The Argumentative Mediator

The Argumentative Mediator Carles Sierra1(B) , Ramon Lopez de Mantaras1 , and Simeon Simoff2 1 Artificial Intelligence Research Institute (IIIA-CSIC), Barcelona, Spain {sierra,mantaras}@iiia.csic.es 2 Western Sydney University, Sydney, Australia [email protected] Abstract. In this paper we introduce a negotiation mediator in a multiagent context. When negotiation fails, a mediator can interact with the parties, find out about their goals, ontologies, and arguments for and against negotiation outcome, and suggest solutions based on previous experience. An algorithmic schema to be instantiated with particular argumentation, semantic alignment and case-base reasoning techniques is presented. The proposal is neutral with respect to which particular technique is selected. An example illustrates the approach that is framed in the existing body of literature on argumentation and mediation. 1 Introduction Achieving an agreement in disputes and deals is a process by which two or more parties reach a mutually acceptable outcome. The focus of this work is in consensual dispute resolution, where the parties themselves make the decision about the process and the outcome. Among the consensual dispute resolution processes, this work addresses mediation – the confidential process where an independent and neutral third party assists the disputants to negotiate and reach a decision about their dispute. Unlike arbitration or expert appraisal, the mediator cannot impose a binding solution upon the parties.1 However, if the parties do not reach a solution and a case goes to an arbitration, the documented intermediate solutions and parties positions through the mediation process can be provided in assistance to the arbitration process. Through problem interpretation and reframing capabilities as well as through various facilitation strategies and procedures, mediators are able to assist negotiating parties to explore the negotiation issues in depth and reach acceptable joint decisions, in many cases, among the best feasible solutions that benefit all negotiating parties under the given circumstances. The long term goal of this work targets the integrative “value creating” mediation strategies [31], which, in addition to interest-based mediation, consider alternative approaches, where the mediator and the parties involved go beyond the “zero sum” view, arguing about the solutions, sometimes reconsidering the original problem in order 1 The Institute of Arbitrators and Mediators: http://www.iama.org.au/mediation. htm. c Springer International Publishing AG 2017  N. Criado Pacheco et al. (Eds.): EUMAS 2016/AT 2016, LNAI 10207, pp. 439–454, 2017. DOI: 10.1007/978-3-319-59294-7 36 440 C. Sierra et al. to create more potential solutions and, if possible, to expand resources under negotiation. In line with the above, from the four categories of contemporary mediation approaches - evaluative, facilitative (also known as interest-based), transformative and narrative [23], we consider transformative (or deliberative) mediation, where the mediator’s function is to persuade disputants to transform their respective perceptions of and responses to the dispute or conflict [23]. The motivation for this work is the transformative view, first expressed in [9], that conflict is primarily related to human interaction rather than just conflict of interests of self-interested individuals, aiming only at maximising their individual gain. In some sense, we view mediation as a process of creating value in disputes in line with [28]. We are further motivated by the developments of the cognitive negotiation theory, which focused on what negotiators are likely to do rather than what they should do [44]. Through the process mediators have to remain neutral and to move parties through various impasse-points in the negotiation. How to get to the “win-win” solution or convince the parties to revisit their stance is the know-how that distinguishes a successful mediation process and a competent mediator. Designing such evolving process is essential for designing a skilful computerised mediator. In [40] we formulated the issues facing the development of an automated mediation agent. The paper formulated the necessary and sufficient conditions for a mediation to take place and demonstrated the validity of those conditions on examples from the area of international relations. The title of the paper — “Mediation = Information Revelation + Analogical Reasoning” summarised, respectively, the two intertwined sets of requirements towards computational automated mediator: (a) capabilities to seek and utilise relevant information, and (b) capabilities to “think out of the box”, i.e. to approach the problem that has stalled negotiation from a fresh perspective, if necessary, reframe it and present to negotiating parties the new solution, possibly unseen by them when remaining within their “original boxes”. Subsequently, the authors have focused on the development of the computational ability to “think out of the box.”2 In Sect. 4 in [40] we have introduced a high level view of the MediaThor mediating agent, which utilises past experiences and information from negotiating parties to mediate disputes and change positions of negotiating parties. The realisation of MediaThor required the specification of the mental models Mt of the agents at time t, introduced in [40] and the mechanisms for aligning of/agreeing on the ontologies of the dispute they used. The architecture of the mediator, presented in [2], implemented MediaThor’s case-based reasoning (CBR) approach to mediation integrating analogical and common sense reasoning, achieving both the ability to utilise experience with cases in different domains and the ability to structurally transform the set of issues of the dispute for a better solution. The above mentioned problem reframing has been implemented as a combination of case-based reasoning and common sense reasoning with structure mapping. 2 Not to be confused with the term “computational thinking” as introduced and discussed in [48]. The Argumentative Mediator 441 This paper continues the development of an automated mediation agent within the ‘curious negotiator’ framework [39]. The automated mediator MediaThor presented in [40] and [2] generates the solution and presents it to the negotiating parties. Both works [2,40] are focused on solution construction aspects of mediation, based on the information revealed by the negotiating agents, including their goals and reservations. An acceptable solution was constructed in a single CBR cycle. What if one of the negotiating agents does not accept the solution proposed by the mediator and argues against it? What if both agents argue against parts of the solution and the mediator has to support the proposed solution with arguments relevant to the stance of each negotiator? These questions, related to the dynamics of the mediation process, were beyond the scope of both works [2,40]. They are the focus of the developments presented in this paper. The contribution of this paper includes the integral analysis of the interplay of mediation and argumentation and the development of a high-level computational model of the transformative mediation process. Specifically, Sect. 3 presents five aspects of mediation, where structured argumentation offers means for realising automated mediation process. These are the overarching five principles for building an automated mediator, which uses argumentation through the mediation process for extracting additional information about the position of the negotiating agents, finding solutions and justifying them. The section then presents the high level modifications of the formal models of negotiating agents and the cases in the case base of the mediating agent, and the suitability of bipolar argumentation frameworks. Sections 4 and 5 present a high level view of the way a computational mediator can use argumentation and a case study which demonstrates how that works. 2 Computational Mediators Early work on computational mediation has recognised the role of the mediator as a problem solver. The MEDIATOR [25,26] focused on case-based reasoning as a single-step for finding a solution to a dispute resolution problem. The casebased cycle of the MEDIATOR operated within a single domain. In the example with the Israel-Egypt dispute, the similarity was sought within political disputes that involved land and military force (see details in [26], p. 512). The selection of the closest case was biased towards the similarity of the arguments thrown in the dispute rather than the object of the dispute. 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. Computational capabilities for problem restructuring in negotiation and mediation has been investigated in [41] as means for manipulating mediated parties in order to change their perceptions of the issues. The PERSUADER operated within the game theory paradigm, applied to labor management disputes. It deployed mechanisms for problem restructuring that operated over the goals and the relationships between the goals. It used means to manipulate the utility 442 C. Sierra et al. values of negotiating parties. To some extent this work is a precursor of another game-theoretic approach to mediation, presented in [47] and the interest-based negotiation approach in [32]. Manipulative mediation of human parties involved in dispute resolution has been attempted in the area of decision support systems. The Family Winner [3] treats the dispute resolution process as a series of “mutual trade-offs” aiming at modifying the initial preferences of the parties in order to converge eventually to a feasible and mutually acceptable solution. Further, this line of works considered the incorporation of the notion of fairness in the mediation strategies [1]. MArCo is a theoretical framework, presented in [42], which stands aside of the mainstream works on computational mediation. It recognises that the computational system has to analyse the ongoing interaction and have the capability to identify a conflict and to mediate it. It does not necessarily aim at achieving conflict resolution per se. MArCo mediation framework is geared towards conflict control strategy, which attempts to reduce the negative consequences of conflict, rather than solely looking for a negotiation outcome that resolves the conflict. The mediator is oriented towards facilitating group development, hence the goal of the mediation is to suggest courses of action that provoke articulation and reflection [42]. Notable is the recent series of publications about the computational mediators AutoMed [13,14] and AniMed [29,30] for multi-issue bilateral negotiation under time constraints. Common to this family of game-theoretic creatures is that the solution space is known and that the mediator can offer either specific complete instances out of this space (AutoMed) or incremental partial solutions which are subsets of the solution set (AniMed). The later offers a better interaction interface. Similar to the mediator proposed in the ‘curious negotiator’ [39], both mediators monitor negotiations and intervene when there is a conflict between negotiators. One of the reasons why negotiation may end up in a need for mediation is that in real settings information only about negotiation issues is not sufficient to derive the outcome preferences [46]. An exploratory study [36] of a multiple (three) issue negotiation setting suggest the need for developing integrative (rather than position-based) negotiation processes which take into account information about 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 [17,18,38] and the LOGIC framework [37]. These works are part of our broader series of works which consider the incorporation of information extracted from the illocutions of the negotiation dialogue as well as information provided by external information mining agents in response to a query from a negotiating agent. The research in value-focused thinking [24], value-based argumentation frameworks [5], interest-based negotiation [33] and interest-based reasoning [46] considers the treatment of information related to the preferences of parties involved in negotiation and decision making, in addition to the concrete negotiable matter (aspect, issue). These are the fundamental objectives, values, concerns, goals and desires, labeled as interests - any kind of motivational information that leads to a preference [46]. The Argumentative Mediator 443 Before getting into the technical aspects, it is worth mentioning that the award of the 2002 Nobel Peace Prize to Jimmy Carter recognises the role of successful mediation in contemporary world.3 Distinct element of Jimmy Carter’s mediation strategies is the intertwining of the settlement-centred strategies, in which the mediator is highly manipulative in order to bring the parties to a resolution, proposed by the mediator, and relationship-centred (transformative) where the mediator assists parties in building mutual trust and understanding, and developing mutually-acceptable solutions on their own. Both types of mediation strategies involve elements of argumentation [35]. 3 Unfolding Argumentation in the Mediation Process Below we consider the aspects of mediation, where computational argumentation offers means for realising computational mediation. I. Mediation is a fluid and evolving process [23]. Argumentation offers the machinery, which will enable the evolution of the process. It is very unlikely that the mediator is an “oracle”, who knows the overall solution set at the beginning of the process. The mediator constructs the alternative solution sets with the help of the information extracted from the interaction with the negotiating parties. In real world a solution may emerge as a result of a change of the problem space. This is in fact what a skilful mediator does. This implies that the mediator will need to convince negotiators that the problem space needs to be and can be changed. II. The mediator should be capable to justify (explain) its suggestions. Argumentation offers such justification mechanism. The approach in mediation can be analogous to the approach developed in argumentation-based machine learning [7], where an inductive learning algorithm is extended to use part of the data to form explanatory arguments for the outputs. III. The mediator should be capable to develop, adjust or extend an agreed ontology. The agreed ontology, established at the beginning of the mediation session, may evolve as a result of the mediation process. Argumentation offers means to justify changes in the agreed ontology. The ontology is both means in the mediation and argumentation process (it is essential in the 3 Though Jimmy Carter as a President launched a number of controversial weapons programs, see “The Nobel Peace Prize 2002 - Presentation Speech.” [http://www. nobelprize.org/nobel prizes/peace/laureates/2002/presentation-speech.html] for the supportive argument about his contribution as a mediator. Whilst Jimmy Carter’s mediation between Israel and Egypt (the Camp David Accords) is a well-known classics, less known are his other numerous successes. For example, in 1994 his mediation resulted in a four-month cease-fire agreement in Bosnia at the height of the ethnic violence in the Balkans, and a pledge from all sides to resume peace talks, which eventually led to a peace agreement between Croatia, Bosnia, and Serbia in 1995. In 2008, his mediation led to the re-establishment in 2009 of relations at the level of charge d’affaires between Colombia and Ecuador. 444 C. Sierra et al. implementation of analogy in [40]) or can be the object of the argumentation when mediator develops the ontology on which both parties agreed, or attempt to change it. IV. The mediator should be capable to extract information (intelligence) and use it in the mediation process. Such information comes from the mediation process and from external sources. Argumentation can provide information about the process, encoded in the arguments, and can trigger external information queries. V. The mediator should be capable to combine different argumentation systems. Each of the negotiators, involved in the mediation process most likely will have, loosely speaking, a collection of arguments in support of their position. If mediation allows argumentation, then the mediator will need to combine these argumentation systems in an argument that supports its proposed solution. We develop further the mediation approach, introduced in [40] and developed further in [2]. In layman terms, the approach views the problem solving process in mediation as a combination of analogous reasoning and information revelation,4 and part of the mediator’s strategy is guiding the process of information revelation. The framework assumes that negotiating agents α and β are willing or are required to achieve a mutually beneficial agreement; that α and β are seeking or will accept mediation; and a mediating agent µ is available, hence, the set of agents involved is A = {α, β, µ}. A mediator analyses the way negotiation parties have built their views on the disputed issues [22], i.e. the sets of arguments or argumentation systems that underpin their respective positions when negotiation stalled. This is in accordance with the view that negotiation can be conceptualised as a problemsolving enterprise in which mental models guide the behaviour of negotiating parties [45]. The mental model5 Mt at time t, introduced in [40], denotes the internal model (representation) of the agent of the problem about which it negotiates. It represents the knowledge of an agent about a dispute, including the arguments that support her stance Γ t ; about the views of the other parties on that dispute that the agent is aware and the expected outcomes. This knowledge is internal to the agent and is being updated as the process progresses, so t will go from t1 when the mediation starts to tn when the mediation ends. At each time instant the ontology, goals and arguments may get modified due to the interaction.6 We thus modify the mental model Mt presented in [2], and 4 5 6 The utilisation of information in negotiation is central to the ‘curious negotiator’ framework [39]. The term was introduced by Craik in [16] to label the models of reality that the mind forms and uses to anticipate events; we follow the terminology introduced and used in [2, 40]. In a previous work [40] we introduced reservations as those constraints that an agent requires the solution to satisfy. Here we will consider reservations as properties of the solution that the agent is never giving up and thus simply consider them a special kind of goal. The Argumentative Mediator 445 include the agent’s set of arguments as Mt = {ot , Gt , Γ t }, where ot , Gt , Γ t denote the agent’s ontology, goals, and set of arguments at time t, respectively. We also extend the case-base format in [2], so that each case ci in the case base is described by ci = {oi , Ai , Gi , Γit1 , Γitn , Si }, denoting respectively the finally agreed ontology of the dispute, the participating agents, the (consistent) union of their goals at time tn , their joint argumentation system at the beginning and at the end of the mediation, and the final solution itself. In this work we reuse Dung’s theory of argumentation7 [20], as it reduces argumentation to a completely abstract system consisting of a set of “atomic” arguments and (a set of) binary relation(s) over these. For example, such an atomic argument can be represented in a rule-based fashion as a pair {Antecedent, Consequent}, where Antecedent is a set of premises. Dung’s original work [20] follows the majority of argumentation frameworks, which consider only conflicts between arguments, represented by a single type of binary relation — “attack”, “defeat”. In order to use argumentation, the mediator, will have to create an acceptable (by both parties) sets of arguments for each proposed solution that it offers. The concept of acceptability is well explored and developed in [20] in a setting abstracted from the nature of the arguments, and interaction between the arguments limited to the “attack” relation. However, this limitation on the relations is counter-intuitive to the way we operate. Indeed, a seres of recent works from Cayrol and Lagasquie-Schiex [10–12] strongly argue in favour of modeling bipolarity in argumentation, when the argumentation system supports both defeat and support relations. This distinction has been supported by studies in cognitive psychology which have shown that the two kinds of preferences are completely independent and are processed separately in the mind [10]. For instance, it is not clear how an “attack”-based argumentation system will help our mediator µ to handle a situation when negotiating agent α advances an argument that confirms premises used by an argument provided earlier to µ by negotiating agent β. We adapt and extend bipolar argumentation frameworks, developed by Cayrol and Lagasquie-Schiex [10–12] as they reuse the principles, properties and algorithms of Dung’s framework. We also consider mechanisms for building a “common” argumentation system acceptable to both α and β and mechanisms for merging argumentation frameworks as discussed in [15]. Every argument coming from α and β is a piece of information available to the mediator µ. Dubois and Prade’s analysis of bipolarity of information for the needs of knowledge representation [19] supports the need for separate treatment of support relation, so that µ can assess such piece of information as a positive or negative with respect to another argument. Definition 1. An Argumentation System AS = A, R is defined by a set of arguments A = {ai |i ∈ N+ } and a set of binary relations between arguments R = {rk }k∈K where rk = {(ai , aj )|ai ∈ A, aj ∈ A, i, j ∈ N+ }. 7 For a broader and detailed overview of the state-of-the-art in argumentation the reader is referred to the editorial [4] to the special issue on argumentation of the Artificial Intelligence journal and to the recent collection of chapters [34]. 446 C. Sierra et al. For Dung’s framework R = {attack}; for bipolar argumentation frameworks R = {attack; support}. We recall the three postulates for the automated mediator, formulated in [40]: Postulate 1. An automated mediator µ should start interaction with extracting information about the position of the parties on the negotiation; This information is formulated as a collection of arguments A ⊂ Γ t . Postulate 2. An automated mediator µ should develop an independent “grand view” of the problem, which is more comprehensive than the individual views of α and β; Postulate 3. An automated mediator µ should operate from the initial stance that α and β are willing to achieve a mutually beneficial agreement and will accept mediation by µ. In this paper we have committed to deliberative mediation, hence, we add the following postulate for the automated mediator. Postulate 4. An automated mediator µ should be capable of developing an argumentation system ASµt supporting the proposed solution, which is acceptable under agreed semantics by α and β. For instance, this may be achieved by the incorporation of the argumentation systems ASαt and ASβt in line with the ways proposed in [15], or with the ArgMed algorithm, presented in next section. 4 The Argumentative Mediator - Integrating CBR and Argumentation In this section we present in layman terms how the mediator can use argumentation. At t1 the mediator µ requests α and β for their respective ontologies of the dispute otα1 and otβ1 . If otα1 and otβ1 are not the same, µ aligns these ontologies through argumentation 8 with α and β into the agreed ontology otµ1 . This step can adapt the methodology of the DILIGENT argumentation process in ontology engineering [43] and elements of the argumentation based approaches for ontology alignments presented in [6,27]. Further, µ provides to α and β the agreed otµ1 . The mediator µ requests the goals Gtα1 and Gtβ1 from α and β in terms of the working ontology otµ1 . If Gtα1 and Gtβ1 do not conflict, then S t1 = Gtα1 ∪ Gtβ1 . If there is a conflict then µ requests the argumentation systems that agents want to make public at time t1 , ASαt1 = Aα , Rα , such that Aα ⊆ Atα1 , Rα ⊆ Rtα1 and ASβt1 = Aβ , Rβ , such that Aβ ⊆ Atβ1 , Rβ ⊆ Rtβ1 , and merges them into ASµt1 . Next the mediator queries the CBR system. The query includes structural and semantic compositions of otµ1 , Gtα1 , Gtβ1 , and ASµt1 , with capability to retrieve 8 See [21] for a compact overview of the area. The Argumentative Mediator 447 cases analogous to the current conflict/dispute and not necessarily in the same problem domain. If the solution is not accepted by the parties the process iterates until a solution is accepted or no progress can be made. During the process agents α and β update their mental models. Algorithm 1. ArgM ed Require: A = {α, β} the set of agents Ensure: S a solution to the conflict 1: t = t0 2: S t = ∅ 3: repeat 4: t=t+1 ′ ′ 5: get otα {otα ⊑ otα if t′ ≤ t} ′ ′ 6: get otβ {otβ ⊑ otβ if t′ ≤ t} 7: otµ = agree(otα , otβ ) {via [6, 27, 43]} 8: send otµ to α and β 9: Gtα = get(α, Gtα |otµ ) {goals aligned to otµ } 10: Gtβ = get(β, Gtβ |otµ ) {goals aligned to otµ } 11: if conflict(Gtα , Gtβ ) then 12: get ASαt 13: get ASβt 14: ASµt = merge(ASαt , ASβt ) 15: S t = Adapt(CBR(otµ , Gtα , Gtβ , ASµt )) 16: else 17: S t = Gtα ∪ Gtβ 18: end if 19: until accept({α, β}, S t ) or S t = S t−1 {repeat until the agents agree or there is no progress} 20: if accept({α, β}, S t ) then 21: memorise(otµ , {α, β}, Gtα ∪ Gtβ , ASµt1 , ASµt , S t ) 22: return S t 23: else 24: return ∅ 25: end if The solution sets in the case base can include two types of solutions - those that are directly applicable and those that require reframing of the problem. For example, in the case of resource disputes, the equal division of the resource between the disputing parties is a directly applicable solution. Reconsideration of the resource, as a collection of different structural parts, can lead to splitting the resource in different sets of its parts. This is restructuring of the problem; the solution in this case is offering different sets to the disputing parties. 5 Case Study: The Orange Dispute Revisited We show the interplay of argumentation and case-based reasoning in the mediation process following an extended version of the Orange Dispute, introduced 448 C. Sierra et al. in [25] and considered in [40]. Two sisters need an orange each and there is one orange left, hence, they negotiate. The sisters are the negotiation agents α and β. Negotiation stalled at t1 and the mediating agent µ intervenes, following the ArgM ed procedure of previous section. In order to show the approach we extend the formulation of the orange dispute scenario with additional facts, that contribute to the rationale about why each sister wanted the orange — the set of arguments which each sister has, some of which or all can be used in support of having the orange, namely: – α is expecting a business visitor to come for an afternoon tea. α plans to prepare an orange chiffon cake, as its interesting history9 can be a good conversation starter. The recipe requires both orange zest and orange juice. She plans to serve it with a Calvados cocktail, which also requires orange juice. As the orange is a large one, α believes the juice of the orange will be sufficient for both. – β has a flu. She wants to immediately start treatment as her timely recovery is critical due to forthcoming performance on stage over the weekend. She follows treatment with natural remedies, so she plans to take orange juice for the high concentration of vitamin C. We represent the narrative in terms of propositions that constitute the argumentation knowledge bases Γαtx and Γβtx which are part of the mental models Mtαx and Mtβx of α and β, respectively, for t1 ≤ tx ≤ tn . We denote by ai , bi and mi the propositional symbols representing the facts in Γαtx , Γαtx and Γµtx . The sets of arguments Γαt1 and Γβt1 are shown in Tables 1 and 2. Table 1. The set of arguments Γαt1 that α has at t1 a1 = α plans to impress the business visitor a2 = α’s selection of a cake with interesting history is part of the plan a3 = α’s selection of the accompanying drink with interesting history is part of the plan a4 = the orange chiffon cake has an interesting history, dating back to 1927 a5 = Calvados has an interesting history, dating back to Napoleonic times a6 = accompanying drink matches selected cake a7 = the recipe of the orange chiffon cake requires orange zest and juice a8 = the recipe of the Calvados cocktail requires orange juice a9 = one large orange is sufficient for both the cake and the cocktail a10 = α knows the visitor likes citruses and citrus flavour a11 = α respects her sister β commitment to performances a12 = α needs an orange 9 Harry Baker (1883–1974), a Los Angeles insurance agent turned caterer, is said to have invented the original chiffon cake in 1927. Baker kept the recipe secret for 20 years, baking the popular creation for the Hollywood elite. Finally, in 1947, he sold the recipe to Betty Crocker’s parent company, General Mills, which released it to the public in 1948, naming it “the first really new cake in 100 years”. The Argumentative Mediator 449 Table 2. The set of arguments Γβt1 that β has at t1 b1 = β plans immediately to take measures against the flu to restore her health b2 = β needs timely recovery b3 = β aims to be ready for the performance over the weekend b4 = orange juice is an excellent natural source of vitamin C b5 = β prefers treatment with natural remedies b6 = β likes cakes with orange flavour b7 = β needs the juice of an orange Step t1 : When negotiation between α and β stalled at t1 , the mediator µ, following the ArgM ed procedure, requests from α and β their respective ontologies of the dispute otα1 and otβ1 . In this case otµ1 is a replica of either of otα1 and otβ1 , as they are aligned, representing orange as a dividable resource with peel, pulp and juice, as shown in [40]. The mediator µ received from α and β their goals Gtα1 = {a12 − need a full orange; a1 − impress a business visitor} and Gtβ1 = {b7 −need the juice of a full orange; b2 −need timely recovery}. The working ontology otµ1 recognises the divisibility of the orange, hence the conflict in the two goals is in the requirement for the orange juice. As conflict(Gtα1 , Gtβ1 ) = T rue, µ requests the argumentation systems ASαt1 and ASβt1 . The argumentation systems are described in terms of support and attack relations: R = {rk }k∈{supp,att} . ASαt1 = Atα1 , Rtα1  = {a1 , a3 , a5 , ..., a10 , a12 }, rsupp = {(a6 , a9 ), (a5 , a3 ), (a3 , a1 ), (a10 , a12 ), (a8 , a9 ), (a9 , a12 ), (a12 , a1 )} ASβt1 = Atβ1 , Rtβ1  = {b1 , ..., b5 , b7 }, rsupp = {(b1 , b3 ), (b2 , b3 ), (b3 , b7 ), (b4 , b7 ), (b5 , b7 ), (b7 , b2 )} The operator merge(ASαt1 , ASβt1 ) returns the merged argumentation system in which µ finds out that argument b7 attacks both a7 and a8 . Arguments b7 and a12 mutually attack each other as shown in Fig. 1a. This means S t = ∅, which result triggers the case base retrieval and case adaptation operator ASµt1 , Fig. 1. The merged argumentation system ASµt1 before (a) and after (b) the application of the case adaptation operator Adapt(CBR(·)) in t1 . 450 C. Sierra et al. Adapt(CBR(otµ1 , Gtα1 , Gtβ1 , ASµt1 )) of µ. As a result of this operation, µ adds to ASµt1 two new arguments: m1 = the recipe of the almond pound cake with orange glaze requires only orange zest and m2 = the recipe of limoncello does not require orange juice, which both support a1 , and attack a12 as shown in Fig. 1b. µ returns to α and β the following solution S t1 = {m1 , m2 , b7 , b2 , a1 }. Step t2 : The operator accept({α, β}, S t1 ) = f alse, meaning that S t1 has not been accepted, triggers the beginning of the next step. During this step α uses argumentation to inform µ that m1 does not have an interesting history. There are no changes in the agreed ontology: otµ2 = otµ1 . The mediator µ receives from α and β their revised goals Gtα2 = Gtα1 ∪{a2 } and Gtβ2 = Gtβ1 , and the updated argumentation systems ASαt2 = Atα1 ∪{a2 , m1 , m2 }, Rtα1 ∪{{rsupp = (a2 , a1 )}, {ratt = (a2 , m1 ), (a2 , m1 )}} and ASβt2 = ASβt1 . The operator merge(ASαt2 , ASβt2 ) returns the merged argumentation system ASµt2 , shown in Fig. 2a, in which µ finds out that its suggestion m1 and m2 is attacked by a2 , which in turn supports a1 . This results in S1t = ∅, which triggers the case base retrieval and case adaptation operator Adapt(CBR(otµ2 , Gtα2 , Gtβ2 , ASµt2 )) of µ. As a result of this operation, µ replaces m1 and m2 in ASµt2 with two new arguments: m3 = the recipe of the orange Santiago tart requires only zest and has an interesting history and m4 = crema de limoncello does not require orange juice, which both support a1 and a2 , and attack a12 as shown in Fig. 2b. µ returns to α and β the following solution S t2 = {m3 , m4 , b7 , b2 , a1 , a2 }. The proposed solution S t2 satisfies the goals Gtα2 and Gtβ2 of α and β, and accept({α, β}, S t2 ) = T rue. Consequently, the operator memorise(otµ2 , {α, β}, Gtα2 ∪ Gtβ2 , ASµt1 , ASµt2 , S t2 ) updates the case base of µ and this concludes the execution of ArgM ed. Fig. 2. The merged argumentation system ASµt1 before (a) and after (b) the application of the case adaptation operator Adapt(CBR(·)) in t2 . 6 Conclusions In this paper we have proposed a negotiation mediator, which builds on and develops further the work presented in [2,40]. The mediator µ in [40] demonstrated the problem reframing capabilities and the case-based reasoning approach to implementing such capabilities [2]. These works assumed that α and The Argumentative Mediator 451 β provided all the information, requested by µ, and accepted the solutions provided by µ. Whilst both assumptions served the purpose of the work developed in [2,40], it is unlikely that these assumptions will hold in a majority of real world problems, which require mediation. The work presented in this paper demonstrates the next step towards the development of mediation agents, which can utilise argumentation in the mediation process. The proposed mediator follows an algorithmic schema to be instantiated with particular argumentation semantic alignment and CBR techniques. Similar to [40], the case study uses the popular Orange Dispute problem, extending the information about the reasons for the position of each party involved. This information is then utilised by the mediator in the subsequent cycles. The proposal is neutral with respect to which particular technique is selected. The interplay between argumentation and the mediation process, presented in Sect. 3, has not discussed the time dependency of arguments. Arguments, for instance those related to specific legislation, may be valid until a new legislation is put in place and then become invalid. Capturing the time dependency of arguments and argumentation systems will require extensions of argumentation frameworks, like the ones proposed in [8], and modification of the description of each case ci in the case base, the case-based reasoning cycle CBR(·) and the Adapt(CBR(·)) operator. Acknowledgments. This research has been supported by Generalitat de Catalunya project 2014 SGR 118. References 1. Abrahams, B., Bellucci, E., Zeleznikow, J.: Incorporating fairness into development of an integrated multi-agent online dispute resolution environment. Group Decis. Negot. 21, 3–28 (2012) 2. Baydin, A.G., López de Mántaras, R., Simoff, S., Sierra, C.: CBR with commonsense reasoning and structure mapping: an application to mediation. In: Ram, A., Wiratunga, N. (eds.) ICCBR 2011. LNCS, vol. 6880, pp. 378–392. Springer, Heidelberg (2011). doi:10.1007/978-3-642-23291-6 28 3. Bellucci, E., Zeleznikow, J.: Developing negotiation decision support systems that support mediators: case study of the Family Winner system. Artif. Intell. Law 13(2), 233–271 (2005) 4. Bench-Capon, T.J.M., Dunne, P.E.: Argumentation in artificial intelligence. Artif. Intell. 171, 619–641 (2007) 5. Bench-Capon, T.J.M.: Persuasion in practical argument using value-based argumentation frameworks. J. Logic Comput. 13(3), 429–448 (2003) 6. Black, E., Hunter, A., Pan, J.Z.: An argument-based approach to using multiple ontologies. In: Godo, L., Pugliese, A. (eds.) SUM 2009. LNCS (LNAI), vol. 5785, pp. 68–79. Springer, Heidelberg (2009). doi:10.1007/978-3-642-04388-8 7 7. Bratko, I., Žabkar, J., Možina, M.: Argument-based machine learning. In: Rahwan, I., Simari, G.R. (eds.) Argumentation in Artificial Intelligence. Springer US, New York (2009). doi:10.1007/978-0-387-98197-0 23 8. Budán, M.C.D., Gómez Lucero, M., Chesñevar, C., Simari, G.R.: Modeling time and valuation in structured argumentation frameworks. Inf. Sci. 290, 22–44 (2015) 452 C. Sierra et al. 9. Bush, R.A.B., Joseph, F.: The Promise of Mediation: Responding to Conflict Through Empowerment and Recognition. Jossey-Bass Publishers, San Francisco (1994) 10. Cayrol, C., Lagasquie-Schiex, M.C.: On the acceptability of arguments in bipolar argumentation frameworks. In: Godo, L. (ed.) ECSQARU 2005. LNCS, vol. 3571, pp. 378–389. Springer, Heidelberg (2005). doi:10.1007/11518655 33 11. Cayrol, C., Lagasquie-Schiex, M.-C.: Bipolar abstract argumentation systems. In: Rahwan, I., Simari, G.R. (eds.) Argumentation in Artificial Intelligence, pp. 65–84. Springer, Heidelberg (2009). doi:10.1007/978-0-387-98197-0 4 12. Cayrol, C., Lagasquie-Schiex, M.-C.: Coalitions of arguments: a tool for handling bipolar argumentation frameworks. Int. J. Intell. Syst. 25(1), 83–109 (2010) 13. Chalamish, M., Kraus, S.: AutoMed - an automated mediator for bilateral negotiations under time constraints. In: Proceedings of the International Conference on Autonomous Agents and Multi Agent Systems, AAMAS 2007, Honolulu, Hawaii, USA. IFAAMAS (2007) 14. Chalamish, M., Kraus, S.: AutoMed: an automated mediator for multi-issue bilateral negotiations. Auton. Agents Multi-agent Syst. 24, 536–564 (2012) 15. Coste-Marquis, S., Devred, C., Konieczny, S., Lagasquie-Schiex, M.-C., Marquis, P.: On the merging of Dung’s argumentation systems. Artif. Intell. 171, 730–753 (2007) 16. Craik, K.J.W.: The Nature of Explanation. Cambridge University Press, Cambridge (1943) 17. Debenham, J.: Bargaining with information. In: Jennings, N.R., Sierra, C., Sonenberg, L., Tambe, M. (eds.) Proceedings Third International Conference on Autonomous Agents and Multi Agent Systems AAMAS-2004, pp. 664–671. ACM Press, New York (2004) 18. Debenham, J.K., Simoff, S.: Negotiating intelligently. In: Bramer, M., Coenen, F., Tuson, A. (eds.) Proceedings 26th International Conference on Innovative Techniques and Applications of Artificial Intelligence, Cambridge, UK, pp. 159–172 (2006) 19. Dubois, D., Prade, H.: A bipolar possibilistic representation of knowledge and preferences and its applications. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds.) WILF 2005. LNCS, vol. 3849, pp. 1–10. Springer, Heidelberg (2006). doi:10. 1007/11676935 1 20. Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artif. Intell. 77, 321–358 (1995) 21. Ermolayev, V., Davidovsky, M.: Agent-based ontology alignment: basics, applications, theoretical foundations, and demonstration. In Proceedings of the 2nd International Conference on Web Intelligence, Mining and Semantics WIMS 2012. ACM Press, New York (2012) 22. Gentner, D., Stevens, A.L. (eds.): Mental Models. Erlbaum, Hillsdale (1983) 23. Jarett, B.: The future of mediation: a sociaological perspective. J. Disput. Resol. 2009(1), 49–75 (2010) 24. Keeney, R.L., Thinking, V.-F.: A Path to Creative Decisionmaking. Harvard University Press, Cambridge (1992) 25. Kolodner, J.: Case-Based Reasoning. Morgan Kaufmann Publishers Inc., San Mateo (1993) 26. Kolodner, J.L., Simpson, R.L.: The MEDIATOR: Analysis of an early case-based problem solver. Cogn. Sci. 13(4), 507–549 (1989) The Argumentative Mediator 453 27. Laera, L., Tamma, V., Bench-Capon, T.J.M., Euzenat, J.: Agent-based argumentation for ontology alignments. In Proceedings of the Workshop on Computational Models of Natural Argument, CMNA 2006 (2006) 28. Letia, I.A., Groza, A.: Structured argumentation in a mediator for online dispute resolution. In: Baldoni, M., Son, T.C., Riemsdijk, M.B., Winikoff, M. (eds.) DALT 2007. LNCS, vol. 4897, pp. 193–210. Springer, Heidelberg (2008). doi:10.1007/ 978-3-540-77564-5 12 29. Lin, R., Gev, Y., Kraus, S.: Bridging the gap: face-to-face negotiations with automated mediator. IEEE Intell. Syst. 26(6), 40–47 (2011) 30. Lin, R., Gev, Y., Kraus, S.: Facilitating better negotiation solutions using AniMed. In: The Fourth International Workshop on Agent-Based Complex Automated Negotiations (ACAN 2011), Taipei, Taiwan, May 2011 31. Mnookin, R.H., Peppet, S.R., Tulumello, A.S., Winning, B.: Negotiating to Create Value in Deals and Disputes. Harvard University Press, Cambridge (2000) 32. Rahwan, I.: Interest-based negotiation in multi-agent systems. Ph.D. thesis, University of Melbourne, Melbourne, Australia (2004) 33. Rahwan, I., Pasquier, P., Sonenberg, L., Dignum, F.: A formal analysis of interestbased negotiation. Ann. Math. Artif. Intell. 55(3–4), 253–276 (2009) 34. Rahwan, I., Simari, G. (eds.): Argumentation in Artificial Intelligence. Springer, Heidelberg (2009) 35. Raiffa, H., Richardson, J., Metcalfe, D.: Negotiation Analysis: The Science and Art of Collaborative Decision Making. Belknap Press of Harvard University Press, Cambridge (2002) 36. Schei, V., Rognes, J.K.: Knowing me, knowing you: own orientation and information about the opponent’s orientation in negotiation. Int. J. Confl. Manag. 14(1), 43–60 (2003) 37. Sierra, C., Debenham, J.K.: The logic negotiation model. In: Proceedings Sixth International Joint Conference on Autonomous Agents and Multi-agent Systems (AAMAS 2007), pp. 1026–1033 (2007) 38. Sierra, C., Debenham, J.: Information-based agency. In: Proceedings of Twentieth International Joint Conference on Artificial Intelligence IJCAI 2007, pp. 1513–1518, Hyderabad, India (2007) 39. Simoff, S., Debenham, J.: Curious negotiator. In: Klusch, M., Ossowski, S., Shehory, O. (eds.) CIA 2002. LNCS (LNAI), vol. 2446, pp. 104–111. Springer, Heidelberg (2002). doi:10.1007/3-540-45741-0 10 40. Simoff, S., Sierra, C., López de Màntaras, R.: Mediation = information revelation + analogical reasoning. In: Meyer, J.-J.C., Broersen, J. (eds.) KRAMAS 2008. LNCS, vol. 5605, pp. 145–160. Springer, Heidelberg (2009). doi:10.1007/ 978-3-642-05301-6 10 41. Sycara, K.P.: Problem restructuring in negotiation. Manag. Sci. 37(10), 1248–1268 (1991) 42. Tedesco, P.A.: MArCo: building an artificial conflict mediator to support group planning interactions. Int. J. Artif. Intell. Educ. 13, 117–155 (2003) 43. Tempich, C., Studer, R., Simperl, E., Luczak, M., SofiaPinto, H.: Argumentationbased ontology engineering. IEEE Inetell. Syst. 22(6), 52–59 (2007) 44. Thompson, L., Neale, M., Sinaceur, M.: The evolution of cognition and biases in negotiation research: an examination of cognition, social perception, motivation and emotion. In: Gelfand, M.J., Brett, J.M. (eds.) The Handbook of Negotiation and Culture, pp. 7–44. Standford University Press, Palo Alto (2004) 45. Van Boven, L., Thompson, L.: A look into the mind of the negotiator: mental models in negotiation. Group Process. Intergroup Relat. 6(4), 387–404 (2003) 454 C. Sierra et al. 46. Visser, W., Hindriks, K.V., Jonker, C.M.: Interest-based preference reasoning. In: Proceedings of International Conference on Agents and Artificial Intelligence, ICAART 2011, pp. 79–88 (2011) 47. Wilkenfeld, J., Kraus, S., Santmire, T.E., Frain, C.K.: The role of mediation in conflict management: conditions for successful resolution. In: Multiple paths to knowledge in international relations. Lexington Books (2004) 48. Wing, J.M.: Computational thinking. Commun. ACM 49(3), 33–35 (2006)