states, Algorithm 1 calcu-
lates Nout of each activity state only once. Addition and removal of normative
positions from a activity state require that Nout for that activity state and its
sub-states are recursively set to null using Algorithm 3.
Algorithm 3 Clear-ANP(q, h)
Require: q = 〈Agq, Acq, Iq, Nq, N inq , Noutq , τq , Oq , Ωq〉 and h = 〈Q,E〉
Ensure: For q and its sub-states, Nout = null
1: Noutq ← null
2: children← {q′ | 〈q′, q〉 ∈ E}
3: for all child ∈ children do
4: Clear-ANP(child)
5: end for
5 EXAMPLE
In this section, we introduce an example of a regulated compound activity. Pic-
ture a set of auctioning activities, regulated by their own norms, that constitute
a trading activity. At the trading activity level there is a norm stating that a
buyer that makes an unsupported bid in a auctioning activity will be banned to
bid in any of the auctioning activities except in the auctioning activity called
auction2. The meta-ordering to be applied will be (≻P ) ≺ (≻S) ≺ (≻T ): the
salience criterion prevails over the speciality and the chronological ones, while
the speciality criterion prevails over the chronological one.
Algorithm 2 Get-ConflictFreeNPs(q)
Require: q = 〈Agq, Acq, Iq, Nq, N inq , Noutq , τq , Oq , Ωq〉
Ensure: anp is the list of applicable normative positions
1: anp← ∅
2: nps← Nq ∪N inq
3: for all np ∈ nps do
4: s← Get-SetInConflict(np,nps)
5: if Length(s) > 1 then
6: pnp← Get-PriorityNP(Ωq , s)
7: if pnp 6∈ anp then
8: anp← anp ∪ pnp
9: end if
10: else if Length(s) = 1 then
11: anp← anp ∪ np
12: end if
13: end for
14: return anp
Although different activity states can share super-states, Algorithm 1 calcu-
lates Nout of each activity state only once. Addition and removal of normative
positions from a activity state require that Nout for that activity state and its
sub-states are recursively set to null using Algorithm 3.
Algorithm 3 Clear-ANP(q, h)
Require: q = 〈Agq, Acq, Iq, Nq, N inq , Noutq , τq , Oq , Ωq〉 and h = 〈Q,E〉
Ensure: For q and its sub-states, Nout = null
1: Noutq ← null
2: children← {q′ | 〈q′, q〉 ∈ E}
3: for all child ∈ children do
4: Clear-ANP(child)
5: end for
5 EXAMPLE
In this section, we introduce an example of a regulated compound activity. Pic-
ture a set of auctioning activities, regulated by their own norms, that constitute
a trading activity. At the trading activity level there is a norm stating that a
buyer that makes an unsupported bid in a auctioning activity will be banned to
bid in any of the auctioning activities except in the auctioning activity called
auction2. The meta-ordering to be applied will be (≻P ) ≺ (≻S) ≺ (≻T ): the
salience criterion prevails over the speciality and the chronological ones, while
the speciality criterion prevails over the chronological one.
Page 12
12 A. Garc´ıa-Camino et al.
trading
N
Nout
N in = ∅ N in = ∅
auction1
N
Nout
per(bidag1 , 0, 0)
per(bidag1 , 0, 0)
auction2
N
Nout
per(bidag1 , 1, 0)
per(bidag1 , 1, 0)
(a) activity states before an unsupported
bid
trading
N
Nout
N in = {prh(bidag1 ,1, 1)} N in = {prh(bidag1 , 1, 1)}
prh(bidag1 , 1, 1)
prh(bidag1 , 1, 1)
auction1
N
Nout
per(bidag1 ,0, 0)
prh(bidag1 ,1, 1)
auction2
N
Nout
per(bidag1 , 1, 0)
per(bidag1 , 1, 0)
(b) activity states after an unsupported bid
Fig. 3. Example of the normative state of the activity structure
Figure 3 shows an example of execution for a trading activity compound of
two auctioning activities and a buyer agent. Figure 3(a) illustrates the state of the
activities prior to any unsupported bid. Activity state trading has no normative
position associated. Thus, its set of applicable normative positions is empty.
Activity state auction1 only has associated a permission with normal priority
(salience 0). Since Nout of the super-state is empty, its Nout only contains the
associated permission. Activity state auction2 only has associated a permission
with higher priority (salience 1). Since the Nout of the super-state is empty, its
Nout only contains the associated permission.
Figure 3(b) shows the state of the activities after an unsupported bid per-
formed by agent ag1. Activity state trading has associated the prohibition (with
salience 1) for ag1 to bid. Since the trading state has no super-states, its Nout
is equal to its associated normative positions, i.e., the prohibition. Recall that
activity state auction1 only has associated a permission with normal priority
(salience 0). Since the prohibition in N in (inherited from trading activity state)
has higher salience, it will belong to the Nout of auction1 state. Recall that
trading
N
Nout
N in = ∅ N in = ∅
auction1
N
Nout
per(bidag1 , 0, 0)
per(bidag1 , 0, 0)
auction2
N
Nout
per(bidag1 , 1, 0)
per(bidag1 , 1, 0)
(a) activity states before an unsupported
bid
trading
N
Nout
N in = {prh(bidag1 ,1, 1)} N in = {prh(bidag1 , 1, 1)}
prh(bidag1 , 1, 1)
prh(bidag1 , 1, 1)
auction1
N
Nout
per(bidag1 ,0, 0)
prh(bidag1 ,1, 1)
auction2
N
Nout
per(bidag1 , 1, 0)
per(bidag1 , 1, 0)
(b) activity states after an unsupported bid
Fig. 3. Example of the normative state of the activity structure
Figure 3 shows an example of execution for a trading activity compound of
two auctioning activities and a buyer agent. Figure 3(a) illustrates the state of the
activities prior to any unsupported bid. Activity state trading has no normative
position associated. Thus, its set of applicable normative positions is empty.
Activity state auction1 only has associated a permission with normal priority
(salience 0). Since Nout of the super-state is empty, its Nout only contains the
associated permission. Activity state auction2 only has associated a permission
with higher priority (salience 1). Since the Nout of the super-state is empty, its
Nout only contains the associated permission.
Figure 3(b) shows the state of the activities after an unsupported bid per-
formed by agent ag1. Activity state trading has associated the prohibition (with
salience 1) for ag1 to bid. Since the trading state has no super-states, its Nout
is equal to its associated normative positions, i.e., the prohibition. Recall that
activity state auction1 only has associated a permission with normal priority
(salience 0). Since the prohibition in N in (inherited from trading activity state)
has higher salience, it will belong to the Nout of auction1 state. Recall that
Page 13
An Algorithm for Conflict Resolution in Regulated Compound Activities 13
auction2 state only has associated a permission with salience 1. Since the prohi-
bition in N in (inherited from trading state) has the same salience, the speciality
criterion is applied. The permission will belong to the Nout of auction2 state
because it belongs to N , i.e., it is associated to the sub-state.
6 RELATED WORK
There are many works in deontic conflicts (e.g., [8,9,10,11,12] ) from a logical
point of view but there are few works that implement computational strategies
to solve deontic conflicts in the area of multi-agent systems. Two developments
are related quite directly with the problems we face in our proposal [13,14].
In [13], the authors present an agent architecture where obligations, permis-
sions and prohibitions can be added to the agents’ plans. Contrary to our work,
in which deontic conflicts appear when defining sub-activities, deontic conflicts
appear in this work when the agent has to adopt non-hierarchical norms. They
(explicitly or implicitly) associate norms to Instantiation Graphs which represent
an action or state declaration as a hierarchy of all its possible forms of partial
instantiation of variables. Thus, norms are also ordered: explicit norms over-
ride implicit norms; and new norms override old norms. Although they consider
deontic conflicts, they only adopt an agent-centred stance.
In [14], the author proposes the use of RuleML for representing business
contracts. The underpinning of the proposal is the use of Defeasible Logic (DL) as
the inferential mechanism for RuleML. The primary use of DL in that work is the
resolution of conflicts that might arise from clauses of a contract. DL analyses the
conditions laid down by each rule in the contract, identifies the possible conflicts
that may be triggered and uses the priorities defined over the rules to eventually
resolve a conflict. By using DL, a normative position receive different priority
depending on the antecedents of the rule and not on the normative position by
itself. In contrast, our priorities are defined at the normative position level, i.e.,
we assign a priority to each normative position.
7 FINAL REMARKS
We took an unconventional approach to a complex problem and in this paper we
made many simplifying assumptions that we intend to relax in future work. For
the moment we wanted to keep our framework simple so that we could explore the
main components of the problem. We also wanted to keep it concrete enough
so that it could be applied to real organisations and because of that aim we
wanted to profit from implemented systems that are already available to deal
with regulated simple activities.
In spite of the austerity of this proposal, it is evident that most intuitions we
have explored here are prone to a serious logical treatment. Conflict resolution in
this paper has been limited to a total ordering of normative positions. It is true
that this type of resolution may be adequate in some conflicts and some activi-
ties. However, we realise that this issue may be treated in other interesting ways
auction2 state only has associated a permission with salience 1. Since the prohi-
bition in N in (inherited from trading state) has the same salience, the speciality
criterion is applied. The permission will belong to the Nout of auction2 state
because it belongs to N , i.e., it is associated to the sub-state.
6 RELATED WORK
There are many works in deontic conflicts (e.g., [8,9,10,11,12] ) from a logical
point of view but there are few works that implement computational strategies
to solve deontic conflicts in the area of multi-agent systems. Two developments
are related quite directly with the problems we face in our proposal [13,14].
In [13], the authors present an agent architecture where obligations, permis-
sions and prohibitions can be added to the agents’ plans. Contrary to our work,
in which deontic conflicts appear when defining sub-activities, deontic conflicts
appear in this work when the agent has to adopt non-hierarchical norms. They
(explicitly or implicitly) associate norms to Instantiation Graphs which represent
an action or state declaration as a hierarchy of all its possible forms of partial
instantiation of variables. Thus, norms are also ordered: explicit norms over-
ride implicit norms; and new norms override old norms. Although they consider
deontic conflicts, they only adopt an agent-centred stance.
In [14], the author proposes the use of RuleML for representing business
contracts. The underpinning of the proposal is the use of Defeasible Logic (DL) as
the inferential mechanism for RuleML. The primary use of DL in that work is the
resolution of conflicts that might arise from clauses of a contract. DL analyses the
conditions laid down by each rule in the contract, identifies the possible conflicts
that may be triggered and uses the priorities defined over the rules to eventually
resolve a conflict. By using DL, a normative position receive different priority
depending on the antecedents of the rule and not on the normative position by
itself. In contrast, our priorities are defined at the normative position level, i.e.,
we assign a priority to each normative position.
7 FINAL REMARKS
We took an unconventional approach to a complex problem and in this paper we
made many simplifying assumptions that we intend to relax in future work. For
the moment we wanted to keep our framework simple so that we could explore the
main components of the problem. We also wanted to keep it concrete enough
so that it could be applied to real organisations and because of that aim we
wanted to profit from implemented systems that are already available to deal
with regulated simple activities.
In spite of the austerity of this proposal, it is evident that most intuitions we
have explored here are prone to a serious logical treatment. Conflict resolution in
this paper has been limited to a total ordering of normative positions. It is true
that this type of resolution may be adequate in some conflicts and some activi-
ties. However, we realise that this issue may be treated in other interesting ways
Page 14
14 A. Garc´ıa-Camino et al.
accommodating other culturally accepted conflict resolution mechanisms like ne-
gotiation, arbitration or argumentation. Likewise, the current conflict resolution
components of the framework could be revisited to incorporate other pertinent
normative aspects like peer to peer conflict settlements, contract breaches and
blame assignment, enforcement policies, etc.
To define normative positions, in this paper we use an action identifier a that
hides too much information. Here we only wanted to be able to decide whether
two actions are the same or not. However, that makes the crude handling of
normative positions to be simplistic stand-in for commitments. In a system that
does serious commitment management, action identifiers will very likely be terms
that adequately reflect the state the activity and the organisation at the time of
establishing the commitment: in particular, who are the agents involved in the
commitment and what are the specific current values of the parameters involved
in the definition of the commitment and its fulfilment or up-keeping.
In a similar vein, we have assumed a somewhat obscure notion of activity
state because we have hidden many significant elements inside the “transition
function”. One option we have at hand to make our notion of transition functions
clear is to use the notion of performative structures [1]. In that light, the transi-
tion function correspond to their speech-acts labelled finite-states machines of a
scene together with the scene transitions. Another option is to think of activities
as logical theories with a deduction mechanism. In that case, transitions occur
when a new action (or possibly concurrent actions) is added to the theory and
its consequences deducted. In both cases, performative structures and logical
theories, for each transition we still need to keep track of the starting and termi-
nating states of the activity. For that purpose, we may take from [1] the notion
of scene state and institutional state and extend them by including the state of
the normative positions in the activity and in the compound activities. As part
of the state of an activity we need to take into account those commitments that
are active, but also their relevance to the actions that take place so that their
propagation is correct (sound and complete).
The propagation of normative positions that we discuss in this paper is hand-
wired and fix on top of the activities hierarchy. The paths of commitment prop-
agation should be an inherent outcome of the way activities are regulated and
combined to constitute the regulated environment. Furthermore, although it may
be rather natural to assume nested hierarchies of activities, the express assump-
tion of acyclicity is questionable from an applications point of view, no matter
how convenient it may be for formal and algorithmic reasons. In this respect, it
looks attractive to distinguish between propagation links among activities that
are established through the flow transitions designed into the compound activi-
ties on one hand and propagation between states whenever an action takes place
anywhere in the organisation and for that purpose a notion of pertinence would
be welcome.
We have taken care to make our proposal compatible with the model from
[1] and as such it constitutes an extension of that model. In that language we
can say that our activities correspond to scenes, performative structures, and
accommodating other culturally accepted conflict resolution mechanisms like ne-
gotiation, arbitration or argumentation. Likewise, the current conflict resolution
components of the framework could be revisited to incorporate other pertinent
normative aspects like peer to peer conflict settlements, contract breaches and
blame assignment, enforcement policies, etc.
To define normative positions, in this paper we use an action identifier a that
hides too much information. Here we only wanted to be able to decide whether
two actions are the same or not. However, that makes the crude handling of
normative positions to be simplistic stand-in for commitments. In a system that
does serious commitment management, action identifiers will very likely be terms
that adequately reflect the state the activity and the organisation at the time of
establishing the commitment: in particular, who are the agents involved in the
commitment and what are the specific current values of the parameters involved
in the definition of the commitment and its fulfilment or up-keeping.
In a similar vein, we have assumed a somewhat obscure notion of activity
state because we have hidden many significant elements inside the “transition
function”. One option we have at hand to make our notion of transition functions
clear is to use the notion of performative structures [1]. In that light, the transi-
tion function correspond to their speech-acts labelled finite-states machines of a
scene together with the scene transitions. Another option is to think of activities
as logical theories with a deduction mechanism. In that case, transitions occur
when a new action (or possibly concurrent actions) is added to the theory and
its consequences deducted. In both cases, performative structures and logical
theories, for each transition we still need to keep track of the starting and termi-
nating states of the activity. For that purpose, we may take from [1] the notion
of scene state and institutional state and extend them by including the state of
the normative positions in the activity and in the compound activities. As part
of the state of an activity we need to take into account those commitments that
are active, but also their relevance to the actions that take place so that their
propagation is correct (sound and complete).
The propagation of normative positions that we discuss in this paper is hand-
wired and fix on top of the activities hierarchy. The paths of commitment prop-
agation should be an inherent outcome of the way activities are regulated and
combined to constitute the regulated environment. Furthermore, although it may
be rather natural to assume nested hierarchies of activities, the express assump-
tion of acyclicity is questionable from an applications point of view, no matter
how convenient it may be for formal and algorithmic reasons. In this respect, it
looks attractive to distinguish between propagation links among activities that
are established through the flow transitions designed into the compound activi-
ties on one hand and propagation between states whenever an action takes place
anywhere in the organisation and for that purpose a notion of pertinence would
be welcome.
We have taken care to make our proposal compatible with the model from
[1] and as such it constitutes an extension of that model. In that language we
can say that our activities correspond to scenes, performative structures, and
Page 15
An Algorithm for Conflict Resolution in Regulated Compound Activities 15
nested normative structures. Because of this last possibility, we need an extended
notion of transition to handle connections between all of these that produces non-
nested compound activities. In addition, this richer activity composition leads
us to consider an enriched notion of transition that deals in a smooth way with
commitment propagation. We are also interested in profiting from expressive
extensions to that model so that conventions may be stated not only as transition
graphs but as normative expressions of good expressive power endowed also with
a deduction mechanism. Our proposal, as it stands, should work properly with
our recent production rules extensions [15].
In this prospective paper, we have followed an unconventional approach to the
problem of managing dynamic commitment-making in regulated agent systems.
We think that the problem is a fundamental one for regulated environments
where the autonomy of participants is an essential ingredient. Although we are
aware that what we propose here is far from being a solution to that problem, we
acknowledge that the approach has brought to light many challenging questions
that we believe deserve further analysis.
Acknowledgements
This work was partially funded by the Spanish Science and Technology Ministry
as part of the Web-i-2 project (TIC-2003-08763-C02-00). Garc´ıa-Camino enjoys
an I3P grant from the Spanish Scientific Research Council (CSIC).
References
1. Arcos, J.L., Esteva, M., Noriega, P., Rodr´ıguez-Aguilar, J.A., Sierra, C.: Engineer-
ing open environments with electronic institutions. Engineering Applications of
Artificial Intelligence 18(2) (2005) 191–204
2. Hannoun, M., Boissier, O., Sichman, J.S., Sayettat, C.: MOISE: An organizational
model for multi-agent systems. In Monard, M.C., Sichman, J.S., eds.: Advances in
Artificial Intelligence. Volume 1952 of LNAI. Springer-Verlag (2000)
3. Dignum, V.: A model for organizational interaction: based on agents, founded in
logic. PhD thesis, Utrecht University (2003)
4. Yolum, P., Singh, M.: Flexible protocol specification and execution: Applying event
calculus planning using commitments. In: Proceedings of the First International
Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS’02).
(2002)
5. Sergot, M.: A Computational Theory of Normative Positions. ACM Trans. Com-
put. Logic 2(4) (2001) 581–622
6. Pacheco, O., Carmo, J.: A role based model for the normative specification of
organized collective agency and agents interaction. Autonomus Agents and Multi-
Agent Systems 6 (2003) 145–184
7. Garc´ıa-Camino, A., Rodr´ıguez-Aguilar, J.A., Sierra, C., Vasconcelos, W.: Norm-
Oriented Programming of Electronic Institutions: A Rule-based Approach. In:
Coordination, Organization, Institutions and Norms in agent systems (COIN’06)
in Fifth International Joint Conference on Autonomous Agents and Multiagent
Systems. (AAMAS’06). (2006)
nested normative structures. Because of this last possibility, we need an extended
notion of transition to handle connections between all of these that produces non-
nested compound activities. In addition, this richer activity composition leads
us to consider an enriched notion of transition that deals in a smooth way with
commitment propagation. We are also interested in profiting from expressive
extensions to that model so that conventions may be stated not only as transition
graphs but as normative expressions of good expressive power endowed also with
a deduction mechanism. Our proposal, as it stands, should work properly with
our recent production rules extensions [15].
In this prospective paper, we have followed an unconventional approach to the
problem of managing dynamic commitment-making in regulated agent systems.
We think that the problem is a fundamental one for regulated environments
where the autonomy of participants is an essential ingredient. Although we are
aware that what we propose here is far from being a solution to that problem, we
acknowledge that the approach has brought to light many challenging questions
that we believe deserve further analysis.
Acknowledgements
This work was partially funded by the Spanish Science and Technology Ministry
as part of the Web-i-2 project (TIC-2003-08763-C02-00). Garc´ıa-Camino enjoys
an I3P grant from the Spanish Scientific Research Council (CSIC).
References
1. Arcos, J.L., Esteva, M., Noriega, P., Rodr´ıguez-Aguilar, J.A., Sierra, C.: Engineer-
ing open environments with electronic institutions. Engineering Applications of
Artificial Intelligence 18(2) (2005) 191–204
2. Hannoun, M., Boissier, O., Sichman, J.S., Sayettat, C.: MOISE: An organizational
model for multi-agent systems. In Monard, M.C., Sichman, J.S., eds.: Advances in
Artificial Intelligence. Volume 1952 of LNAI. Springer-Verlag (2000)
3. Dignum, V.: A model for organizational interaction: based on agents, founded in
logic. PhD thesis, Utrecht University (2003)
4. Yolum, P., Singh, M.: Flexible protocol specification and execution: Applying event
calculus planning using commitments. In: Proceedings of the First International
Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS’02).
(2002)
5. Sergot, M.: A Computational Theory of Normative Positions. ACM Trans. Com-
put. Logic 2(4) (2001) 581–622
6. Pacheco, O., Carmo, J.: A role based model for the normative specification of
organized collective agency and agents interaction. Autonomus Agents and Multi-
Agent Systems 6 (2003) 145–184
7. Garc´ıa-Camino, A., Rodr´ıguez-Aguilar, J.A., Sierra, C., Vasconcelos, W.: Norm-
Oriented Programming of Electronic Institutions: A Rule-based Approach. In:
Coordination, Organization, Institutions and Norms in agent systems (COIN’06)
in Fifth International Joint Conference on Autonomous Agents and Multiagent
Systems. (AAMAS’06). (2006)
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8. Sartor, G.: Normative conflicts in legal reasoning. Artificial Intelligence and Law
1(2-3) (1992) 209–235
9. : International Workshop in Deontic Logic in Computer Science. DEON. (1991-
2006)
10. Cholvy, L., Cuppens, F.: Solving normative conflicts by merging roles. In: Fifth In-
ternational Conference on Artificial Intelligence and Law, Washington, USA (1995)
11. Cholvy, L., Cuppens, F.: Reasoning about norms provided by conflicting regula-
tions. In McNamara, P., Prakken, H., eds.: Norms, Logics and Information Sys-
tems. New Studies in Deontic Logic and Computer Science. Volume 49 of Frontiers
in Artificial Intelligence and Applications. IOS Press, Washington, USA (1999)
247–262
12. Boella, G., van der Torre, L.: Permission and Obligations in Hierarchical Normative
Systems. In: Procs. 8th Int’l Conf. in AI & Law (ICAIL’03), Edinburgh, ACM
(2003)
13. Kollingbaum, M., Norman, T.: Strategies for resolving norm conflict in practical
reasoning. In: ECAI Workshop Coordination in Emergent Agent Societies 2004.
(2004)
14. Governatori, G.: Representing business contracts in RuleML. International Jour-
nal of Cooperative Information Systems 14(2-3) (2005) 181–216
15. Garc´ıa-Camino, A., Noriega, P., Rodr´ıguez-Aguilar, J.A.: Implementing Norms in
Electronic Institutions. In: Fourth International Joint Conference on Autonomous
Agents and Multiagent Systems (AAMAS’05), Utrecht, The Nederlands (2005)
667–673
8. Sartor, G.: Normative conflicts in legal reasoning. Artificial Intelligence and Law
1(2-3) (1992) 209–235
9. : International Workshop in Deontic Logic in Computer Science. DEON. (1991-
2006)
10. Cholvy, L., Cuppens, F.: Solving normative conflicts by merging roles. In: Fifth In-
ternational Conference on Artificial Intelligence and Law, Washington, USA (1995)
11. Cholvy, L., Cuppens, F.: Reasoning about norms provided by conflicting regula-
tions. In McNamara, P., Prakken, H., eds.: Norms, Logics and Information Sys-
tems. New Studies in Deontic Logic and Computer Science. Volume 49 of Frontiers
in Artificial Intelligence and Applications. IOS Press, Washington, USA (1999)
247–262
12. Boella, G., van der Torre, L.: Permission and Obligations in Hierarchical Normative
Systems. In: Procs. 8th Int’l Conf. in AI & Law (ICAIL’03), Edinburgh, ACM
(2003)
13. Kollingbaum, M., Norman, T.: Strategies for resolving norm conflict in practical
reasoning. In: ECAI Workshop Coordination in Emergent Agent Societies 2004.
(2004)
14. Governatori, G.: Representing business contracts in RuleML. International Jour-
nal of Cooperative Information Systems 14(2-3) (2005) 181–216
15. Garc´ıa-Camino, A., Noriega, P., Rodr´ıguez-Aguilar, J.A.: Implementing Norms in
Electronic Institutions. In: Fourth International Joint Conference on Autonomous
Agents and Multiagent Systems (AAMAS’05), Utrecht, The Nederlands (2005)
667–673
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