Wietske Visser, Koen V. Hindriks and Catholijn M. Jonker
Man-Machine Interaction Group, Delft University of Technology, Delft, The Netherlands
Qualitative preferences, Underlying interests, Argumentation.
In the context of practical reasoning, such as decision making and negotiation, it is necessary to model pref-
erences over possible outcomes. Such preferences usually depend on multiple criteria. We argue that the
criteria by which outcomes are evaluated should be the satisfaction of a person’s underlying interests: the
more an outcome satisfies his interests, the more preferred it is. Underlying interests can explain and eliminate
conditional preferences. Also, modelling interests will create a better model of human preferences, and can
lead to better, more creative deals in negotiation. We present an argumentation framework for reasoning about
interest-based preferences. We take a qualitative approach and provide the means to derive both ceteris paribus
and lexicographic preferences.
We present an approach to qualitative, multi-criteria
preferences that takes underlying interests explicitly
into account. Reasoning about interest-based prefer-
ences is relevant in decision making, negotiation, and
other types of practical reasoning. Since our long-
term goal is the development of a negotiation support
system, the motivations and examples in this paper
are mainly taken from the context of negotiation, but
the main ideas apply equally well in other contexts.
The goal of a negotiation support system is to help
a human negotiator reach a better deal in negotiation.
The quality of a deal is determined for a large part by
the user’s personal preferences. A deal generally con-
sists of multiple issues. For example, when applying
for a new job, some issues are the position, the salary,
and the possibility to work part-time. For a complete
deal, negotiators have to agree on the value for every
issue. The satisfaction of a negotiator with a possible
outcome depends on his preferences.
Since the number of possible outcomes is typ-
ically very large (exponential in the number of is-
sues), it is not feasible to have the user express his
preferences over all possible outcomes directly. It
is common to compute or derive preferences over
possible outcomes from preferences over the possi-
ble values of issues and a weighing or importance
ordering of the issues. One of the best-known ap-
proaches is multi-criteria utility theory (Keeney and
Raiffa, 1993), a quantitative approach where prefer-
ences are expressed by numeric utilities. Since such
quantities are hard for humans to provide, qualitative
approaches have been proposed too, e.g. (Brewka,
2004). Our approach is also of a qualitative nature.
In this paper we argue that issues alone are not
enough to derive outcome preferences. Instead, we
will focus on modelling underlying interests and their
relation to issues. There are several reasons for taking
interests into account. First, underlying interests can
explain and eliminate conditional preferences. Con-
sider the following example. If it rains, I prefer to
take my umbrella, but if it doesn’t, I prefer not to take
it. This is a conditional preference; my preference
over taking my umbrella depends on the circumstance
of rain. Underlying interests can explain such condi-
tional preferences: I prefer to take my umbrella when
it rains because I do not want to get wet, and I pre-
fer not to take it when it’s dry because I don’t want
to carry things unnecessarily. If we take such inter-
ests as criteria on which to base preference, we can
eliminate conditional preferences entirely. We will
get back to this in more detail later. Second, interest-
based negotiation is said to lead to better outcomes
than position-based negotiation (Keeney, 1992; Rah-
wan et al., 2007). By understanding one’s own and
the other party’s reasons behind a position and dis-
cussing these interests, people are more likely to find
more creative options in a negotiation and by that
reach a mutually acceptable agreement more easily. A
well-known example is that of the two sisters negoti-
ating about the division of an orange. They both want
Visser W., V. Hindriks K. and M. Jonker C..
DOI: 10.5220/0003141300790088
In Proceedings of the 3rd International Conference on Agents and Artificial Intelligence (ICAART-2011), pages 79-88
ISBN: 978-989-8425-40-9
2011 SCITEPRESS (Science and Technology Publications, Lda.)
the orange, and end up splitting it in half. Had they
known each other’s underlying interests, they would
have reached a better deal: one sister only needed the
peel to make a cake and would gladly have let the
other sister have all of the flesh for her juice. Third,
thinking about underlying interests is a very natural,
human thing to do. Interests are what really matters
to people, they are what drive them in their decisions
and opinions. Taking underlying interests explicitly
into account will result in a better model of human
preferences. Such a model is also suited for explana-
tion of the reasoning and advice of a support system.
This last point brings us to the motivation for us-
ing argumentation to reason about interest-based pref-
erences. Reasoning by means of arguments is a very
human type of reasoning. People often base their de-
cisions on (mental) lists of arguments in favour of and
against certain decisions. Therefore argumentation is
suitable for explanation of a system’s reasoning to a
human user. Another advantage of argumentation is
that it is a kind of defeasible reasoning. It is able to
reason with incomplete, uncertain and contradictory
information. Finally, argumentation can be used to
(try to) persuade the opponent during negotiation (but
this is outside the scope of this paper).
The paper is organised as follows. In Section 2
we introduce and discuss the most important con-
cepts that we will use throughout the paper. Then,
in Section 3, we give an overview of existing ap-
proaches to preferences and underlying interests. We
give some more details about qualitative multi-criteria
preferences in Section 4. In Section 5 we motivate
the explicit modelling of underlying interests, illus-
trated with examples. Our own approach is presented
in Section 6. Finally, Section 7 concludes the paper.
Before we go on, we will clarify some important con-
cepts that we will use. In negotiation, issues are the
matters which are under negotiation. An issue is a
concrete, negotiable aspect such as monthly salary or
number of holidays. Every issue has a set or range
of possible values. The value of an issue in a given
instance can be objectively determined (e.g. e2400,
30 days). Issues and their possible values typically
depend on the domain. Besides the issues under ne-
gotiation, there may be other properties of a deal that
influence preferences. For example, the location of
the company that you are applying to work for can be
very important, because it determines the duration of
your daily commute, but it is hardly negotiable. Still,
such properties are important in negotiation. If, for
example, you already got an offer from another com-
pany near your home, you will only consider offers
that are better taking the location into account.
A possible outcome or possible deal has a spec-
ified value for every issue. All bids made during a
negotiation are possible outcomes. For example, a
possible outcome could be a job contract for the posi-
tion of programmer, with a salary of e3000 gross per
month, with 25 holidays, for the duration of one year
with the possibility of extension. Any other assign-
ment to the issues would constitute a different out-
come. It is the user’s preferences over such possible
outcomes that we are interested in.
With criteria we mean the features on which a
preference between outcomes is based. It is common
to base preferences directly on the negotiated issues;
in that case the issues are the criteria. In this paper we
argue that not issues, but underlying interests should
be used as criteria.
Many terms are used for what we consider to be
underlying interests, such as fundamental objectives,
values, concerns, goals and desires. In our view, an
interest can be any kind of motivation that leads to a
preference. Essentially, a preference depends on how
well your interests are met in the outcomes to be com-
pared. The degree to which interests are met is in-
fluenced by the issues, but there is not necessarily a
one-to-one relation between issues and interests. For
example, an applicant with childcare responsibilities
will have the interest that the children are taken care
of after school. This interest can be met by various
different issues, for example part-time work, the pos-
sibility to work from home, a salary that will cover
childcare expenses, etc. One issue may also con-
tribute to multiple interests. Many issues that deal
with money do so, because the interests different peo-
ple have for using the money will be diverse.
Existing literature about preferences is abundant and
very diverse. In this section we briefly discuss the ap-
proaches that are most closely related to our interests.
Interest-based negotiation is discussed in (Rah-
wan et al., 2007). However, this approach has a par-
ticular view on negotiation as an allocation of indi-
visible and non-sharable resources. The resources are
needed to carry out plans to reach certain goals. Even
though the goals can be seen as underlying interests, it
is hard to model e.g. negotiation about a job contract
as an allocation of resources. Salary might be an allo-
cation of money, but other issues, like position or start
date, cannot be translated as easily into resources.
ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence
Argumentation about preferences has been stud-
ied extensively in the context of decision making
(Amgoud et al., 2005; Amgoud and Prade, 2009;
Ouerdane et al., 2008; Ouerdane et al., 2010). The
aim of decision making is to choose an action to per-
form. The quality of an action is determined by how
well its consequences satisfy certain criteria. For ex-
ample, (Amgoud et al., 2005) present an approach in
which arguments of various strengths in favour of and
against a decision are compared. However, it is a two-
step process in which argumentation is used only for
epistemic reasoning. In our approach, we combine
reasoning about preferences and knowledge in a sin-
gle argumentation framework.
Within the context of argumentation, an approach
that is related to underlying interests is value-based
argumentation (Bench-Capon, 2003; Bench-Capon
and Atkinson, 2009). Values are used in the sense
of ‘fundamental social or personal goods that are de-
sirable in themselves’ (Bench-Capon and Atkinson,
2009), and are used as the basis for persuasive argu-
ment in practical reasoning. In value-based argumen-
tation, arguments are associated with values that they
promote. Values are ordered according to importance
to a particular audience. An argument only defeats
another argument if it attacks it and the value pro-
moted by the attacked argument is not more impor-
tant than the value promoted by the attacker. We will
illustrate this with a little example. Consider two job
offers a and b. a offers a higher salary, but b offers
a better position. We can construct two mutually at-
tacking preference arguments, A: ‘I prefer job offer a
over job offer b because it has a higher salary’, and B:
‘I prefer job offer b over job offer a because it has a
better position’. In Dung-style argumentation frame-
works (Dung, 1995), there is no way to choose be-
tween two mutually attacking arguments (unless one
is defended and the other is not). In value-based argu-
mentation, we could say that preferring a over b pro-
motes the value of wealth (w), and preferring b over
a promotes the value of status (s), and e.g. wealth is
considered more important than status. In this case A
defeats B, but not the other way around.
In this framework, every argument is associated
with only one value, while in many cases there are
multiple values or interests at stake. (Kaci and van der
Torre, 2008) define so-called value-specification ar-
gumentation frameworks, in which arguments can
support multiple values, and preference statements
about values can be given. However, the preference
between arguments is not derived from the preference
between the values promoted by the arguments. Be-
sides, there is no guarantee that a value-specification
argumentation framework is consistent, i.e., some sets
of preference statements do not correspond to a pref-
erence ordering on arguments.
In value-based argumentation, we cannot argue
about what values are promoted by the arguments
or the ordering of values; this mapping and order-
ing are supposed to be given. But these might well
be the conclusion of reasoning, and might be defea-
sible. Therefore, it would be natural to include this
information at the object level. (van der Weide et al.,
2009) describe some argument schemes regarding the
influence of certain perspectives on values. However,
for the aggregation of multiple values, they assume a
given order on sets of values, whereas we want to de-
rive such an order from an order on individual values.
Regardless of whether we take issues or interests as
criteria, we need to be able to model multiple criteria.
In any realistic setting, preferences are determined
by multiple criteria and the interplay between them.
Therefore we shortly introduce two well-known ap-
proaches to multi-criteria preferences which we will
use in our framework.
One approach is ceteris paribus (‘all else being
equal’) comparison. One outcome is preferred to an-
other ceteris paribus, if it is better on some criteria and
the same on all other criteria. This approach has been
widely used since (von Wright, 1963). Also (Well-
man and Doyle, 1991) derive preferences from sets
of goals in a ceteris paribus way. In (Boutilier et al.,
2004), ceteris paribus comparison is combined with
conditional preferences in a graphical preference lan-
guage called CP-nets. The preference order resulting
from ceteris paribus comparison is not complete; an
outcome satisfying criterion G but not H cannot be
compared to an outcome satisfying H but not G.
Another well-known approach is the lexico-
graphic preference ordering (see e.g. (Brewka, 2004),
where it is denoted #). Here, preferences over out-
comes are based on a set of relevant criteria, which are
ranked according to their importance. The importance
ranking of criteria is defined by a total preorder ,
which yields a stratification of the set of criteria into
importance levels. Each importance level consists of
criteria that are equally important. The lexicographic
preference ordering first considers the highest impor-
tance level. If some outcome satisfies more criteria on
that level than another, then the first is preferred over
the second. If two outcomes satisfy the same num-
Table 1: Satisfaction of issues and interests.
a. Issues b. Interests
high high full-
salary position time
a 3 3 3
b 3 3 7
c 3 7 3
d 3 7 7
e 7 3 3
f 7 3 7
g 7 7 3
h 7 7 7
wealth status time
a 3 3 7
b 3 3 3
c 3 3 7
d 3 3 3
e 7 3 7
f 7 3 3
g 7 7 7
h 7 7 3
ber of criteria on this level, the next importance level
is considered, and so on. Two outcomes are equally
preferred if they satisfy the same number of criteria
on every level.
We use a slightly more abstract definition of pref-
erence that covers both ceteris paribus and lexico-
graphic preferences. Let C be a set of binary criteria,
ordered according to importance by a preorder . If
P Q and not Q P, we say that P is strictly more
important than Q and write P Q. If P Q and
Q P, we say that P is equally important as Q and
write P Q. C can be divided into equivalence classes
induced by , which we call importance levels. An
importance level L is said to be more important than
iff the criteria in L are more important than the cri-
teria in L
. Let O be a set of outcomes, and sat a
function that maps outcomes a O to sets of criteria
. If P sat(a), we say that a satisfies P.
Definition 1. (Preference). An outcome a is strictly
preferred to another outcome b if it satisfies more cri-
teria on some importance level L, and for any impor-
tance level L
on which b satisfies more criteria than
a, there is a more important level on which a satisfies
more criteria than b. An outcome a is equally pre-
ferred as another outcome b if both satisfy the same
number of criteria on every importance level.
The least specific importance order possible is the
identity relation, in which case the importance lev-
els are all singletons and no importance level is more
important than any other. In this case, the preference
definition is equivalent to ceteris paribus preference
(if a is preferred to b ceteris paribus, there are no cri-
teria that b satisfies but a does not). If the importance
order is a total preorder, the definition is equivalent
to lexicographic preference. In general, the more in-
formation about the relative importance of interests
is known, the more preferences can be derived. We
note that lexicographic preferences subsume ceteris
paribus preferences in the sense that if one outcome
is preferred to another ceteris paribus, it is also pre-
a) For Mark. b) For Jones.
Figure 1: Ceteris paribus preference orderings (arrows point
towards more preferred outcomes).
ferred lexicographically, regardless of the importance
ordering on criteria.
We will illustrate the ideas presented in this paper by
means of an example. Mark has applied for a job at a
company called Jones. After the first interview, they
are ready to discuss the terms of employment. There
are three issues on the table: the salary, the position,
and whether the job is full-time or part-time. All pos-
sible outcomes are listed in Table 1a. After some
thought, Mark has determined that the interests that
are at stake for him are wealth, status, and time with
his family. A high position will give status. A high
salary will provide both wealth and status. A part-
time job will give him time to spend with his family.
Table 1b shows which interests each of the outcomes
All information is encoded in a knowledge base,
which consists of three parts.
Facts about the properties of the outcomes to be
compared. When comparing offers in negotiation,
these may be the values for each issue, or any
other relevant properties. Facts are supposed to
be objectively determined.
A set of interests of a negotiator. Underlying in-
terests are personal and subjective, although they
can sometimes be assumed by default. Interests
may vary according to importance. If no impor-
tance ordering is given, the ceteris paribus princi-
ple can be used to derive preferences. The more
information about the relative importance of in-
terests is known, the more preferences can be de-
rived. If there is a total preorder of interests ac-
cording to importance, a complete preference or-
dering over possible outcomes can be derived us-
ing the lexicographic principle.
Rules relating issues and other outcome proper-
ties to interests. These rules can be very sub-
jective, e.g. some people consider themselves
very wealthy if they earn e3000 gross salary per
ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence
Table 2: Outcomes in the evening dress example.
a. Issues b. Interests
jacket pants shirt
i b b w
j b b r
k b w w
l b w r
m w b w
n w b r
o w w w
p w w r
i 7
j 3
k 3
l 7
m 3
n 7
o 7
p 3
month, while for others this may be a pittance.
Even so, there can still be default rules that apply
in general, e.g. that a high salary promotes wealth
for the employee. The relation between issues and
interests does not have to be one-to-one. There
may be multiple issues that can satisfy an inter-
est, some issues may satisfy multiple interests at
once, or a combination of issues may be needed
to fulfill an interest. As is common in defeasible
reasoning, there may be exceptions to rules. For
example, one might say that a high position en-
sures status in general, but this effect is cancelled
out if the job is badly paid.
With the inference scheme of defeasible modus
ponens (see scheme 1 in Table 4), arguments can be
constructed that derive statements about what inter-
ests are satisfied by possible outcomes, based on their
issue values and the rules relating issues to interests.
The conclusions from these arguments are summa-
rized in Table 1b. If we compare the possible out-
comes ceteris paribus, we can construct a partial pref-
erence order for Mark, with b and d being the most
preferred options, and g the least preferred (see Fig-
ure 1a). This preference order is not complete. To
determine Mark’s preference between a and c on the
one hand and f on the other hand, we need to know
whether wealth or family time is more important to
him. If wealth is more important, Mark will prefer a
or c. If family time is more important, he will prefer
f . Similarly, to determine a preference between e and
h, we need to know whether status or family time is
more important.
The company Jones has two major interests: it
needs a manager and it has to cut back on expenses.
These interests relate directly (one-to-one) to high po-
sition and low salary. The ceteris paribus preference
ordering for Jones is displayed in Figure 1b.
a) Preference graph
induced by CP-net.
b) Ceteris paribus or-
dering with interests.
c) Ceteris paribus or-
dering with interests,
good combination
most important.
Figure 2: Preference orderings (arrows point towards more
preferred outcomes).
The Added Value of Interests. It may seem that
using interests next to issues just introduces an extra
layer in reasoning. From the issues and the relations
between issues and interests, we derive the interests
that are met by outcomes, and from that we derive
preferences. Would it not be easier to derive the pref-
erences directly from the issues? We could just state
that Jones has the interests of high position and low
salary, optionally with an ordering between them, and
we would be able to derive Jones’ preferences from
that. This is because in this case there is a one-to-one
relation between interests and issues: every interest is
met by exactly one issue, and every (relevant) issue
meets exactly one interest.
There are good reasons, however, why this ap-
proach is not always a good solution. Consider for
example Mark’s preferences. A high salary satisfies
both wealth and status, and status can be satisfied by
either a high salary or a high position. Because of
this, the (partial) preference ordering we determined
for Mark cannot be defined as a ceteris paribus order-
ing if the issues are taken as criteria. This is because
high position as criterion is dependent on high salary:
if the salary is not high, then high position is a distin-
guishing criterion, but if the salary is high, high po-
sition is not relevant anymore, since the only interest
that it serves, status, is already satisfied by high salary.
So with a fixed set of issues as criteria, ceteris paribus
or lexicographic models cannot represent every pref-
erence order. In many cases, this can be solved intu-
itively by taking underlying interests into account.
There are other approaches to deal with this mat-
ter. Instead of assuming independence of the criteria,
one can also model conditional preferences, where
criteria may be dependent on other criteria. A well-
known approach to represent conditional preferences
is CP-nets (Boutilier et al., 2004), which is short for
conditional ceteris paribus preference networks. A
CP-net is a graph where the nodes are variables (com-
parable to our notion of issues). Every node is anno-
tated with a conditional preference table, which lists
a user’s preferences over the possible values of that
variable. If such preferences are conditional (depen-
dent on other variables), each condition has a sepa-
rate entry in the table, and the variables that influ-
ence the preference are parent nodes of this variable
in the graph. In (Boutilier et al., 2004), an example of
conditional preference is given regarding an evening
dress. A man unconditionally prefers black to white
as a colour for both the jacket and the pants. His pref-
erence between a white and a red shirt is conditioned
on the combination of jacket and pants. If they have
the same colour, he prefers a red shirt (for a white
shirt will make his outfit too colourless). If they are
of different colours, he prefers a white shirt (because
a red shirt will make his outfit too flashy). The com-
plete assignments (outcomes in our terminology) are
listed in Table 2a. The preference graph induced by
the CP-net for this example is displayed in Figure 2a.
We propose to replace the variables the prefer-
ences over which are conditional with underlying
interests the reason for the dependency. In the
evening dress example, the underlying interest is that
the colours of jacket, pants and shirt make a good
combination, which in this case is defined by being
neither too colourless nor too flashy. The satisfaction
of this interest by the different outcomes is listed in
Table 2b. The variables jacket and pants are uncondi-
tional, so they can remain as criteria. If we take jacket,
pants, and good combination as criteria, we can con-
struct the preference graph in Figure 2b, using the ce-
teris paribus principle. The difference with the prefer-
ences induced by the CP-net is that in the CP-net case,
outcome i is more preferred than k and m, and p is
less preferred than l and n, while in the interest-based
case they are incomparable. This is due to the fact
that in CP-nets, conditional preferences are implicitly
considered less important than the preferences on the
variables they depend on ((Boutilier et al., 2004), p.
145). In fact, if we would specify that both jacket
and pants are more important than a good combina-
tion, our preference ordering would be the same as in
Figure 2a. But the interest approach is more flexible;
it is possible to specify any (partial) importance or-
dering on interests. For example, we could also state
that a good combination is more important than either
the jacket or the pants, which results in the preference
ordering in Figure 2c. In our opinion, there is no a pri-
ori reason to attach more importance to unconditional
variables as is done in the CP-net approach.
Table 3: The knowledge base for the example.
highsal(c) I
(wealth) highsal(x) wealth(x)
¬highpos(c) I
(status) highsal(x) status(x)
full-time(c) I
(family) highpos(x) status(x)
¬highsal( f ) ¬full-time(x) family(x)
highpos( f ) I
(manager) highpos(x) manager(x)
¬full-time( f ) I
(cutback) ¬highsal(x) cutback(x)
In this section, we present an argumentation frame-
work (AF) for reasoning about qualitative, interest-
based preferences. An abstract AF in the sense of
Dung (Dung, 1995) is a pair hA, →i where A is a
set of arguments and is a defeat relation (infor-
mally, a counterargument relation) among those ar-
guments. To define which arguments are justified, we
use Dung’s (Dung, 1995) preferred semantics.
Definition 2. (Preferred Semantics) . A preferred
extension of an AF hA, →i is a maximal (w.r.t. ) set
S A such that: A, B S : A 6→ B and A S: if B
A then C S : C B. An argument is credulously
(sceptically) justified w.r.t. preferred semantics if it is
in some (all) preferred extension(s).
Informally, a preferred extension is a coherent point
of view that can be defended against all its attack-
ers. In case of contradictory information, there will
be multiple preferred extensions, each advocating one
point of view. The contradictory conclusions will be
credulously, but not sceptically justified.
We instantiate an abstract AF by specifying the
structure of arguments and the defeat relation.
Arguments. Arguments are built from formulas of
a logical language, that are chained together using
inference steps. Every inference step consists of
premises and a conclusion. Inferences can be chained
by using the conclusion of one inference step as a
premise in the following step. Thus a tree of chained
inferences is created, which we use as the formal def-
inition of an argument (cf. e.g. (Vreeswijk, 1997)).
Definition 3. (Argument). An argument is a tree,
where the nodes are inferences, and an inference can
be connected to a parent node if its conclusion is a
premise of that node. Leaf nodes only have a con-
clusion (a formula from the knowledge base), and no
premises. A subtree of an argument is also called a
subargument. inf returns the last inference of an ar-
gument (the root node), and conc returns the conclu-
sion of an argument, which is the same as the conclu-
sion of the last inference.
ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence
Table 4: Inference schemes.
, . . . , L
, L
, . . . , L
. . . L
. . . L
2 L
asm( L)
(a) . . . P
(a) P
. . .
) . . . I
sat(a, [P
, n)
count(a, [P
, {P
, . . . , P
asm( L) is inapplicable
asm( L)uc
(a) . . . P
(a) P
. . .
) . . . I
count(a, [P
, S {P
, . . . , P
}) is inapplicable
count(a, [P
, S)uc
4 sat(a, [P]
, 0)
count(a, [P]
, )
sat(a, [P]
, n) sat(b, [P
, m) P
n > m
(a, b)
prefinf(a, b, [P]
sat(a, [Q]
, n) sat(b, [Q
, m) Q
P n < m
prefinf(a, b, [P]
) is inapplicable
prefinf(a, b, [P]
sat(a, [P]
, n) sat(b, [P
, m) P
n = m
(a, b)
eqprefinf(a, b, [P]
sat(a, [Q]
, n) sat(b, [Q
, m) Q
n 6= m
eqprefinf(a, b, [P]
) is inapplicable
eqprefinf(a, b, [P]
Definition 4. (Language). Let P be a set of predicate
names with typical elements P,Q; O a set of outcome
names with typical elements a, b; α an audience; and
n a non-negative integer. The input language L
full language L are defined as follows.
ϕ L
::= L | I
(P) | P
Q | P
Q |
, . . . , L
, L
, . . . , L
where L
= P(a) or ¬P(a).
ψ L ::= ϕ L
| L | sat(a, [P]
, n) |
(a, b) | eqpref
(a, b)
We make a distinction between an input and full lan-
guage. A knowledge base, which is the input for an
argumentation framework, is specified in the input
language. The input language allows us to express
facts about the criteria that outcomes (do not) satisfy,
statements about interests of an audience and their im-
portance ordering, and defeasible rules. The knowl-
edge base for the job contract example (the facts re-
stricted to outcomes c and f ) is displayed in Table 3.
Other formulas of the language that are not part of the
input language, e.g. expressing a preference between
two outcomes, can be derived from a knowledge base
using inference steps that build up an argument (such
formulas are not allowed in a knowledge base because
they might contradict derived statements).
Inferences. Table 4 shows the inference schemes
that are used. The first inference scheme is called
defeasible modus ponens. It allows to infer conclu-
sions from defeasible rules. The next two inference
rules define the meaning of the weak negation . Ac-
cording to inference rule 2, a formula ϕ can always
be inferred, but such an argument will be defeated by
an undercutter built with inference rule 3 if ϕ is the
case. Inference schemes 4 and 5 are used to count the
number of interests of equal importance (according to
audience α) as some interest P
that outcome a sat-
isfies. This type of inference is inspired by accrual
(Prakken, 2005), which combines multiple arguments
with the same conclusion into one accrued argument
for the same conclusion. Although our application
is different, we use a similar mechanism. Inference
scheme 4 can be used when an outcome satisfies no
interests. It is possible to construct an argument that
does not count all interests that are satisfied, a so-
called non-maximal count. But we want all interests
to be counted, otherwise we would conclude incor-
rect preferences. To ensure that only maximal counts
are used, we provide an inference scheme to construct
arguments that undercut non-maximal counts (infer-
ence scheme 6). An argument of this type says that
any count which is not maximal is not applicable. In-
ference scheme 7 says that an outcome a is preferred
over an outcome b if the number of interests of a cer-
tain importance level that a satisfies is higher than the
number of interests on that same level that b satisfies.
Inference scheme 8 undercuts scheme 7 if there is a
more important level than that of P on which a and b
do not satisfy the same number of interests. Finally,
inference schemes 9 and 10 do the same as 7 and 8,
but for equal preference.
Defeat. The most common type of defeat is re-
buttal. An argument rebuts another argument if its
conclusion contradicts conclusion of the other ar-
gument. Conclusions contradict each other if one
is the negation of the other, or if they are prefer-
Table 5: Example arguments.
highsal(c) highsal(x) wealth(x)
wealth(c) I
sat(c, [wealth]
, 1) sat( f , [wealth]
, 0) wealth
wealth 1 > 0
(c, f )
¬full-time( f ) ¬full-time(x) family(x)
family( f ) I
sat( f , [family]
, 1) sat(c, [family]
, 0) family
family 1 > 0
( f , c)
highsal(c) highsal(x) wealth(x)
wealth(c) I
sat(c, [wealth]
, 1) sat( f , [wealth]
, 0) wealth
family 1 6= 0
β is inapplicable
¬full-time( f ) ¬full-time(x) family(x)
family( f ) I
sat( f , [family]
, 1) sat(c, [family]
, 0) family
wealth 1 6= 0
α is inapplicable
ence or importance statements that are incompatible
(e.g. pref
(a, b) and pref
(b, a), or pref
(a, b) and
(a, b)). Defeat by rebuttal is mutual. Another
type of defeat is undercut. An undercutter is an ar-
gument for the inapplicability of an inference used in
another argument. Undercut works only one way. De-
feat is defined recursively, which means that rebuttal
can attack an argument on all its premises and (inter-
mediate) conclusions, and undercut can attack it on
all its inferences.
Definition 5. (Defeat) . An argument A defeats an
argument B (A B) if conc(A) and conc(B) are con-
tradictory (rebuttal), or conc(A) =inf(B) is inappli-
cable’ (undercut), or A defeats a subargument of B.
Let us return to the example. With the informa-
tion from the knowledge base, the arguments A and
B in Table 5 can be formed. A advocates a preference
for c, based on the interest wealth. B advocates a pref-
erence for f , based on the interest family. Without an
ordering on these interests, no decision between these
arguments can be made. But if wealth
family is
known, argument C can be made, which undercuts B.
Similarly, with family
wealth, argument D can be
made, which undercuts A.
Validity. If some conditions in the input knowledge
base (KB) hold, it can be shown that the proposed
argumentation framework models ceteris paribus and
lexicographic preference. In the following, we con-
sider a single audience and leave out the subscript α.
Condition 1. Let C be a set of interests to be used as
criteria, with importance order .
(1) For all P, ‘I(P)’ is in KB iff P C.
(2) For all P C, a, P(a) is a conclusion of a scep-
tically justified argument iff a satisfies P.
(3) The relative importance among interests is
(a) a total preorder,
(b) the identity relation,
and for all P, Q C, P Q is in KB iff P Q, and
P Q’ is in KB iff P Q.
Theorem 1. (i) If conditions 1.1, 1.2 and 1.3a hold,
then pref(a, b) (resp. eqpref(a, b)) is a sceptically jus-
tified conclusion of the argumentation framework iff
a is strictly (resp. equally) preferred over b according
to the lexicographic preference ordering.
(ii) If conditions 1.1, 1.2 and 1.3b hold, then pref(a,b)
(resp. eqpref(a,b)) is a sceptically justified conclu-
sion of the argumentation framework iff a is strictly
(resp. equally) preferred over b according to the ce-
teris paribus preference ordering.
Proof. We prove the theorem for strict preference.
The same line of argument can be followed for equal
(i) : Suppose a is strictly lexicographically pre-
ferred over b. This means that there is an impor-
tance level on which a satisfies more interests (say,
, . . . , P
) than b (say, P
, . . . , P
, n > m), and on all
more important levels, a and b satisfy an equal num-
ber of interests. In this case, we can construct the fol-
lowing arguments, where the first two arguments are
subarguments of the third (note that these arguments
can also be built if m is equal to 0, by using the empty
set count).
ICAART 2011 - 3rd International Conference on Agents and Artificial Intelligence
(a) . . . P
(a) I(P
) . . . I(P
) P
. . . P
sat(a, [P
], n)
(b) . . . P
(b) I(P
) . . . I(P
) P
. . . P
sat(b, [P
], m)
sat(a, [P
], n) sat(b, [P
], m) P
n > m
pref(a, b)
We will now try to defeat this argument. Premises of
the type P(a) are justified by condition 1.2. Premises
of the type I(P) and P
cannot be defeated (con-
ditions 1.1 and 1.3a). There are three inferences we
can try to undercut (the last inference of the argument
and the last inferences of two subarguments). For the
first count, this can only be done if there is another
such that I(P
) and P
P and P
6∈ {P
, . . . , P
and P
(a) is the case. However, P
. . . P
all interests that a satisfies on this level, so count un-
dercut is not possible. The same argument holds for
the other count. At this point it is useful to note that
these two counts are the only ones that are undefeated.
Any lesser count will be undercut by the count under-
cutter that takes all of P
. . . P
(resp. P
. . . P
) into
account. Such an undercutter has no defeaters, so any
non-maximal count is not justified. The undercutter
of prefinf(a, b, [P
]) is based on two counts. We have
seen that any non-maximal count will be undercut. If
the maximal counts are used, we have n = m for un-
dercutter arguments that use Q P, since we have
that on all more important levels than [P
], a and b
satisfy an equal number of interests. So the under-
cutter inference rule cannot be applied since n 6= m is
not true. For that reason, a rebutting argument with
conclusion pref(b, a) will not be justified. This means
that for every possible type of defeat, either the defeat
is inapplicable or the defeater is itself defeated by un-
defeated arguments. This means that the argument is
sceptically justified.
: Suppose that a is not strictly lexicographically
preferred over b. This means that for all impor-
tance levels [P], either a does not satisfy more in-
terests than b on that level, or there exists a more
important level where b satisfies more interests than
a. This means that any argument with conclusion
pref(a, b) (which has to be of the form above) is ei-
ther undercut by count(b, [P], S)uc because it uses a
non-maximal count, or by prefinf(a, b, [P])uc because
there is a more important level where a preference for
b over a can be derived. This means that any such
argument will not be sceptically justified.
(ii) : Suppose a is strictly ceteris paribus preferred
over b. This means that there is (at least) one interest,
let us say P, that a satisfies and b does not, and there
are no interests that b satisfies and a does not. In this
case, we can construct the following argument.
P(a) I(P)
sat(a, [P], 1) sat(b, [P], 0) P P 1 > 0
pref(a, b)
Premise P(a) is justified by condition 1.2. Premise
I(P) cannot be defeated (condition 1.1). Note
that, since there is no importance ordering specified,
counts can only include 0 or 1 interest(s). So the first
count cannot be undercut, because there are no other
interests that are equally important as P (condition
1.3b). The second count cannot be undercut because
b does not satisfy P. Since there are no interests that b
satisfies but a does not, the last inference can only be
undercut by an undercutter that uses a non-maximal
count and so will be undercut itself.
: Suppose a is not strictly ceteris paribus preferred
over b. This means that either there is no interest that
a satisfies but b does not, or there is some interest that
b satisfies and a does not. In the first case, the only ar-
guments that derive a preference for a over b have to
use non-maximal counts and hence are undercut. In
the second case, any argument that derives a prefer-
ence for a over b is rebut by the following argument,
Q(b) I(Q)
sat(b, [Q], 1) sat(a, [Q], 0) Q Q 1 > 0
pref(b, a)
and is not sceptically justified.
In this paper we have made a case for explicitly mod-
elling underlying interests when reasoning about pref-
erences in the context of practical reasoning. We have
presented an argumentation framework for reasoning
about qualitative interest-based preferences that mod-
els ceteris paribus and lexicographic preference.
In the current framework, we have only consid-
ered Boolean issues and interests. While this suffices
to illustrate the main points discussed in this paper,
multi-valued scales would be more realistic. Such
an approach would open the way to modelling dif-
ferent degrees of (dis)satisfaction of an interest. For
example, (Amgoud et al., 2005) take into account the
level of satisfaction of goals on a bipolar scale. In
the Boolean case, the lexicographic preference order-
ing is based on counting the number of interests that
are satisfied by outcomes. This is no longer possi-
ble if multi-valued scales are used. In that case, we
could count interests that are satisfied to a certain de-
gree (like e.g. (Amgoud et al., 2005)), or compare out-
comes in a pairwise fashion and count the number of
interests that one outcome satisfies to a higher degree
than another (like e.g. (Ouerdane et al., 2008; van der
Weide et al., 2009)).
Currently, we suppose that the interests and im-
portance ordering among them are given in a knowl-
edge base. We can make our framework more flexible
by allowing such statements to be derived in a way
that is similar to the derivation of statements about
the satisfaction of interests.
We would also like to look into the interplay
between different issues promoting or demoting the
same interest. For example, a high salary and a high
position both lead to status, but together they may
lead to even more status. Or a low salary may pro-
mote cutback, but providing a lease car will demote
it. Do these effects cancel each other out? The prin-
ciples that play a role here are related to the questions
posed in the context of accrual of arguments (Prakken,
Since our long-term goal is the development of
an automated negotiation support system, we plan
to look into negotiation strategies that are based on
qualitative, interest-based preferences as described
here, as opposed to utility-based approaches cur-
rently in use. For the same reason, we plan to im-
plement the argumentation framework for reasoning
about interest-based preferences that we have pre-
sented here. Another interesting question in this con-
text is how interest-based preferences can be elicited
from a human user.
We thank Henry Prakken for useful comments on ear-
lier drafts of this paper. This research is supported by
the Dutch Technology Foundation STW, applied sci-
ence division of NWO and the Technology Program
of the Ministry of Economic Affairs. It is part of the
Pocket Negotiator project with grant number VICI-
project 08075.
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