Veenen, Prakken - A Protocol for Arguing About Rejections.pdf - Psychologia - koni86

A Protocol for Arguing About Rejections

in Negotiation

Jelle van Veenen 1 and Henry Prakken 2 , 3

Faculty of Law, Tilburg University, The Netherlands

j.vanveenen@uvt.nl

Department of Information and Computing Sciences,

Utrecht University, The Netherlands

henry@cs.uu.nl

Centre for Law & ICT, Faculty of Law, University of Groningen, The Netherlands

Abstract. One form of argument-based negotiation is when agents

argue about why an oﬀer was rejected. If an agent can state a reason

for a rejection of an oﬀer, the negotiation process may become more e-

cient since the other agent can take this reason into account when making

new oﬀers. Also, if a reason for rejection can be disputed, the negotiation

process may be of higher quality since ﬂawed reasons may be revised as

a result. This paper presents a formal protocol for negotiation in which

reasons can be asked and given for rejections and in which agents can try

to persuade each other that a reason is or is not acceptable. The proto-

col is modelled as a persuasion dialogue game embedded in a negotiation

protocol. It has a social semantics since the protocol does not refer to

the internal state of negotiating agents.

1 Introduction

Recently argumentation-based approaches to negotiation have become popular

(see [1] for an overview and motivation). The idea is that if negotiating agents

exchange reasons for their proposals and rejections, the negotiation process may

become more ecient and the negotiation outcome may be of higher quality.

This paper especially focuses on reasons given for rejections of proposals. If an

agent explains why he rejects a proposal, the other agent knows which of her

future proposals will certainly be rejected so she will not waste eﬀort at such

proposals. Thus eciency is promoted. In such exchanges, reasons are not only

exchanged, they can also become the subject of debate. Suppose a car seller oﬀers

a Peugeot to the customer but the customer rejects the oﬀer on the grounds that

French cars are not safe enough. The car seller might then try to persuade the

customer that he is mistaken about the safety of French cars. If she succeeds

in persuading the customer that he was wrong, she can still oﬀer her Peugeot.

Thus the quality of the negotiation is promoted, since the buyer has revised his

preferences to bring them in agreement with reality.

This example illustrates that a negotiation dialogue (where the aim is to reach

a deal) sometimes contains an embedded persuasion dialogue (where the aim is

S. Parsons et al. (Eds.): ArgMAS 2005,

LNAI

4049, pp. 138– 153, 2006.

Springer-Verlag Berlin Heidelberg 2006

A Protocol for Arguing About Rejections in Negotiation

139

to resolve a conﬂict of opinion). The aim of this paper is to formulate a pro-

tocol for negotiation with embedded persuasion dialogues about the reasons for

rejecting a proposal. The key idea is that the propositional commitments in-

curred by the agents in the embedded persuasion dialogue constrain their be-

haviour in the surrounding negotiation dialogue. In agreement with the current

trend [2] we intend the combined protocol to have a social semantics. For this

reason we will completely abstract from the internal design of the communi-

cating agents; in particular, the protocol will only refer to the agents’ publicly

observable behaviour within a dialogue. According to [2] a social semantics is

desirable for agent interaction protocols since if a protocol refers to an agent’s

mental state, there is no gurantee that an outside observer can verify whether

the agent complies with a protocl.

The main novelty of the present research lies in the fact that current protocols

for argument-based negotiation only allow arguments supporting proposals. One

exception is [3], which also allows arguments about rejections. However, their

protocol does not have a social semantics, since whether an agent is allowed to

assert a claim or an argument partly depends on their internal mental state. The

protocol has some other limitations, which will be discussed in Section 5.

Our proposal will be stated in a dialogue game form. It will combine a negoti-

ation protocol and language of [4] with a persuasion protocol based on [5], which

adapts and extends work of [6]. In the following sections we will ﬁrst introduce

these two systems and sketch the underlying argumentation logic that we will

use. Then we will present our combined protocol, investigate some of its formal

properties and illustrate it with an example.

2 The Building Blocks

In this section we present the negotiation and persuasion system that we aim

to combine. Both systems are formulated as a dialogue game. Dialogue games

formulate principles for coherent dialogue, and coherence depends on the goal of

a dialogue. The goal of negotiation dialogues is to reach agreement on the division

of scarce resources [1] and the goal of persuasion dialogues is to resolve a conﬂict

of opinion [7]. Formal dialogue games have a topic language L t with a logic

2.1 A Language and Protocol for Multi-attribute Negotiation

The negotiation system we will use is that of Wooldridge and Parsons [4]. The

negotiation topic language L t of this system assumes that in a negotiation

agents try to reach agreement over the values of a ﬁnite set V =

{

and a communication language L c with a protocol P . The protocol speciﬁes the

allowed moves at each point in a dialogue. A dialogue system also has eﬀect

rules , which specify the eﬀects of utterances on the participants’ commitments,

and outcome rules , deﬁning the outcome of a dialogue.

v 1 , ..., v m }

of negotiation issues . Each issue v can be assigned at most one value from a

range C ( v )ofvalues.An outcome of a negotiation is an assignment of values to

140

J. van Veenen and H. Prakken

C ( v )

or c =?, (where ? technically is a free variable, capturing that the issue has not

been assigned a value) and R denotes one of the relations = ,<,>,

∈

V and c

∈

The negotiation communication language L c can be used to talk about

proposals. The left column of table 1 shows the speech acts that agents can

perform and the right column their possible replies. The formulas ϕ and ϕ

are elements of L t . Request(ϕ) is a request for an oﬀer. Here ϕ typically is

wholly or partially uninstantiated (i.e., it may contains occurrences of ?): the

speech act request ( price =?

≤

≥

warranty = 12) can be read as “What is the

price if I want a 12 months warranty?”. The speech act oﬀer ( ϕ ) makes a fully

instantiated proposal ϕ ,andwith accept ( ϕ ) an agent accepts an oﬀer ϕ made

by another agent. With reject ( ϕ ) such an oﬀer is rejected. With withdraw an

agent withdraws from the negotiation.

We next outline the negotiation protocol of [4] for this language, with no-

tation slightly adapted to our purposes. A negotiation takes place between two

agents, one of whom starts with either an oﬀer or a request . The agents then

take turns after each utterance, selecting their replies from Table 1. As the table

indicates, a negotiation terminates when an agent accepts an oﬀer or withdraws

from the negotiation. Finally, moves may not be repeated by the same player.

∧

Table 1. Speech acts and replies in L c

Acts Replies:

request(ϕ)oﬀer(ϕ )

oﬀer(ϕ) ϕ ) or accept(ϕ) or

reject(ϕ) or withdraw

reject(ϕ)oﬀ ϕ ) or withdraw

accept(ϕ) end of negotiation

withdraw end of negotiation

( ϕ = ϕ )

To ensure that the oﬀers exchanged during a negotiation and its outcome are

related to an initial request, we add the following rule to the protocol of [4]:

– If request ( ϕ ) is the initial request of a dialogue then for any move oﬀer ( ψ )

in the dialogue:

•

ψ is logically consistent with ϕ ;and

•

ψ contains at least the same issues as ϕ .

Since issues have at most one value, this rule implies that an instantiated part of

a request cannot be changed by an oﬀer (but the oﬀer may contain more issues

than the request). Therefore:

Proposition 1. If a negotiation that starts with a request terminates with accep-

tance of an oﬀer, that oﬀer is consistent with and fully instantiates the request.

a subset of V . A proposal is expressed in a subset of the language of ﬁrst-order

logic as a conjunction of expressions of the form vRc ,where v

A Protocol for Arguing About Rejections in Negotiation

141

We illustrate the system with an example in which two agents, Paul ( P )and

Olga ( O ), negotiate over the sale of a car. The dialogue starts when Paul requests

to buy a car, and shows that he is interested in the brand and the price.

P 1 : request ( brand =?

∧

price = 10000)

(Olga has oﬀered a Peugeot for 10000, but Paul has rejected the oﬀer. Olga

makes him another oﬀer.)

O 4 : oﬀer ( brand = renault

∧

price = 8000

∧

stereo = yes )

P 5 : reject ( brand = renault

∧

price = 8000

∧

stereo = yes )

O 6 : oﬀer ( brand = audi

∧

price = 10000)

(Olga oﬀers a Renault with stereo for 8000. Paul again rejects after which Olga

oﬀers a non-French car for 10000. Paul accepts and the dialogue terminates.

Move O 4 illustrates that an oﬀer may introduce additional issues, for instance,

to make an oﬀer more attractive or to make a trade-oﬀ possible.)

∧

2.2 The Underlying Argumentation Logic

. In doing so we will abstract

from details of the language and inference rules wherever possible, to allow for

diﬀerent instantiations of the logic and language. Thus we in fact specify a set

of constraints on L t and

assumed by our persuasion dialogue system.

Much other work on argument-based dialogue, e.g. [3, 8], regards arguments

as classical proofs from consistent sets of propositional formulas and allows clas-

sical inconsistency of the premises of two arguments as the only source of attack

on arguments. We argue that the present application requires a richer language

and notions of argument and attack. The topic language L t must include a

suitable subset of ﬁrst-order predicate logic, to express arguments about val-

ues for negotiation issues. Since in persuasion dialogues arguments are often

attacked by counterarguments, the logic

must be a logic for defeasible argu-

mentation, or ‘argumentation system’ for short (cf. [9]). We want our system to

be an instance of the well-understood abstract framework of [10], in particular

of his grounded semantics (also used by e.g. [11, 12]), since this semantics can

be easily incorporated into a persuasion dialogue game. Since the arguments

exchanged in persuasion dialogues are often constructed stepwise during a di-

alogue in reply to challenges of the premises, the argumentation system must

allow for a tree structure of arguments, where inference rules are chained into

trees. As for notation, prem ( A )and conc ( A ) denote the premises and conclu-

sion of argument A , i.e. the leaves and root of the tree structure. Furthermore,

since arguments exchanged in persuasion dialogues are often based on defeasi-

ble argumentation schemes (such as schemes for practical reasoning or default

reasoning), the rules for constructing arguments must include defeasible as well

as deductive inference rules. Each defeasible inference rule comes with one or

more undercutters , which specify the circumstances under which the inference

price =?)

O 2 : oﬀer ( brand = peugeot

P 3 : reject ( brand = peugeot

P 7 : accept ( brand = audi

We next present the logical elements assumed by our persuasion protocol, i.e.,

the persuasion topic language L t and its logic

142

J. van Veenen and H. Prakken

rule cannot be applied. Accordingly, a defeasible argument can be defeated in

two ways. It can be rebut with an argument for the opposite conclusion, while it

can be undercut with an argument why an inference rule does not apply in the

given circumstances. To be successful, an attack should be of a certain strength.

In the present paper, we will not discuss issues of strength and therefore implic-

itly assume a given measure of relative strength between arguments. Also, since

our persuasion dialogue system is intended for any underlying logic satisfying

the above constraints, we will not further specify the defeasible inference rules

here but rather introduce them semiformally when discussing our examples. For

technical details the reader is referred to e.g. [13] and [9].

Given a set of arguments and a binary defeat relation deﬁned over it, an argu-

mentation system classiﬁes the arguments into justiﬁed, defensible and overruled

arguments. Our persuasion system presupposes a game-theoretic formulation of

Dung’s grounded semantics [14, 11]. The proponent and opponent of a certain

argument play a game where proponent starts with an argument he wants to

defend and then both players take turns, defeating the preceding argument with

a counterargument. A player wins if the other player has run out of moves. Now

an argument is justiﬁed if proponent has a winning strategy in a game starting

with the argument; and a proposition is justiﬁed if it is the conclusion of a jus-

tiﬁed argument. This game can be optimised in several ways (see e.g. [11]) but

in order to focus on the essence we leave them undiscussed here.

2.3 A Dialogue Game for Persuasion

We now present a dialogue game for persuasion. As noted above, this game is an

instance of the framework of [5], which adapts and further develops the system

of [6]. We are particularly interested in using this framework’s idea of reply

structure on the communication language and its notions of dialogical status

of relevance. A crucial feature of our game is that its protocol is ﬂexible in

that it allows for alternative replies to moves and for postponement of replies,

sometimes even indeﬁnitely. This is important since when an agent sees that a

line of attack or defence fails, s/he should be allowed to play other available lines

of attack or defence. However, in order to still ensure a strong focus of dialogues

this ﬂexibility is constrained by the notion of relevance, to be deﬁned below.

The dialogue game will be presented here in detail since its format plays a

crucial role in Section 3 in the combination of the persuasion and negotiation

dialogue game. Dialogues are between a proponent P and opponent O of a single

dialogue topic t

∈

L t . The game is based on the following ideas. Each dialogue

move except the initial one replies to one earlier move in the dialogue of the other

party (its target ). Thus a dialogue can be regarded in two ways: as a sequence

(reﬂecting the order in which the moves are made) and as a tree (reﬂecting the

reply relations between the moves). Each replying move is either an attacker

or a surrender . For instance, a claim ( p ) move can be attacked with a why ( p )

move and surrendered with a concede ( p )move.Anda why ( p )movecanbe

attacked with an argue ( A )movewhere A is an argument with conclusion p ,

and surrendered with a retract ( p ) move. When s is a surrendering and s is

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