Dispute Resolution Using Argumentation-Based Mediation
Mediation is a process, in which both parties agree to resolve their dispute by negotiating over alternative solutions presented by a mediator. In order to construct such solutions, mediation brings more information and knowledge, and, if possible, resources to the negotiation table. The contribution of this paper is the automated mediation machinery which does that. It presents an argumentation-based mediation approach that extends the logic-based approach to argumentation-based negotiation involving BDI agents. The paper describes the mediation algorithm. For comparison it illustrates the method with a case study used in an earlier work. It demonstrates how the computational mediator can deal with realistic situations in which the negotiating agents would otherwise fail due to lack of knowledge and/or resources.
1 Introduction and Motivation
Dispute resolution is a complex process, depending on the will of involved parties to reach consensus, when they are satisfied with the result of negotiation, which allows them to partially or completely fulfil their goals with the available resources. In many cases, such negotiation depends on searching for alternative solutions, which requires an extensive knowledge about the disputed matter for sound argumentation. Such information may not be available to the negotiating parties and negotiation fails. Mediation, a less radical alternative to arbitration, can assist both parties to come to a mutual agreement. This paper presents an argumentation-based mediation system that builds on previous works in the field of argumentation-based negotiation. It is an extension of the work presented in [Parsons1998] and focuses on problems where negotiation stalled and had no solution. In [Parsons1998] agents contain all the knowledge and resources needed to resolve their dispute - a relatively strong assumption in the context of real world negotiations. Agents present arguments, which their opponent can either accept, reject, or they can negotiate on a possible solution. As mentioned earlier, lacking knowledge or resources may lead to an unsuccessful negotiation. In many cases, such knowledge or even alternative resources may be available, but agents are not aware of them.
Our extension proposes a role of a trust-worthy mediator that possesses extensive knowledge about possible solutions of mediation cases, which it can adapt to the current case. Mediator also has access to various resources that may help to resolve the dispute. Using this knowledge and resources, as well as knowledge and resources obtained from agents, the mediator creates alternative solutions, which become subject to further negotiation.
In the next section, we summarise related work in the field of automatic mediation and argumentation-based negotiation. In Section 3, we recall the agent architecture proposed by Parsons et al. [Parsons1998] and extend it with the notion of resources for the purposes of the mediation system. Section 4 presents our mediation algorithm. In Section LABEL:section:example, we revisit the home improvement agents example from [Parsons1998] and apply our mediation process. Section LABEL:sec:conclusion concludes this work.
2 Previous Work
Computational mediation has recognized the role of the mediator as a problem solver. The MEDIATOR [Kolodner1989] focused on case-based reasoning as a single-step for finding a solution to a dispute resolution problem. The mediation process was reduced to a one-step case-based inference, aimed at selecting an abstract “mediation plan”. The work did not consider the value of the actual dialog with the mediated parties. The PERSUADER [Sycara1991] deployed mechanisms for problem restructuring that operated over the goals and the relationships between the goals within the game theory paradigm, applied to labor management disputes. To some extent this work is a precursor of another game-theoretic approach to mediation, presented in [Wilkenfeld2004] and the interest-based negotiation approach in [Rahwan2009b]. Notable are recent game-theoretic computational mediators AutoMed [Chalamish2012] and AniMed [Lin2011a] for multi-issue bilateral negotiation under time constraints. They operate within known solution space, offering either specific complete solutions (AutoMed) or incremental partial solutions (AniMed). Similar to the mediator proposed in the ‘curious negotiator’ [Simoff2002], both mediators monitor negotiations and intervene when there is a conflict between negotiators. The Family_Winner [Bellucci2005] manipulative mediator aimed at modifying the initial preferences of the parties in order to converge to a feasible and mutually acceptable solution. This line of works incorporated “fairness” in the mediation strategies [Abrahams2012].
In real settings information only about negotiation issues is not sufficient to derive the outcome preferences [Visser2011]. An exploratory study [Schei2003] of a multiple (three) issue negotiation setting suggests the need for developing integrative (rather than position-based) negotiation processes which take into account information about the motivational orientation of negotiating parties. Incorporation of information beyond negotiation issues has been the focus of a series of works related to information-based agency [Debenham2004, Debenham2006, Sierra2007]. Value-based argumentation frameworks [Bench-Capon2003], interest-based negotiation [Rahwan2009b] and interest-based reasoning [Visser2011] considers the treatment of any kind of motivational information that leads to a preference in negotiation and decision making.
In this paper we propose a new mechanism for automatic mediation using argumentation-based negotiation (ABN) as a principal framework for mediation. ABN systems evolved from classical argumentation systems, bringing power to agents to resolve potential dispute deadlocks by persuasion of agents in their beliefs and finding common acceptance grounds by negotiation [Sycara1990, Parsons1998, kakas2006, Rahwan2003]. ABN is performed by exchanging arguments, which represent a stance of an agent related to the negotiated subject and constructed from beliefs of the agent. Such a stance can support another argument of the agent, explain why a given offer is rejected, or provide conditions upon which the offer would be accepted. Disputing parties can modify their offer or present a counter-offer, based on the information extracted from the argument. Arguments can be used to attack [Dung1995] other arguments, supporting or justifying the original offer. With certain level of trust between negotiating agents, arguments serve as knowledge exchange carriers [Parsons1998] - here we use such mechanisms to exchange information between negotiating parties and the mediator. The decision of whether to trust the negotiating party or not is a part of the strategy of an agent. Different strategies are proposed in [Hadidi2011, Dung2008, Dijkstra2007]. Apart from the strategy, essential are the reasoning mechanisms and negotiation protocols. Relevant to this work are logic frameworks that use argumentation as the key mechanism for reasoning [Krause1995, Prakken1997, Dung2006, Oren2007]. Negotiation protocols, which specify the negotiation procedures include either finite-state machines [Parsons1998], or functions based on the previously executed actions [Amgoud2007]. The reader is referred to [Rahwan2009] for the recent state-of-the-art in ABN frameworks.
Our ABN framework for mediation allows us to seamlessly design and execute realistic mediation process, which utilises the power of argumentation, using agent logics and a negotiation procedure to search for the common agreement space. We have decided to extend the ABN framework in [Parsons1998], due to the clarity of its logics. In the next section we recall the necessary aspects of the work in [Parsons1998]. We describe the agent architecture in the ABN systems and define the components that we reuse in our work. Our agents reason using argumentation, based on a domain dependent theory specified in a first-order logic. Within the theory, we encode agent strategies, by defining their planning steps. Apart from agent theories, strategy is defined also in bridge rules, explained further in the text. We do not explore a custom protocol, therefore we adopt the one from [Parsons1998].
3 Agent Architecture
The ABN system presented in [Parsons1998] is concerned with BDI agents in a multi-context framework, which allows distinct theoretical components to be defined, interrelated and easily transformed to executable components. The authors use different contexts to represent different components of an agent architecture, and specify the interactions between them by means of the bridge rules between contexts. We recall briefly the components of the agent architecture within the ABN system in [Parsons1998] and add a new “resources” component for mediation purposes.
Units are structural entities representing the main components of the architecture. There are four units within a multi-context BDI agent, namely: the Communication unit, and units for each of the Beliefs, Desires and Intentions. Bridge rules connect units, which specify internal agent architecture by determining their relationship. Three well-established sets of relationships for BDI agents have been identified in [Rao1995]: strong realism, realism and weak realism. In this work, we consider strongly realist agents.
Logics is represented by declarative languages, each with a set of axioms and a number of rules of inference. Each unit has a single logic associated with it. For each of the mentioned B, D, I, C units, we use classical first-order logic, with special predicates B, D and I related to their units. These predicates allow to omit the temporal logic CTL modalities as proposed in [Rao1995].
Theories are sets of formulae written in the logic associated with a unit. For each of the four units, we provide domain dependent information, specified as logical expressions in the language of each unit.
Bridge rules are rules of inference which relate formulae in different units. Following are bridge rules for strongly realist BDI agents:
Resources are our extension of the contextual architecture of strongly realist BDI agents. Each agent can possess a set of resources with a specific importance value for its owner. This value may determine the order in which agents are willing to give up their resources during the mediation process. We define a value function , which for each resource specifies a value , . Set is ordered according to function .
Units, logics and bridge rules are static components of the mediation system. All participants have to agree on them before the mediation process starts. Theories and resources are dynamic components, they change during the mediation process depending on the current state of negotiation.
4 Mediation Algorithm
In a mediation process both parties try to resolve their dispute by negotiating over alternative solutions presented by a mediator. Such solutions are constructed, using available knowledge and resources. Agent knowledge is considered private and is not shared with the other negotiating party. Resources to obtain alternative solutions may have a high value for their owners or be entirely missing. Thus, we propose that the role of the mediator is to obtain enough knowledge and resources to be able to construct a new solution. The mediator presents a possible solution to agents (in the form of an argument), which they either approve, or reject (attack). Parties can negotiate over a possible solution to come to a mutual agreement. Below we formally define the foundations of our algorithm.
is a set of formulae in language . An argument is a pair , and such that: (1) ; (2) ; and (3) is a minimal subset of satisfying 2.
A mediation game is executed in one or more rounds, during which both mediator and agents perform various actions in order to resolve the dispute. Algorithm LABEL:algorith:mediation contemplates our proposal of the mediation game. In the beginning of each round, agents and have an opportunity to present new knowledge to the mediator . This new knowledge is helping their case, or helping to resolve the dispute. Agents can either present knowledge in the form of formulas from their theory or new resources. Resources can be presented in ascending order of importance, one resource in each round or altogether, depending on the strategy of agents. The mediator obtains knowledge by executing function , where . The mediator incorporates knowledge into theory , obtaining . Please note, that the belief revision operator is responsible for eliminating conflicting beliefs from the theory. Using the knowledge in , the mediator tries to construct a new by executing the function. If the does not exist and agents did not present new knowledge in this round, mediation fails. Therefore, it is of utmost importance that agents try to introduce knowledge in each round. In the next step, the possible outcomes are: