D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNBI 4115, pp. 211 – 222, 2006. © Springer-Verlag Berlin Heidelberg 2006

Interest Based Negotiation Automation

Xuehong Tao1, Yuan Miao2, ZhiQi Shen3, ChunYan Miao4, and Nicola Yelland5

1 School of Education, Victoria University, P.O. Box 14428, Melbourne, VIC 8001, Australia xuehongTao@gmail.com

2 School of Computer Science and Mathematics, Victoria University, P.O. Box 14428, Melbourne, VIC 8001, Australia yuan.Miao@vu.edu.au

3 Information Communication Institute of Singapore, Nanyang Technological University, Nanyang Ave, Singapore 639798

zqshen@ntu.edu.sg

4 School of Computer Engineering, Nanyang Technological University, Nanyang Ave, Singapore 639798

ascymiao@ntu.edu.sg 5 School of Education, Victoria University, P.O. Box 14428, Melbourne, VIC 8001, Australia

nicola.Yelland@vu.edu.au

Abstract. The negotiation in general sense, as one of the most fundamental and powerful interaction of human beings, represents the dynamic process of ex-changing information and perspectives towards mutual understanding and agreements. Interest based negotiation allows negotiators to discuss the concerns behind the negotiation issues so that a mutually acceptable win-win solution is more likely to be reached. This paper, for the first time, proposes a computational model for interest based negotiation automation which enables the automation of the fundamental elements of negotiation. Based on the model, algorithms are designated to automate the fundamental elements with practical computational complexity. This model provides not only a theoretical founda-tion for software agent based negotiation automation, but also a practical approach.

1 Interest Based Negotiation

Negotiation, as one of the most fundamental and powerful interaction, represents comprehensive human interactive activities, varying from simple information inter-changes, to cooperation and coordination, in wide areas including education, business process, entertainment and other social activities. Similar as Information Systems which free people from the repeated or routine works, negotiation automation is able to free people from tedious interactions including both trivial actions, e.g. selection of a new laptop computer for purchase, and complex tasks, e.g. supply chain manage-ment, learning path selection and composition of interactive movies.

The traditional negotiation is Position Based Negotiation (PBN). In a PBN, the in-volved parties are firmly committed to their bargaining positions. They exchange proposals and counter proposals in the anticipation that one or more parties will com-promise to achieve a settlement of the dispute. It is also know as win-lose negotiation. A position of a negotiation party tells others what he/she wants, and reflects his/her

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point of view on a certain issue. It does not tell others about the complex decision making process that lead to the position; nor does it provide others the opportunity to take his/her interests into account. In position based negotiation, the involved parties argue only their positions. Their underlying interests may never be explicitly men-tioned. If no agreement on the positions, the negotiation fails.

Interest Based Negotiation (IBN) [1] is a process that seeks to discover and satisfy the underlying interests of parties rather than to meet the stated positions or demands that they bring to negotiation. It is also known as win-win negotiation. Interests of a negotiation party tell others why he/she wants something. They reflect his/her under-lying concern, needs or desire behind an issue. In interest based negotiation, the inter-ests of participants are identified and explored, which helps them to understand the others' perspectives instead of simply reacting to the positions. By discussing the reasons behind the positions, mutually acceptable agreement is more likely to be reached. Interest based negotiation is therefore not only a much more powerful tool for conflict resolution, but also a good tool for coordination and cooperation.

For example, both party A and party B want to buy a same land. The position of each party is to have the land. There is no settlement in PBN unless one party gives in. Though, the underlying reason for having the land could be that, party A, as an international company, wants to have a local office in that location, and party B, as a real estate developer, wants to generate income by building something on the land for sale. Using IBN, the agreement could be that, B builds an office block and sells to A.

Software (intelligent) agent, as a new type of autonomous components for con-struction of open, complex and dynamic systems, is one of the most suitable software entities to carry out negotiation automation. In fact, software agent based negotiation automation has gained increasing prominence. On the other hand, agent community also takes negotiation as a core part of agent interactions. Some negotiation defini-tions are even presented in software agent context. For example, Jennings et al.[2] defined negotiation as the process by which a group of agents try to come to a mutu-ally acceptable agreement on some matter. Negotiation underpins attempts to cooper-ate and coordinate and is required both when the agents are self interested and when they are cooperative. However, these pioneer work limits at introducing negotiation into computer science or software agent literature. They remain at a high level of abstraction, which lack of theoretical foundation for turning this opportunity into reality.

The research of negotiation automation in software agent community can be cate-gorized into three main approaches: game theoretic approach [3][4], heuristic approach [5][6] and argumentation-based approach [7][8]. The game theoretic approach models a negotiation situation as a game, and attempts to find dominant strategies for each participant by applying game theory techniques. The heuristic-based approach models agents’ decision making heuristically during the course of the negotiation. In both of the approaches, negotiators are not allowed to exchange additional information other than the proposal. This is a restriction on supporting general negotiations especially when the participants have limited information about the environment, or when their decisions depend on those of the others.

The Argumentation-Based approach allows agents to exchange additional informa-tion such as justifications, critiques, and other forms of persuasive information within the interactions. It enables agents to gain a wider understanding of their counterparts,

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thereby make it easier to resolve certain conflicts, for an instance, conflicts due to incomplete knowledge. This approach has been advocated as a promising means of resolving conflicts within agent societies. For example, Rahwan et al [9] tried to equip intelligent agents with the ability to conduct interest based negotiation using argumen-tation based approach. They studied the relationships between agent’s goals and the types of arguments that may influence other agents' decision, as well as defined a set of locutions that can be used in the negotiation procedure.

Overall, the existing literature in argumentation based negotiation automation re-mains at a high level discussion. Theoretical foundation has not yet been reported towards the realization of negotiation automation. For example, there is no research to automatically generate the arguments for the process of interest based negotiation. This paper proposes a general computational model for negotiation automation, based on which, algorithms are proposed to automate the process. The rest of the paper is organized as the follows. Section 2 proposes the general computational model for interest based negotiation automation. Section 3 are the algorithms to automate the negotiation. Section 4 illustrates the approach with a case study and Section 5 con-cludes the paper.

2 Computational Model of Interest Based Negotiation

The Computational Model of Interest Based Negotiation (CMIBN) proposed in this section is a generic conceptual model representing the core parts of negotiation in a form that can be feasibly realized by computing techniques. It includes belief base, plan base, reasoning engine and negotiation engine. The CMIBN is defined as CMIBN = <B b , P b , R e , Ne >, Ne = <PJG, CD, R, A>, where B b is the belief base, P b is the plan base, R e is the reasoning engine and Ne is the negotiation engine.

Fig. 2.1. Computational model of interest based negotiation

In the CMIBN, each party negotiates according to the reasoning over his/her belief and plan. Fig. 2.1 illustrates the architecture of the CMIBN, followed by details.

Belief base is the knowledge base of the negotiator. It can be defined by a set of rules.

Belief Base

Plan Base

Reasoning Engine

Negotiation Engine

PJG CD R A

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Plan Base keeps the knowledge about how to achieve each position. In the Plan Base, each plan is defined by a set of organized actions to be performed towards a position. Plan base and the corresponding negotiation will be covered by a separate paper.

Reasoning Engine, based on the needs of the negotiation and the Belief Base, gen-erates negotiation positions and makes selections among different positions to pursue.

Negotiation Engine, with the support of the Reasoning Engine, manages the nego-tiation process and generates the negotiation related arguments automatically. It has four components, namely, PJG – Proposal and Justification Generation; CD- Conflict Discovery; R – Recommendation; A – Adjustment.

<1> PJG, proposal and justification generation: To make proposal and provide justifications (reasons) for the proposal.

<2> CD, conflict discovery: To find the conflicts between the participants. By questioning the justifications behind the proposal (such as giving proof of incorrect information used), one party can persuade the other party to change the decision.

<3> R, recommendation: To recommend alternative solutions and provide justi-fications for a new solution. If the alternative option is more attractive to the counterparties, the counterparties may change the original decision.

<4> A, adjustment: To revise its knowledge base to incorporate new informa-tion obtained from the counterparties during the negotiation process. The negotiation process is also the process for the participants to gain more complete information about the environment.

For example, the PJG of a personal agent (A1) can make a proposal “Book a next Monday ticket of Air China from Melbourne to Shanghai” to a travel agency’s agent (A2), with the justification “I would travel to Shanghai on Monday. Air China has directly flight from Melbourne to Shanghai”. The CD of A2, for an instance, provides information that “Air China does not have direct flight from Melbourne to Shanghai on next Monday”. This can persuade A1 to change proposal. Alternatively, compo-nent R of A2, for an instance, makes recommendation “Book a ticket of Qantas Air-line from Melbourne to Shanghai on next Monday” with the justification “Qantas Airline flies from Melbourne to Shanghai on Monday”. In the negotiation process, A1 acquires new information that Qantas Airline flies from Melbourne to Shanghai on Monday while Air China does not. The component A of A1 may adjust its belief base accordingly.

3 Interest Based Negotiation Automation

Interest based negotiation is to solve conflicts by discussing the underlying reasons behind the positions and seek alternative solutions. The conflicts may be due to some conflicting belief or contention on the resources while perusing the position. It can be therefore categorized into two types of negotiation: belief negotiation and plan nego-tiation, to address the different types of conflicts. For example, the father of a kid believes that the happiness of his child relies on the success of his career, which leads to a high requirement on the kid’s school performance. The mother of the kid how-

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ever, believes that the happiness of her child comes from the freely growth with little pressure. This is a belief conflict. On the other hand, if there is no belief conflict. Both of the father and mother believe that they should spend a good amount of time with their kid. They can still have conflicts for example how to arrange their time. This becomes a plan conflict. This paper focuses on the belief negotiation and leaves plan negotiation to another report.

The belief conflicts are normally due to the incomplete or incorrect knowledge of the environment. Through argumentation, negotiation parties may form a more com-plete and accurate understanding of the environment. Agreement between negotiators could be possibly reached through the decision making on the new belief.

To automate interest based negotiation, a key issue is to automate the arguments generation for the basic components of the negotiation engine, namely, proposal gen-eration, conflict discovery, recommendation and adjustment.

The rest of the paper considers belief base as a set of rules in propositional logic. Namely, given a language L of propositional logic with finite variable set U, a belief base is a finite set of propositional formulas in L. Every u∈U is an atom, and any atom or negated atom is a literal. We use “~” to denote negation. We consider the case that all formulas are disjunction of two literals, i.e. in the form of x∨ y (or ~ x y), where x, y are literals (If a formula is a fact x, it can be represented in the form of x ∨ x for consistency). Usually the belief of negotiators can be represented as the “IF … THEN …” format. For example, a young man believes that to become a software engineer, he needs to have a software engineering degree, hence he should enter a university. His belief can be modeled as: become a software engineer

have a software engineering degree, have a software engineering degree enter a university.

3.1 Conflict Discovery

In the interest based negotiation process, if the participants have conflicts in their posi-tions, they may exchange the justifications (set of rules used in the reasoning process) leading to the position. One party may start the conflict discovery process, trying to break the logic flow in other parties’ justifications. Obviously, a computational model of conflict discovery is fundamental to automate interest based negotiation.

Identifying the apparent conflict, e.g. party A believes “Pre-school children can study math” while party B believes “pre-school children cannot study math”, is easy. However, it is not easy to discover the implied conflicts caused by steps of deduction over a large amount of rules among the negotiation parties. This sub-section presents the Conflict Discovery Algorithm, as a fundamental enabling component, to discover conflicts of two parties automatically.

The Conflict Discovery Algorithm of a negotiation party takes one rule from the opposing party’s justification, generates a proof (knowledge subset) of the negation of that rule automatically. If such a proof exists, the arguments of proof can be passed to the counterpart as a challenge to its justification.

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Definition 3.1. Graph Representation of a Formula Set: For a formula set S={x1∨y1, x2∨y2, …, xn∨yn}, let U={ u1, u2, …, um} be the atom set of S. A graph G=(V, E) is defined as the graph representation of S, where

V={ ui, ~ ui | 1≤ i ≤ m}, E={( ~ xi , yi ), (~yi , xi )| xi ∨ yi ∈ S, 1≤ i ≤ n}.

Algorithm 3.1. Conflict Discovery Algorithm (CDA) Input: Formula p=x0∨y0 // a rule from the opposing party Formula set S={ x1∨y1, x2∨y2, …, xn∨yn}

// belief base of the negotiator, or the subset of the belief base relevant to p. Let U={ u1, u2, …, um} be the atom set of S∪{p}

Output: If there is formula subset S’⊂S such that S’ ⇒ ~p , output S’. Otherwise output “no proof”.

(1) Construct a graph G=(V, E) corresponding to S∪{p}, where, V={ ui, ~ ui | 1≤ i ≤ m} E={( ~ xi , yi ), (~yi , xi )| xi ∨ yi ∈ S∪{p}, 0≤ i ≤ n}

(2) If there is no ui ∈U such that there are directed paths from ui to ~ ui and from ~ ui to ui (directed closed walks containing ui and ~ ui), return “no proof”.

(3) Let E’ be the directed closed walk containing ui and ~ ui found in (2) Let S’={(x ∨ y)| (~x, y) ∈E’}-{ x0∨y0 }, return S’ // the proof for ~p

Computational Complexity Analysis of Conflict Discovery Algorithm In the CDA algorithm, step (1) has complexity of O(m+n). In step (2), the directed path from one vertex to another can be found using DFS algorithm in time O(m+n). At most m atoms in U are tested, which gives the complexity of O(m(m+n)). Step (3) has complexity of O (n). So the algorithm can be implemented in an order of O(m(m+n)). Theorem 3.1 There are conflicts between a rule and a belief base if and only if the algorithm CDA presents a proof for the negation of the rule.

Proof According to CDA, if the ui exists, there are directed paths from ui to ~ ui and vice versa, each of these directed closed walks provides evidence that S∪{p} is unsaitisfi-able[10], which is a resolution refutation for S∪{p}[11]. If S is consistent and there is a resolution refutation for S∪{p}, S ⇒ ~p [12]. In other words, S’ ⇒ ~p, S’ is the proof for ~p. If there is no such ui exists, S∪{p}is consistent[10] and no proof for ~p.

3.2 Recommendation

The belief bases regulate the behavior of the involved parties in an automated negotia-tion process. Based on the belief base, each party makes proposals to others. If they cannot reach an agreement, one party may try to persuade the other parties to change their minds by recommending alternative solutions. If the alternative solution is more attractive, the opposing party may change the original position. This process is a fun-damental component of interest based negotiation: recommendation. The following result is to enable the automation of recommendation.

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Definition 3.2.1. Transitive Closure: Let G be a directed graph with n vertices. The transitive closure of the adjacency matrix of G is an n×n matrix A, where

⎪⎩

⎪⎨⎧ =

=otherwise

jtoivertexfrompathdirectedaexiststhereorjijiA

,0

,1],[

Definition 3.2.2. Matrix Representation of a Formula Set: Suppose G is the graph representation of a formula set S, A is the transitive closure of the adjacency matrix of graph G. A is called the Matrix Representation of S.

The computational model of recommendation automation proposed in this paper is called Belief Base Matrix (BBM). The idea behind BBM is as follows. If A[i, j] =1, there exists a path from i to j . That is, j can be derived from i by applying the formu-las following the order they appear in the path. So the matrix representation can be used as a model for the reasoning process of recommendation. It can be stored and reused until the belief base is revised.

In the follows, the Belief Base Matrix Algorithm is to compute the matrix repre-sentation of a belief base. The recommendation automation is then modeled by the Recommendation Algorithm. Given one interest from the other party, the algorithm will automatically generate the recommendation and the justification based on its knowledge (the belief base matrix).

Algorithm 3.2.1. Belief Base Matrix Algorithm (BBMA) Input: Formula set S={ x1∨y1, x2∨y2, …, xn∨yn} // S is consistent

Let U={ u1, u2, …, um} be the atom set of S Output: The matrix representation of S. (1) Construct a graph G=(V, E) corresponding to S, where,

V={ ui, ~ ui | 1≤ i ≤ m} also noted as V={v1, v2, …v2m} E={( ~ xi , yi ), (~yi , xi )| xi ∨ yi ∈ S , 1≤ i ≤ n}

(2) // Construct the transitive closure of the adjacency matrix of graph G. For each vi , vj ∈ V do If (vi , vj )∈E or vi = vj then A0[vi , vj]=1 Else A0[vi , vj ]=0

End For For k 1 to 2m do

For each vi , vj ∈ V do Ak [vi , vj]= Ak-1 [vi , vj] + Ak-1 [vi , vk] · Ak-1 [vk , vj]

// “·”and “+”are logic multiplication and logic addition End For

End For Return A2m // A2m is the matrix representation of S.

Computational Complexity Analysis of BBMA In the algorithm BBMA, step (1) can be finished in O(m+n) time and the complexity order of step (2) is O(m3). So the complexity of the algorithm is O(m3+n).

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Algorithm 3.2.2. Recommendation Algorithm (RA) Input: Literal v // interest of the opposing party

Formula set S={ x1∨y1, x2∨y2, …, xn∨yn} // belief base, consistent Let U={ u1, u2, …, um} be the atom set of S Matrix A // matrix representation of S Graph G // graph representation of S

Output: Recommendation vr, formula set S’⊂S if S’∪{v}⇒ vr and vr is preferable for itself. Otherwise output “no recommendation”.

(1) If v ∉U and ~v ∉U Then return “no recommendation”. // no relevant information about v according to its knowledge

(2) Let R={ v’ | A [v , v’] =1, v’ ≠ v } If R= { } then return “no recommendation” .

(3) Select vr ∈R as recommendation // R is the set of results can be derived from v, i.e. the set of recommendation // the designation of selection strategy is not a focus of this paper Find a path E’ from v to vr in G Let J={(~vi ∨ vj )| (vi , vj ) ∈E’} , // J is the justification of vr

Return “recommendation:”+ vr + “, its justification: ” + J Computational Complexity Analysis of RA In the algorithm, step (1) and step (2) can be finished in O(m) time. In step (3) the path can be found using DFS algorithm in O(m+n) time, J can be constructed in O(n) time, thus step (3) can be finished in O(m+n) time. So the complexity of the algorithm is O(m+n).

3.3 Proposal and Justification Generation

As proposal generation is a similar process as recommendation, it is omitted in this paper.

3.4 Adjustment

Upon receiving the new knowledge from other parties (for example, new knowledge comes from the proof of a conflict, or the justification of a recommendation), a nego-tiator will exam the new knowledge and adjust its belief, i.e revise its belief base to incorporate the new knowledge. From the adjusted belief base, he/she may make new decision (new positions).

To revise the belief base, the negotiator needs to add new knowledge, remove or modify the old knowledge in the belief base, and keep the consistency at the same time. The relationship among knowledge could be very complicated, which makes the detecting and eliminating inconsistency difficult. Similar to conflict discovery, all the apparent and implied inconsistency are to be addressed. In general, revising a knowl-edge base to incorporate new knowledge is not tractable [13].

Most of the time, different rules in a knowledge base are of different impor- tance. For instance, if the new formula is more certain than others, the least certain

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inconsistent knowledge can be dropped. Alternatively, formulas may also be ordered according to their arrival time in the knowledge base. Then the oldest inconsistent knowledge might be rejected in order to restore consistency.

Based on prioritized knowledge base, it is possible to automate the adjustment process with polynomial complexity algorithms [14]. The detailed result will be re-ported separately.

4 Case Study

Suppose X is a company in the manufacturing industry. It has strong intention to improve its competency in the global market. X believes that developing new prod-ucts and increasing productivity are the steps to improve competency. To increase productivity, X believes it needs to extend working hours, thus needs to update prod-uct line hardware. The belief base of company X can be represented as:

Bb(X)={a1, a1 a2, a1 a3, a3 a4, a4 a5, a6 a7 } , where

a1: improve competency a2: develop new products a3: increase productivity a4: extend working hours a5: update product line hardware a6: improve efficiency a7: update product line software

The belief base can also be represented as

Bb(X)={a1∨ a1, ~ a1∨ a2, ~ a1∨a3, ~ a3∨a4, ~ a4∨ a5, ~ a6 ∨ a7 },

which is a rule set where negotiation automation algorithms proposed in Section 3 apply.

Suppose Y is a computer company specialized in manufacturing software. Y be-lieves that encouraging organizational learning through knowledge management sys-tems is an excellent way to improve the competency of an organisation. It is currently promoting its knowledge management products. The belief base of Y can be repre-sented as:

Bb(Y)={a1, a1 a2, a1 a3, a1 a8, a8 a9, a3 a6, a4 ~a6}.

Or

Bb(Y)={a1∨ a1, ~ a1∨ a2, ~ a1∨a3, ~ a1∨ a8, ~ a8∨ a9, ~ a3∨a6, ~ a4∨ ~ a6},

where a8: encourage organizational learning a9: adopt knowledge management systems

4.1 Making Proposal

X wants to improve the competency, based on its belief {a1, a1 a3, a3 a4, a4 a5}, it makes a proposal a5, that is to buy new product line hardware. Proposal genera-tion is similar to recommendation generation, the detailed procedure is omitted here.

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4.2 Conflict Discovery

Company Y does not have the product line hardware X wants. No agreement can be reached upon this position. After knowing the reason behind X’s position, Y can gen-erate recommendation to X, or provide proof to challenge X’s justification. The automation of generating a proof to challenge a3 a4 in Bb

(X) is illustrated here. The recommendation will be covered in Section 4.3.

The graph representation of Bb(Y) ∪ {a3 a4} is

Fig. 4.2.1. Graph representation of Bb(Y) ∪ {a3 a4}

There is a directed closed walk containing a3 and ~ a3: a3 a4 ~ a6 ~ a3 ~ a1 a1 a3

The logic proof for ~ (a3 a4) is {a4 ~ a6, a3 a6, a1 a3, a1}. The interpretation is that:

increase productivity improve efficiency (a3 a6) , improve efficiency ~ extend working hours (a4 ~ a6 i.e. a6 ~ a4) ,

It tells that productivity can not be increased by extending working hours. This pro-vides a proof to challenge X’s justification a3 a4 for the position to purchase prod-uct line hardware.

4.3 Recommendation

Algorithm BBMA automatically creates the matrix representation of Y’s belief base. The matrix is omitted here due to the restriction of length. Based on the matrix, algorithm RA finds all the results that can be derived from the interest a1 (to improve competency). Among them a9 (adopt knowledge management system) is what Y is promoting.

The path a1 a8 a9 tells that adopting knowledge management systems can also improve the competency, so Y recommends X to buy the knowledge manage-ment system products. If X is satisfied with the recommendation and persuaded by the justification, it will accept the recommendation. Then agreement is reached.

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4.4 Adjustment

X receives the new knowledge during the recommendation or conflict discovery proc-ess from Y, for example, a1 a8, a8 a9, a3 a6, a4 ~ a6. It may store them in a temporary place. If some knowledge appears repeatedly or come from a trust party, X may initiate the adjustment process. Suppose X is going to add {a3 a6, a4 ~ a6} to its belief base, and give them the highest priority. The challenged knowledge a3 a4 is given the lowest priority. After the adjustment the belief base becomes1:

Bb(X)={a3 a6, a4 ~ a6, a1, a1 a2, a1 a3, a4 a5, a6 a7 }

In a later stage, if X wants to improve its competency, probably it will make a new proposal a7 (update product line software) based on the belief { a1, a1 a3, a3 a6, a6 a7 }.

5 Conclusion and Future Work

This paper proposed a computational model for interest based negotiation automation. The negotiation studied in this paper is in general sense, which includes general proc-esses of exchanging information and perspectives towards mutual understanding and agreements. It represents wide range of activities in most areas that involves dynamic interactions, including education, organisation management, cooperation, commerce and business.

As interest based negotiation allows involved parties to dig into the reasons be-hind their positions, it is much more powerful and constructive than position based negotiation. It therefore has raised significant attention in various communities including researchers. However, the existing literature is largely limited at high level discussions. This paper addresses the challenge by proposing a computational model of interest based negotiation, including algorithms for the main negotiation automation elements, namely proposal generation, conflict discovery and recom-mendation for belief negotiation. A case study has illustrated how interest based negotiation automation can be feasibly carried out by computational entities, e.g. software agents. Due to the limitation of length, plan negotiation will be reported in a separate paper.

References

1. Fisher, R., Ury, W.: Getting to Yes: Negotiating Agreement without giving in. Penguin boks, new york (1983)

2. Jennings, N.R., Faratin, P., Lomuscio, A. R., Parsons, S., Sierra, C., Wooldridge, M.: Automated Negotiation: Prospects, Methods and Challenges. Int. Journal of Group Deci-sion and Negotiation, Vol. 10, No. 2 (2001) 199–215

3. Hu, W. B., Wang, S. M.: Research on the Negotiation Mechanism of Multi-agent System Based on Game Theory. Proceedings of the Ninth International Conference on Computer Supported Cooperative Work in Design, Vol. 1 (2005) 396 – 400

1 The justification automation will be covered by a separate report.

222 X. Tao et al.

4. Chen, J. H., Chao, K. M., Godwin, N., Reeves, C., Smith, P.: An Automated Negotiation Mechanism Based on Co-evolution and Game Theory. Proceedings of the 2002 ACM symposium on Applied computing (2002) 63 - 67

5. Faratin, P., Sierra, C., Jennings, N.R.: Using Similarity Criteria to Make Issue Trade-offs in Automated Negotiations. Journal of Artificial Intelligence, Vol. 142, No. 2 (2002) 205-237

6. Jonker, C., Robu, V.: Automated Multi-Attribute Negotiation with Efficient Use of In-complete Preference Information. Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems (2004) 1054-1061

7. Karunatillake, N.C., Jennings, N.R., Rahwan, I., Norman, T.J.: Argument-based Negotia-tion in a Social Context. Proceedings of the fourth international joint conference on Autonomous agents and multiagent systems (2005) 1331-1332

8. Rahwan, I., Ramchurn, S.D., Jennings, N.R., McBurney, P., Parsons, S., Sonenberg, L.: Argumentation-based Negotiation. The Knowledge Engineering Review, Vol.18, No.4 (2004) 343-375

9. Rahwan, I., Sonenberg, L., Dignum, F.: On Interest Based Negotiation. Lecture Notes in Computer Science, Springer-Verlag, Vol. 2922 (2004) 383-401

10. Aspvall, B., Plass, M., Tarjan, R.: A Linear-time Algorithm for Testing the Truth of Cer-tain Quantified Boolean Formulas. Information Processing Letters (1979) 121-123

11. Subramani, K.: Optimal Length Tree-Like Resolution Refutations for 2SAT Formulas. ACM Transactions on Computational Logic, Vol.5, No.2 (2004) 316-320

12. Robinson, J.A.: A Machine-oriented Logic Based on the Resolution Principle. Journal of the ACM, Vol. 12 (1965) 23-41

13. Eiter, T., Gottlob, G.: On the Complexity of Propositional Knowledge Base Revision, Up-dates, and Counterfactuals. Artificial Intelligence, Vol. 57, No. 2-3 (1992) 227-270

14. Tao, X. H., Sun, W., Ma, S. H.: A Practical Propositional Knowledge Base Revision Algo-rithm. Journal of Computer Science and Technology, Vol.12, No.2 (1997) 154-159