Using argumentation to model and deploy agent …users.encs.concordia.ca/~bentahar/Publications/KBS (2010...KNOSYS 1895 No. of Pages 16, Model 5G 1 February 2010 ARTICLE IN PRESS Please

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Knowledge-Based Systems xxx (2010) xxx–xxx

KNOSYS 1895 No. of Pages 16, Model 5G

1 February 2010ARTICLE IN PRESS

Contents lists available at ScienceDirect

Knowledge-Based Systems

journal homepage: www.elsevier .com/ locate /knosys

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FUsing argumentation to model and deploy agent-based B2B applications

Jamal Bentahar a,*, Rafiul Alam a, Zakaria Maamar b, Nanjangud C. Narendra c

a Concordia University, Montreal, Canadab Zayed University, Dubai, United Arab Emiratesc IBM India Research Lab, Bangalore, India

202122232425262728

a r t i c l e i n f o

Article history:Available online xxxx

Keywords:B2BArgumentation theoryAgent communicationConflictPersuasion

2930313233

0950-7051/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.knosys.2010.01.005

* Corresponding author. Tel.: +1 514 848 2424; faxE-mail address: [email protected] (J. Ben

Please cite this article in press as: J. Bentahar edoi:10.1016/j.knosys.2010.01.005

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This paper presents an agent-based framework for modeling and deploying Business-to-Business (B2B)applications, where autonomous agents act on behalf of the individual components that form these appli-cations. This framework consists of three levels identified by strategic, application, and resource, withfocus in this paper on the first two levels. The strategic level is about the common vision that indepen-dent businesses define as part of their decision of partnership. The application level is about the businessprocesses that get virtually combined as result of this common vision. As conflicts are bound to ariseamong the independent applications/agents, the framework uses a formal model based on computationalargumentation theory through a persuasion protocol to detect and resolve these conflicts. In this proto-col, agents reason about partial information using partial arguments, partial attack, and partial acceptabil-ity. Agents can then jointly find arguments that support a new solution for their conflicts, which is notknown by any of them individually. Termination, soundness, and completeness properties of this protocolare provided. Distributed and centralized coordination strategies are also supported in this framework,which is illustrated with an online-purchasing example.

� 2010 Elsevier B.V. All rights reserved.

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E1. Introduction

Today’s challenges in terms of performance and competitivenessare putting businesses under a constant pressure of meeting chang-ing requirements. This fuels the need for continuous merge andsometimes re-engineering of business processes, resulting in Busi-ness-to-Business (B2B) applications development. Briefly, a B2Bapplication is a set of business processes that make disparateautonomous entities (e.g., departments, businesses) collaborate toachieve a common set of goals. Despite the abundance of initiativeson B2B applications [15,19,26,28], not much exist in terms of mod-eling and deploying such applications from the perspective of usingintelligent and argumentative agents. By modeling, we mean iden-tifying all the necessary components that connect assets of inde-pendent entities that are engaged in a B2B scenario. Bydeployment, we mean identifying all the necessary technologiesthat allow the connection of these assets happen effectively. Finally,by argumentation, we mean making agents that represent andoperate on behalf of businesses comply with a dialectical processto affirm or disavow the conclusions that these agents wish toreciprocally convey to their peers [4,5]. In a B2B scenario, argumen-tation would broadly assist businesses, through representativeagents, engage in intense negotiation and persuasion sessions prior

ll rights reserved.

: +1 514 848 3171.tahar).

t al., Using argumentation to m

to making any joint decisions. The argumentation capability of anagent representing a business, can assist this business in negotiatingwith its peers during a conflict situation and in collaborating withthem to achieve agreements on their strategies. Although argumen-tation has been extensively investigated in the last decade and manyinteresting frameworks are proposed [3], limited efforts have beenput into using this theory in concrete applications [23]. This paper ad-dresses this challenging issue, which consists of using argumentationtheory for multi-agent systems to develop B2B applications. In termsof validation, theoretical proofs of some properties are provided and aconcrete case study from the industry illustrates the proposed frame-work. This framework is an initiative within the emerging field ofdeveloping intelligent software [11,13]. Many approaches in this fieldare based on new software development techniques such as the Lyeecalculus and methodology [14]. Our approach is different; it usesargumentation theory and agent technology.

This framework suggests three levels, resource, application, andstrategic2 that are connected through rely-on and run-on-top-of rela-tions (Fig. 1). These levels represent the way businesses generallyfunction: the strategic level, associated with a set of Strategic Argu-mentative Agents (S � AAs), sets the goals to reach (e.g., 10% revenueincrease), the application level, associated with a set of ApplicationArgumentative Agents (A� AAs), sets the automatic and manual pro-

1 It is expected that joint decisions will be beneficial for all businesses, althoughpersonal interests might sometimes prevail, but this is outside this paper’s scope.

2 Decisions affecting a business growth are made at this level.

odel and deploy agent-based B2B applications, Knowl. Based Syst. (2010),

http://dx.doi.org/10.1016/j.knosys.2010.01.005

mailto:[email protected]

http://www.sciencedirect.com/science/journal/09507051

http://www.elsevier.com/locate/knosys


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Fig. 1. The argumentative agent framework for B2B applications.

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cesses (e.g., new auditing system) that permit fulfilling these objec-tives, and the resource level, associated with a set of Resource Argu-mentative Agents (R� AAs), sets the means that achieve theperformance of these processes. The framework associates compo-nents (that reside in one of the three levels) with agents equipped withargumentation capabilities to assist a specific component (i) persuadepeers of collaborating, (ii) interact with peers during business processimplementation, (iii) agree with peers on the collaboration outcomes,(iv) resolve conflicts that could impede collaboration, and (v) trackconflict resolution. Still in Fig. 1, the rely-on relation means mappingthe business goals onto concrete system applications, and run-on-top-of relation means performing these system applications’ businessprocesses subject to resource availabilities. In addition, both relationsmake issues at lower levels influence goals at higher levels. For exam-ple, lack of resources could result in reviewing expansion goals.

In Fig. 1, horizontal relations permit linking similar levels ofseparate businesses. We refer to these relations by interconnectivi-ty, composition, and collaboration. Underneath each horizontal rela-tion’s name, an example of conflict that could arise in a B2Bscenario is provided for illustration purposes. Collaboration rela-tion bridges the strategic levels and focusses on how businessesadapt their goals and plans so that these businesses can now reachthe goals that result out of their decision of partnership. Composi-tion relation bridges the application levels and focusses on hownew business processes are developed, either from scratch or afterre-engineering existing processes. Finally, interconnectivity rela-tion bridges the resource levels and focusses on the means thatmake the performance of business processes happen despite distri-bution and heterogeneity constraints.

This paper is organized as follows. Section 2 introduces ouragent-based framework for B2B applications. Section 3 presentsthe argumentation model upon which this framework operates.Section 4 defines and discusses the argumentation-based protocolfor B2B conflict resolution and analyzes its formal and computa-tional properties. To illustrate the proposed framework through arunning example, an industrial case study (provided by IBM Re-search Division) is discussed in Section 5 along with its implemen-tation using Java and logic programming with Prolog. Prior toconcluding and presenting future work in Section 7, related workis discussed in Section 6.

2. The proposed framework for B2B applications

2.1. Brief description of levels and relations

The resource level includes data and software resources (e.g.,DBMS) that a business owns or manages, and the hardware re-sources upon which these software resources operate.

Please cite this article in press as: J. Bentahar et al., Using argumentation to mdoi:10.1016/j.knosys.2010.01.005

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OThe application level is about the software applications thatbusinesses operate such as payroll. From a B2B perspective, theapplication level hosts a number of A� AAs according to the num-ber of these applications. The role of A� AAs is to (i) monitor theexternal business processes that will use software applicationsand (ii) initiate interaction sessions with other A� AAs. These ses-sions frame application compositions according to the guidelinesthat S � AAs set and resolve possible conflicts during these compo-sitions as depicted by composition relation in Fig. 1. For illustrationpurposes we assume that software applications are implementedas Web services [18], although other technologies could be used.

The strategic level is about the planning and decision-makingmechanisms that underpin the growth of a business. Like the appli-cation level, the strategic level hosts a number of S � AAs accordingto the number of active collaborations that a business initiates withits partners. The role of S � AAs is to (i) reason over the businessplans and (ii) initiate interaction sessions with other S � AAs as de-picted by collaboration relation in Fig. 1. These sessions aim at per-suading peers to participate in collaborations, reviewing policies incase of conflicts, optimizing some parameters such as distributionnetwork, etc. A� AAs feed S � AAs with details related to the exe-cution progress of business processes. Particularly, if a conflict dur-ing the composition process cannot be resolved at the applicationlevel, the A� AAs inform their respective S � AAs.

From an argumentation perspective, the S � AAs and A� AAsare equipped with the same reasoning capabilities. However theydiffer in terms of the knowledge they manage and the responsibil-ities they are in charge of. For example, to resolve conflicts at theapplication or strategic levels, the A� AAs or S � AAs use the samepersuasion and negotiation protocols but execute them differently.Protocols publicly describe the allowed moves, but how a certainmove is selected would dependent on the knowledge that feedthe agents’ private strategies.

Fig. 1 shows vertical and horizontal relations. In a B2B context,the focus is on horizontal relations. Interconnectivity relation tar-gets the resource level and allows (i) data to freely and securelyflow between businesses without any format, location, or semanticrestriction and (ii) disparate resources to trigger each other with-out any access rights, time-slot availabilities, or compatibilityrestrictions. Communication protocols incompatibility (e.g., Syn-chronous Optical Networking (SONET) vs. Synchronous DigitalHierarchy (SDH)), incompatible hardware transmission technolo-gies (e.g., circuit switching vs. multiplexing) and different modesof communication (e.g., connection-oriented communication vs.connectionless communication) are key examples of conflicts thatfall under the interconnectivity relation.

Composition relation targets the application level and exhibitshow business processes associated with A� AAs get ‘‘virtually”



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integrated without being subject to any functional or structuralchanges. Lack of common semantics (e.g., different measurementunits) is an example of conflict that falls under the compositionrelation. When it comes to Web services-based applications, com-position targets users’ requests that cannot be satisfied by any sin-gle, available Web service, whereas a composite Web serviceobtained by combining available Web services may be used.

Collaboration relation targets the strategic level and empha-sizes the mechanisms that the S � AAs set-up for coordinatingthe new B2B processes using the A� AAs. These processes arethe result of composing applications, stretch beyond businesses’boundaries, and have to consider the requirements/limitations ofthe resource and application levels per business. For example, inthe context of supply chain networks, many concrete conflicts thatfall under the collaboration relation can arise. Concrete examplesof such conflicts are: taxing policies incompatibility between man-ufactories and warehouses (e.g., various tax rates), incompatiblescheduling policies between suppliers and manufactories (e.g.,scheduling holidays during Christmas vs. summer) and incompat-ible inventory policies between distribution centers and retailers(e.g., lean vs. responsive inventory policies). Policies of businessescan be in contradiction, and some core business policies cannot beeasily re-engineered. By using argumentative agents, we aim athandling these issues. Through their argumentative reasoning,and interaction, negotiation, and persuasion abilities, these agentscould reason about these policies, identify possible conflicts, andupdate their policies to resolve these conflicts. They can, also, per-suade each other for the benefit of collaborating and sharing theirresources and determining alternative agents to work with, in casethe current conflicts cannot be addressed.

2.2. Forms of coordination

Coordination, via explicit interactions between argumentativeagents whether in the same or separate levels, is a pre-requisiteto any successful B2B application. We split coordination in theargumentative agent-based framework into two forms: vertical be-tween strategic and application levels via the rely-on relation, andhorizontal between strategic or application levels via the collabora-tion or composition relations, respectively. We discuss hereafterhow argumentation is injected into coordination using Figs. 2and 3 where plain lines and dotted lines denote interactions andconflict detection/resolution, respectively.

Vertical Coordination occurs within the boundaries of thesame business. Here a S � AA has the authority to execute a setof actions over an A� AA (Fig. 2): ‘‘select”, ‘‘ping”, ‘‘trigger”, ‘‘audi-t”, and ‘‘retract & select”.

– ‘‘select” action makes the S � AA identify the A� AA of an appli-cation that will pursue the interactions with other A� AAs aspart of the partnership decision;

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Fig. 2. Argumentation in vertical coordination.


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– ‘‘ping” action makes the S � AA check the liveness and readinessof an application through its A� AA; this is needed before thisapplication is suggested as a potential candidate for receivingrequests from other A� AAs;

– ‘‘trigger” action makes the S � AA forward the executionrequests to the A� AA of an application; these requests arrivefrom others A� AAs;

– ‘‘audit” action makes the S � AA monitor the performance of anapplication through its A� AA; this is needed if the S � AA hasto guarantee a certain QoS to other S � AAs;

– ‘‘retract & select” make the S � AA withdraw an applicationthrough its A� AA based on the outcome of ”audit” action(e.g., poor performance). This results in starting the search foranother application to offer to other partners.

Argumentation in vertical coordination is illustrated with twocases: Application-to-Strategic (this paper focus) and Strategic-to-Application.

Application-to-Strategic case highlights an A� AA that faces dif-ficulties in resolving conflicts and completing its operations. Forexample, the A� AA was put on hold for a long period of timedue to occupied resources or did not receive information in theright format from other businesses’ A� AAs. As a result, theA� AA notifies its S � AA so that both set-up an argumentationsession for the sake of discussing the current difficulties and thepotential solutions to put forward. This notification is representedwith ‘‘feedback” in Fig. 2. Supply chain management is a concreteillustration of such a coordination. In this context, a conflict canhappen between two partners about the delivery time. S � AAsand A� AAs of each player can argue to change the delivery timeto satisfy the whole supply chain. Briefly, we report on the wayconflict resolution progresses in this argumentation session.

Case 1. The S � AA has an argument supporting the fact that theconflict facing the A� AA could be resolved based onsimilar previous situations for example. Thus, theS � AA argues with the A� AA about the feasibility ofthis solution using persuasion ( Section 4.2). If theA� AA is not convinced (i.e., persuasion fails), theS � AA will decide to select another A� AA to continuethe uncompleted composition work of the A� AA thatwas withdrawn.

Case 2. The S � AA does not have any argument for or againstthe possibility of resolving the conflicts that the A� AAfaces. Thus, the S � AA and A� AA collaborate to find asolution through an inquiry dialogue game like the oneproposed in [7]. As defined by Walton and Krabbe [27],the inquiry dialogues rise from an initial situation of gen-eral ignorance and the purpose is to achieve the growthof knowledge and agreements.

If neither case (1) or (2) succeeds, the respective S � AAs of thecollaborative businesses try to work out a solution via horizontalcoordination. When a solution is found, the S � AAs check withthe same A� AAs if they are still available, or invite new S � AAsto take part in the composition to deploy at the application level.

Fig. 3. Argumentation in horizontal coordination.



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Strategic-to-Application case highlights a S � AA that expects theoccurrence of conflicts if appropriate actions are not taken on time.Examples of actions include reprimanding an A� AA that releasedprivate details to peers. Expecting conflicts is based on the differentfeedbacks that the S � AA receives from their A� AAs. This showsa preventive strategy to conflict occurrence. However, handlingpreventive strategies is beyond the scope of this paper.

Horizontal Coordination spreads over the boundaries of busi-nesses and thus, reflects B2B applications in a better way. We iden-tify two scenarios where each scenario involves either S � AAs orA� AAs. For the sake of simplicity, our description is restrictedto A� AAs. Here an A� AA has the authority to carry out a setof actions over another peer engaged in the same composition (Fig. 3): ‘‘ping” and ‘‘trigger”.

– ‘‘ping” action makes the A� AA check the liveness of a remoteapplication through its A� AA; this is needed before the formerA� AA submits requests;

– ‘‘trigger” action makes the A� AA submit its requests to aremote application through its A� AA.

Argumentation in horizontal coordination is illustrated withtwo cases: Application-to-Application and Strategic-to-Strategic.

Application-to-Application case stresses an A� AA that identifiesa conflict after interacting with peers. Conflicts could be of manytypes like different security policies, different semantics (e.g., dif-ferent measurement units, different ontologies, etc.), conflictingquality of service, different costs associated with an application,etc.A� AAs try to resolve these conflicts via argumentation using a

combination of persuasion and inquiry (Section 4.2). the A� AA en-gage in pure persuasion if one of them has already a solution thatcould be accepted by the other with respect to the beliefs it has.However, merging persuasion with inquiry allows these agents toreach a joint argument.

Strategic-to-Strategic case highlights a S � AA that identifies aconflict and tries to resolve it with its S � AA partner. Some con-flicts at this level concern penalty policies (e.g., collaboration’s con-tract terms and conditions not respected) and payment policies.This case also stresses the situation where two S � AAs of the col-laborative businesses try to work out a solution of a conflict re-ported by the respective A� AAs. This conflict cannot beresolved by vertical coordination. To this end, the S � AAs engagein persuasion and inquiry sessions (Section 4.2).

Before detailing the protocol for persuasion and inquiry, we dis-cuss our argumentative agents framework for B2B applicationsthat is based on computational argumentation theory.
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C3. Formal argumentation framework

3.1. Background

This section discusses the argumentation system that framesthe internal operations in our B2B framework. This discussion in-cludes the configuration featuring argumentative agents as well.We use an abstract formal language L to express agents’ beliefs.Here abstract means that beliefs could be propositional formulaslike in [20], Horn clauses like in [4], or a set of facts and rules likein [7] and [12]. The use of an abstract language would make ourframework generic and capable to capture properties that otherframeworks concentrate on. The set of well-formed formulasðwff Þ built from L is denoted byWF . Agents build arguments usingtheir beliefs. The set ArgðLÞ contains all those arguments. Similarlyto [1,8,9], we abstractly define argumentation as a dialectical pro-cess that underpins the exchange of ‘‘for/against” arguments that


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lead to some conclusion. Since we use an abstract language, weare not interested in the internal form of an argument. Formally,we define our argumentation framework as follows:

Definition 1 (Argumentation Framework). An abstract argumenta-tion framework is a pair A; ATh i, where A # ArgðLÞ and AT # A� Ais a binary relation over A that is not necessarily symmetric. Fortwo arguments a and b, we use AT ða; bÞ instead of AT 2 ða; bÞ toindicate that a is an attack against b.

For example, an argument may be defined as a deduction of aconclusion from a given set of rules, or as a pair ðH; hÞ where h isa sentence in WF and H a subset of a given knowledge base suchthat (i) H ‘ h, (ii) H is consistent, and (iii) there is no subset of Hwith properties (i) and (ii). Like in formal argumentation theory(see for example [2,22,23]), we do not consider in this paper fuzzyarguments that could have a subjective nature. This means, whenan argument is represented during an interaction, the agents cancheck whether an argument os legal or not. For example, if argu-ments are deducted from a given set of rules, the interacting agentsare supposed to share the same rules so they can check if thedeductions are valid, and if arguments are pairs, they can checkif the three aforementioned conditions (i, ii, and iii) are satisfied.Consequently, as commonly supposed in the argumentation the-ory, the agents share the same definition of attack relation. Thismeans, an argument a attacks another argument b iff AT ða; bÞholds for all the interacting agents. In fact, as conflicts betweenarguments might occur, we need to define what an acceptable argu-ment is. Dealing with fuzzy arguments could make the frameworkstronger and more flexible. However, this will raise complicated is-sues on how the arguments can be commonly accepted. Consider-ing such issues is out of scope of this paper, and one of the majorplans for our future work. To define the notion of acceptable argu-ments, we first define the notions of ‘‘defense” and ‘‘admissible setof arguments” (from [9,10]):

Definition 2 (Defense). Let A # ArgðLÞ be a set of arguments overthe argumentation framework, and let S # A. An argument a isdefended by S iff 8b 2 A if AT ðb; aÞ, then 9c 2 S : AT ðc; bÞ.

Definition 3 (Admissible Set). Let A # ArgðLÞ be a set of argumentsover the argumentation framework. A set S # A of arguments isadmissible iff:

(1) 9= a; b 2 S such that AT ða; bÞ and(2) 8a 2 S a is defended by S.

In other words, a set of arguments is admissible iff it is conflict-freeand can counter-attack every attack.

Example 1. Let A ¼ fa; b; c; dg and AT defined as follows:AT ðb; aÞ; AT ðc; aÞ; AT ðd; bÞ; AT ðd; cÞ. The sets: ;; fdg, andfa; dg are all admissible. However, the sets fbg and fd; cg are notadmissible.

Definition 4 (Characteristic Function). Let A # ArgðLÞ be a set ofarguments and let S be an admissible set of arguments over theargumentation framework. The characteristic function of the argu-mentation framework is:

F : 2A ! 2A

FðSÞ ¼ faja is defended by Sg

The following proposition shows a property of the characteristicfunction F. The proof is straightforward from Definitions 3 and 4.

Proposition 1. For all admissible set of arguments S, S # FðSÞ.



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Definition 5 (Extensions). Let S be an admissible set of arguments,and let F be the characteristic function of the argumentationframework.

� S is a complete extension ðScoÞ iff S ¼ FðSÞ.� S is the grounded extension ðSgrÞ iff S ¼ FðSÞ and S is minimal

(w.r.t. set-inclusion) (grounded extension corresponds to theleast fixed point of FÞ.

� S is a preferred extension ðSprÞ iff S ¼ FðSÞ and S is maximal(w.r.t. set-inclusion).

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Example 2. Let us consider the same argumentation framework asin Example 1. We have:

� Fð;Þ ¼ fdg, so the admissible set ; is not a complete extension.� FðfdgÞ ¼ fa; dg, so the admissible set fdg is not a complete

extension.� Fðfa; dgÞ ¼ fa; dg, so the admissible set fa; dg is a complete

extension.

In this example, the only complete extension fa; dg is thegrounded extension and is also the only preferred extension.

Example 3. Let A ¼ fa; b; cg and AT defined as follows: AT ða; bÞand AT ðb; aÞ. The sets: fcg; fa; cg, and fb; cg are the completeextensions of the argumentation framework. The minimal com-plete extension fcg is the grounded extension, and the maximalcomplete extensions fa; cg and fb; cg are the preferred extensions.

According to Definition 5, an admissible set S is a completeextension if and only if S is a fixed point of the function F, whichmeans that all arguments defended by S are also in S. Also, thegrounded extension is the least fixed point of F. Consequently, thegrounded extension contains all the arguments that are not at-tacked (the arguments that are defended by the empty set: Fð;Þ),all the arguments that are defended by these non-attacked argu-ments FðFð;ÞÞ ¼ F2ð;Þ, all the arguments that are defended by thedefended arguments (F3ð;Þ), and so on until a fixed point isachieved. The grounded extension corresponds to the intersectionof all the complete extensions. Finally, a preferred extension is amaximal complete extension that cannot be augmented by addingother arguments while staying complete.

We have the following direct proposition:

Proposition 2. Let hA;AT i be an argumentation framework.9!SgrinhA; AT i.

In other words, there exists a single grounded extension for the ab-stract argumentation framework. We can now define what the accept-able arguments in our system are.

Definition 6 (Acceptable Arguments). Let A # ArgðLÞ be a set ofarguments, and let G ¼ Sgr . An argument a over A is acceptable iffa 2 G.

According to this acceptability semantics, which is based on thegrounded extension, if we have two arguments a and b such thatAT ða; bÞ and AT ðb; aÞ, then a and b are both non-acceptable. In aB2B scenario, this can happen when two A� AAs present two con-flicting arguments about the type of security policies to use for thecurrent transaction: a weak policy that is simple to implement andless expensive or a strong policy that is hard to implement andmore expensive. This notion is important in B2B applications sinceagents should agree on an acceptable opinion, which is supportedby an acceptable argument when a conflict arises. However, duringthe argumentative conversation, agents could use non-acceptablearguments as an attempt to change the status of some argumentspreviously uttered by the addressee, from acceptable to non-

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acceptable. This idea of using non-acceptable arguments in the dis-pute does not exist in the persuasion and inquiry protocols in theliterature. For this reason, we introduce two new types of argu-ments based on the preferred extensions to capture this notion.We call these arguments semi-acceptable and preferred semi-accept-able arguments.

Definition 7 ((Preferred) Semi-Acceptable Arguments). Let G be thegrounded extension in the argumentation framework, and letE1; . . . ; En be the preferred extensions in the same framework. Anargument a is:

� Semi acceptable iff a R G and 9Ei; Ej with ð1 6 i; j 6 nÞ such thata 2 Ei ^ a R Ej.

� Preferred semi-acceptable iff a R G and 8Eið1 6 i 6 nÞa 2 Ei.

In other words, an argument is semi-acceptable iff it is notacceptable and belongs to some preferred extensions, but not to allof them. An argument is preferred semi-acceptable iff it is notacceptable and belongs to all the preferred extensions. Thepreferred semi-acceptable arguments are stronger than the semi-acceptable, and the grounded arguments are the strongest argu-ments in this classification.

Example 4. Let A ¼ fa; b; c; dg and AT is defined as follows:AT ða; bÞ; AT ðb; aÞ; AT ða; cÞ; AT ðb; cÞ, and AT ðc; dÞ.

� ; is the grounded extension in this argumentation framework.� The argumentation framework has two preferred extensions:fa; dg and fb; dg. The arguments a and b are then semi-accept-able, and the argument d is preferred semi-acceptable.

A concrete scenario of this example in a B2B setting would be asfollows: Suppose a transaction Tr along with three possiblesecurity policies: s1; s2, and s3. The four arguments a; b; c and dare as follows:

� a: s1 is the most suitable policy for the transaction Tr.� b: Alone, s2 is not sufficient to secure the transaction Tr, but by

combining it with s3 it becomes the most suitable.� c: s2 is less expensive than s1.� d: s1 is not expensive to implement, and is sufficient to secure

the transaction Tr.

To a certain extent, the argument d is stronger than a and bbecause it is defended by these two arguments against the onlyattacker c, and a and b attack each other. From a chronologicalpoint of view, we can imagine the following scenario leading tobuild these four arguments at the application level of twobusinesses represented by A� AA1 and A� AA2, respectively.First, A� AA1 presents the argument d, then A� AA2 attacks bymoving forward the argument c. A� AA1 replies by attacking cusing the argument a. At that stage, the arguments a and d aregrounded. A� AA2 tries then to degrade one of these twoarguments by attacking a using b. A� AA2 is aware that by usingb to attack a, b is at the same time attacked by a. The idea here isjust to change the status of the argument presented by A� AA1

from acceptable to semi-acceptable.

Proposition 3. Let A # ArgðLÞ be a set of arguments, and letSD ¼ fa 2 Aj 8b 2 AAT ðb; aÞ ) AT ða; bÞ&9= c 2 A : AT ðc; bÞg.8a 2 SD; a is semi-acceptable.

In other words, the arguments defending themselves by only them-selves against all the attackers are semi-acceptable.

Proof. See Appendix. h



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Proposition 4. Complete extensions are not closed underintersection.


Definition 8 (Eliminated Arguments). Let A # ArgðLÞ be a set ofarguments, a 2 A be an argument, and EL be the set of eliminatedarguments over the argumentation framework. Also, let E1; . . . ; En

be the preferred extensions in the same framework. a 2 EL iffa R Ei; 8i 2 ½1; n�.

In other words, an argument is eliminated iff it does not belongto any preferred extension in the argumentation framework. Wehave the following proposition:

Proposition 5. Let a be an argument in A, and AC; PS; and SA berespectively the sets of acceptable, preferred semi-acceptable, andsemi-acceptable arguments over the argumentation framework.a 2 EL iff a R AC [ PS [ SA.

In other words, an argument is eliminated iff it is not acceptable,not preferred semi-acceptable, and also not semi-acceptable.


Consequently, arguments take four exclusive statuses namelyacceptable, preferred semi-acceptable, semi-acceptable, and elimi-nated. The dynamic nature of agent interactions is reflected by the changes in the statuses of the uttered arguments.

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3.2. Partial arguments and conflicts for B2B applications

In a B2B scenario, it happens that the argumentative agentsS � AAs and A� AAs do not have complete information aboutsome facts. In a similar situation, they can build partial argumentsfor some conclusions out of their beliefs. We define a partial argu-ment as follows:

Definition 9 (Partial Arguments). Let x be a wff in WF . A partialargument denoted by ap

x is part of an argument a 2 A, which missesan argument (or a proof) for x. In other words, by adding a proofsupporting x to ap

x an argument is obtained.

For example, if arguments are defined as deductions from a setof rules, x will represent some missing rules, and if arguments aredefined as pairs ðH; hÞ, x will represent a subset of H.

Example 5. Let us suppose that arguments are defined as pairsðH; hÞ using propositional logic. a ¼ ððm; m! nÞ; nÞ is an argumentfor n and ap

x ¼ ððm! nÞ; nÞ is a partial argument for n missing thesupport for x ¼ m.a ¼ ððm; m! n; n! l; l! rÞ; rÞ is an argumentfor r and ap

x ¼ ððn! l; l! rÞ; rÞ is a partial argument for r missingthe support for x ¼ n. In this case, a possible support isððm; m! nÞ; nÞ.

In a B2B scenario, an example where partial arguments areneeded is when A� AA1 of business B1 knows that securitypolicy s2 that another business B2 uses can be substituted bypolicy s1 that B1 uses if some conditions are met whendeploying s2. Thus, A� AA1 can build a partial argumentsupporting the fact that B2 can use s1. To be an argument, thispartial argument needs a support that implementing s2 in B2

meets these conditions.The idea behind building partial arguments by an agent is to

check if the other agent can provide the missing part or a part ofthis missing part so that the complete argument could be jointlybuilt (progressively). This idea which is a part of the inquirydialogue will be made clear in the persuasion protocol defined inSection 4.2.


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As for arguments, we need to define what an acceptable partialargument is. This acceptability is defined in the same way as forarguments. We use the notation ap

x :x to denote the resultingargument of combining the partial argument ap

x and an argumentsupporting x supposing that this latter exists.

Definition 10 (Partial Attack). Let apx be a partial argument over

the argumentation framework. AT ðapx ; bÞ iff AT ðap

x :x; bÞ andAT ðb; ap

xÞ iff AT ðb; apx :xÞ.

Definition 11 (Acceptable Partial Arguments). A partial argumentap

x is acceptable (preferred semi-acceptable, semi-acceptable) iffap

x :x is acceptable (preferred semi-acceptable, semi-acceptable).

Example 6. Let R ¼ fn! m; r ! l; l! t; :lg be a propositionalknowledge base. The partial argument ððn! mÞ; mÞ is acceptable,however the partial argument ððr ! l; l! tÞ; tÞ is not acceptablesince the argument ððr; r ! l; l! tÞ; tÞ is attacked by the argumentð:l; :lÞ.

Proposition 6. Let a be an argument in A. If a is acceptable, then8x 2 WFap

x is acceptable.


After specifying the argumentation model, We define the no-tions of conflict and conflict resolution in our B2B framework asfollows:

Definition 12 (Conflict). Let p and q be two wffs in WF . There is aconflict between two argumentative agents a and b about p and qin the B2B framework iff one of them (e.g., aÞ has an acceptableargument a for p (denoted a " pÞ and the other (i.e., bÞ has anacceptable argument b for q ðb " qÞ such that AT ða; bÞ or AT ðb; aÞ.We denote this conflict by ap�bq.

For example, if p and q represent each a security policy s1 and s2

such that s1 and s2 cannot be used together, then there is a conflictif one agent has an acceptable argument for using s1 while theother agent has an acceptable argument for using s2 (the twoarguments are conflicting). This conflict arises when both agentsneed to agree on which security policy to use.

Before defining the notion of conflict resolution, we need todefine the notions of interaction and outcome of interaction. Anutterance u made by an agent a in a given interaction is denotedu,a.

Definition 13 (Interaction). Let a and b be two argumentativeagents. An interaction (denoted by Ia; bÞ between a and b in the B2Bframework is an ordering sequence of utterances u1; u2; . . . ; un

such that ui,a) uiþ1,b and ui,b) uiþ1,a. CSa (resp. CSb) isthe set (called commitment store) containing the arguments usedby a (resp. b) during the interaction.

Definition 14 (Conflict Resolution). Let p and q be two wffs in WFand a and b be two argumentative agents in the B2B frameworksuch that ap�bq. Also let Ia; b be an interaction in this framework.The conflict ap�bq is resolved by the interaction Ia; b iff the outcomeof Ia; b is a formula r 2 WF such that 9a 2 CSa; b 2 CSb : a " r; b " rand a and b are both acceptable.

In the aforementioned security example, the conflict is resolvediff (i) after interaction, one of the agents can build an acceptableargument from its knowledge base and the arguments exchangedduring this interaction, supporting the use of the other agent’s pol-icy, or (ii) when both agents agree on the use of a new policy suchthat each agent can build an acceptable argument, from its knowl-edge base and the exchanged arguments, supporting the use of this



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policy. The idea here is that by exchanging arguments, new solu-tions (and arguments supporting these solutions) can emerge. Inthis case, the agents should update their beliefs by withdrawing at-tacked (i.e., eliminated) assumptions. However, there is still a pos-sibility that each agent keeps its own viewpoint at the end of theconversation.

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4. Argumentative persuasion for B2B

4.1. Notations

The outcome of an interaction to resolve a conflict in a B2B set-ting depends on the status of the formula representing the conflicttopic. As for arguments, a wff has four statuses depending on thestatuses of the arguments supporting it (an argument supports aformula if this formula is the conclusion of that argument). A wffis acceptable if there exists an acceptable argument supporting it.If not, and if there exists a preferred semi-acceptable argumentsupporting it, then the formula is preferred semi-acceptable.Otherwise, the formula is semi-acceptable if a semi-acceptableargument supporting it exists, or eliminated if such an argumentdoes not exist. Let St be the set of these statuses. We define the fol-lowing function that returns the status of a wff with respect to aset of arguments:

D :WF � 2A ! St

Generally, the interactions that are needed in a B2B scenario in-volve two argumentative agents. For simplicity, we will not refer inthe remainder of the paper to agent types (strategic or application),but denote participating agents by a and b. Each agent has a possi-bly inconsistent belief base Ra and Rb, respectively, that containsfor example, all the policies upon which these agents should rea-son when they manage businesses as explained in the previoussections. Although the argumentation framework presented in Sec-tion 3 does not assume that arguments are truthful, we supposethat the agents participating in resolving B2B conflicts are truthtelling. This means they (i) reveal only the arguments they havein their knowledge bases and (ii) are perfectly cooperative. Pro-moting truth telling in the proposed framework using for instancegame-theoretical techniques, and considering non-cooperativeagents are plans for future work.

Agents use their argumentation systems to decide about thenext move to play (e.g., accept or attack the arguments put forwardduring their interactions). When an agent accepts an argumentthat an addressee suggests, this agent updates its knowledge baseby adding the elements of this argument and removing all the ele-ments that attack this argument. The acceptability we considerhere is purely argumentative as specified in Definition 6. However,if businesses have different power positions in their relationship,the proposed approach still stands if the power positions areclearly stated as shared and agreed upon rules. This simply meansthat acceptability should also consider these rules. For example, anagent can accept an argument if it is associated with a power. Fur-thermore, an argument a can attack another argument b withoutbeing attacked by this argument (i.e., by b) if a is given by an agenthaving a superior power position. However, if these rules are notshared and agreed upon, they can still be used simply by not beingcooperative, which is an assumption for the soundness of ourapproach.

Each agent a has also a commitment store (CSa) that is publiclyaccessible for consultation but only updated by the owner agent.The commitment stores are empty when interaction starts, and up-dated by adding arguments and partial arguments that the agentsexchange. CSa refers to the commitment store of agent a at the cur-rent moment.


The possibility for an agent a to build an acceptable argument a(respectively an acceptable partial argument ap

x ) from its knowl-edge base and the commitment store of the addressee b is denotedby ARðRa [ CSbÞ . a (respectively ARðRa [ CSbÞ . ap

x). Building apartial argument ap

x from a knowledge base means that no argu-ment for or against x can be built. ARðRa [ CSbÞ7a (respectivelyARðRa [ CSbÞ7ap

x ) means that agent a cannot build an acceptableargument a (respectively an acceptable partial argument ap

x) fromRa [ CSb. The symbols D and 4 associated with the semi-accept-
able (partial) arguments are defined in the same way.
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F4.2. Protocol specification

In our B2B framework, the agents engage in persuasion and in-quiry dialogues to resolve conflicts. Atkinson et al. [2], Pasquieret al. [21], and Prakken [22] propose persuasion protocols for mul-ti-agent systems. However, these protocols consider only pure per-suasion without inquiry stages and do not address completeness(or pre-determinism) property [20]. We propose a persuasion pro-tocol that includes inquiry stages in our B2B framework, in whichpre-determinism is considered. The protocol is modeled with dia-logue games [16,17]. Dialogue games are interactions betweenplayers (agents), in which each player moves by performing utter-ances according to a pre-defined set of rules. Let us define the no-tions of protocol and dialogue games.

Definition 15. ProtocolA protocol is a pair hC; Diwith C a finite setof allowed moves and D a set of dialogue games.

The moves in C are of c different types (c > 0). We denote byMiða; b; a; tÞ a move of type i played by agent a and targeting agentb at time t regarding a content a. We consider four types of movesin our protocol: Assert, Accept, Attack, and Question. Generally, inthe persuasion protocol the agents exchange arguments. Exceptthe Question move whose content is not an argument, the contentof other moves is an argument aða 2 ArgðLÞÞ. When replying to aQuestion move, the content of Assert move can also be a partialargument or ? when the agent does not know the answer. Weuse another particular move Stop with no content. It could be usedby an agent to stop the interaction.

Intuitively, a dialogue game in D is a rule indicating the possiblemoves that an agent could play following a move done by an ad-dressee. This is specified formally as follows:

Definition 16. Dialogue Game A dialogue game Dg is either of theform:

Miða;b; ai; tÞ )_

0<j6ni

Mjðb;a; aj; t0Þ

where Mi and Mj are in C; t < t0 and ni is the number of allowedmoves that b could perform after receiving a move of type i froma; or of the form:

)_

0<j6n

Mjða;b; aj; t0Þ

where Mj are in C; t0 is some initial time, and n is the number of al-lowed moves that a could perform initially.

According to this definition, a dialogue game could be eitherdeterministic (if n ¼ 1 and 8ini ¼ 1) or non-deterministic. Becauseagents are autonomous, we consider here non-deterministic dia-logue games, in that, for example, given an incoming move of typei, the receiving agent needs to choose amongst the ni possible re-plies (ni > 1). As proposed in [4,6,7], we combine public dialoguegames with private strategies so that the agents become determin-istic. To this end we introduce the conditions within dialoguegames, each associated with a single reply.



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Definition 17. Strategic Dialogue Game A strategic dialoguegame SDg is a conjunction of rules, specified either as follows:^

0<j6ni

Miða; b; a; tÞ ^ Cj ) Mjðb;a; aj; t0Þ� �

where t < t0 and ni is the number of allowed communicative actsthat b could perform after receiving a move of type i from a; or asfollows:^

0<j6n

Cj ) Mjða;b; aj; t0Þ� �

where t0 is the initial time and n is the number of allowed movesthat a could play initially.

In order to guarantee determinism, conditions Cj need to bemutually exclusive [25]. The agents use their argumentation sys-tems to evaluate, in a private manner, conditions Cj. These argu-mentation systems are based on the private agents’ beliefs andthe public commitments recorded in the commitment stores.

To simplify the notations, we omit the time parameter form themoves and use the notation [CS as an abbreviation of CSa [ CSb. Inour B usiness-to-B usiness Persuasive Protocol (B2B � PP), theagents are not allowed to play the same move (with the same con-tent) more than once. The strategic dialogue games we consider inthis protocol are:

4.2.1. Initial game

Cin 1 ) Assertða; b; aÞwhere:Cin 1 ¼ 9p; q 2 WF : ap�bq ^ ARðRaÞ . a ^ a " p

Although generic, this game is derived from B2B settings wherea business detects a conflict with another business. The persuasionstarts when a conflict is detected and one of the two businesses/agents asserts an acceptable argument that supports its position.In the remainder of this section, we suppose that the persuasiontopic is represented by the wff p.

4.2.2. Assertion game

Assertða;b;lÞ ^ Cas1 ) Attackðb;a; bÞÂssertða;b; mÞ ^ Cas2 ) Questionðb;a; xÞÂssertða;b; mÞ ^ Cas3 ) Acceptðb;a; aÞÂssertða;b; mÞ ^ Cas4 ) Stopðb;aÞ

where l is an argument or partial argument, m is an argument, par-tial argument, or ? and:

Cas1 ¼ Opat1as1_ ð:Opat1

as1^ Opat2

as1Þ

Opat1as1¼ 9b 2 A : ARðRb [ CSaÞ . b

^ Dðp;[CSÞ– Dðp;[CS [ fbgÞOpat2

as1¼ 9b 2 A : ARðRb [ CSaÞDb

^ Dðp;[CSÞ– Dðp;[CS [ fbgÞCas2 ¼ :Cas1 ^ ðOpqu1

as2_ ð:Opqu1

as2^ Opqu2

as2ÞÞ

Opqu1as2¼ 9bp

x ; bpx :x 2 A : ARðRb [ CSaÞ . bp

x

^ Dðp;[CSÞ– Dðp;[CS [ fbpx :xgÞ

Opqu2as2¼ 9bp

x ; bpx :x 2 A : ARðRb [ CSaÞDbp

x

^ Dðp;[CSÞ– Dðp;[CS [ fbpx :xgÞ

Cas3 ¼ 9a 2 A : ARðRb [ CSaÞ . a ^ a " p^ :Opqu1

as2^ :Opqu2

as2

Cas4 ¼ :Opat1as1^ :Opqu1

as2^ :Opqu2

as2^ :Cas3

^ 8b 2 A;ARðRb [ CSaÞDb)Dðp;[CSÞ ¼ Dðp;[CS [ fbgÞ


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In this game, the content of Assert could be an argument, par-tial argument, or ‘‘?”. The last two choices are particularly derivedfrom B2B aplications, where businesses have only partial infor-mation about each other’s activities and should exchange ques-tions to reveal the unkown information that could help inresolving the business conflict. We recall that the two businessesare cooperative because they have interest in resolving the con-flict. Indeed, businesses/agents can use this move to assert newarguments in the initial game or to reply to a question in thequestion game, which is a part of inquiry in our protocol. Themove that agent b can play as a reply to the Assert move dependson the content of this assertion. When a asserts an argument or apartial argument, CSa changes by adding the advanced (partial)argument. Agent b can attack agent a if b can generate an accept-able argument from its knowledge base and the a’s commitmentstore so that this argument will change the status of the persua-sion topic. Consequently, in this protocol the agents do not attackonly the recently advanced argument, but any advanced argu-ment during the interaction, which is still acceptable or (pre-ferred) semi-acceptable (Opat1

as1). This makes the protocol more

flexible and efficient (for example agents can try different argu-ments to attack a given argument). If such an acceptable argu-ment cannot be generated, b will try to generate a (preferred)semi-acceptable argument changing the status of pðOpat2

as1Þ. The

idea here is that if b eliminates a’s arguments, it will try to makethem (preferred) semi-acceptable. This is due to the followingproposition whose proof is straightforward from the definitionof semi-acceptable arguments and the fact that only four statusesare possible.

Proposition 7. If b plays the Attack move with a semi-acceptableargument, then the a’s attacked argument changes the status fromacceptable to semi-acceptable, and the persuasion topic changes thestatus from acceptable to semi-acceptable or preferred semi-acceptable.

We notice that in the Assertion game changing the status of p isa result of an attack relation:

Proposition 8. In the Assertion game we have: 8b 2 A; Dðp; [CSÞ –Dðp; [CS [ fbgÞ ) 9a 2 [CS : AT ðb; aÞ.

If b cannot play the Attack move, then before checking theacceptance of an a’s argument, it checks if no acceptable and then no(preferred) semi-acceptable argument in the union of the knowledgebases can attack this argument (inquiry part). For that, if b cangenerate a partial argument changing the status of p, then it willquestion a about the missing assumptions (Opqu1

as2and Opqu2

as2). This new

feature provides a solution to the ‘‘pre-determinism” problem identi-fied in [20]. If such a partial argument does not exist, and if b cangenerate an acceptable argument supporting p, then it plays theAccept move (Cas3).

Proposition 9. An agent plays the Accept move only if it cannot playthe Attack move and cannot play the Question move.


Agent b plays the Stop move when it cannot accept an a’s argu-ment and cannot attack it. This happens when an agent has a semi-acceptable argument for p and another semi-acceptable argumentagainst p, so the status of p in the union of the commitment storeswill not change by advancing the b’s argument (Cas4). Finally, wenotice that if the content of Assert move is ?, b cannot play the At-tack move. The reason is that such an Assert is played after a ques-tion in the Question game, and the agents play Question moves onlyif an attack is not possible. Using simple logical calculus, we canprove the following proposition:



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4.2.3. Attack game

Attackða;b; aÞ ^ Cat1 ) Attackðb;a; bÞÂttackða;b; aÞ ^ Cat2 ) Questionðb;a; xÞÂttackða;b; aÞ ^ Cat3 ) Acceptðb;a; aÞÂttackða;b; aÞ ^ Cat4 ) Stopðb;aÞ

where:

Cat1 ¼ Opat1at1_ ð:Opat1

at1^ Opat2

at1Þ

Opat1at1¼ Opat1

as1

Opat2at1¼ Opat2

as1

Cat2 ¼ :Cat1 ^ ðOpqu1at2_ ð:Opqu1

at2^ Opqu2

at2ÞÞ

Opqu1at2¼ Opqu1

as2

Opqu2at2¼ Opqu2

as2

Cat3 ¼ ARðRb [ CSaÞ . a ^ :Opqu1at2^ :Opqu2

at2

Cat4 ¼ :Opat1at1^ :Opqu1

at2^ :Opqu2

at2^ :Cat3

^ 8b 2 A;ARðRb [ CSaÞDb)Dðp;[CSÞ ¼ Dðp;[CS [ fbgÞ

The conditions associated with the Attack game are similar tothe ones defining the Assert game. The Attack move also includesthe case where the business/agent that initiates the persuasionputs forward a new argument, which is not attacking any existingargument but changing the status of the persuasion topic. This isparticularly useful in B2B applications when the advanced argu-ments cannot be attacked/defended, so that the business conflictcannot be resolved. However, by trying another way to convincethe addressee, the initiator business/agent can achieve the purposeof resolving successfully the conflict.

4.2.4. Question game

Questionða;b; xÞ ^ Cqu1 ) Assertðb;a; aÞ^Questionða;b; xÞ ^ Cqu2 ) Assertðb;a; yp

x0 Þ^Questionða;b; xÞ ^ Cqu3 ) Assertðb;a; ?Þ

where:

Cqu1 ¼ 9a 2 A : ARðRb [ CSaÞ . a ^ ða " x _ a " �xÞCqu2 ¼ 9yp

x0 ; ypx0 :x

0 2 A : ARðRb [ CSaÞ . ypx0

^ ðypx0 " x _ yp

x0 " �xÞCqu23 ¼ :Cqu1 ^ :Cqu2

Business/agent b can answer the a’s question about the contentx by asserting an argument for or against x. If not, it answers by apartial argument if it can generate it. Otherwise, it answers by ?,which means that it does not know if x holds or not. This gameis particularly derived from B2B applications where the informa-tion about the involved businesses are limited. The game is playedwhen a business/agent has a partial argument and asks the otherbusiness/agent about the missing part that is needed to achievean acceptable resolution of the conflict, so that the answer couldbe the complete missing part, a part of it, or nothing.

4.2.5. Stop game

Stopða;bÞ ^ Cst1 ) Questionðb;a; xÞ^Stopða;bÞ ^ Cst2 ) Stopðb;aÞ

where:


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Cst1 ¼ Opqu1st1_ ð:Opqu1

st1^ Opqu2

st1ÞÞ

Opqu1st1¼ Opqu1

as2

Opqu2st1¼ Opqu2

as2

Cst2 ¼ :Cst1

Before answering the a’s Stop move by another Stop to termi-nate the persuasion, b checks if no other partial arguments chang-ing the status of p could be generated. Consequently, the Stop moveis played only if no such argument could be generated, whichmeans that the conflict cannot be resolved. As mentioned above,checking the existence of other partial arguments is particularlyuseful for B2B applications as the shared information are usuallypartial and incomplete.

4.3. Protocol analysis

In this section, we prove the termination, soundness, and com-pleteness of B2B � PP and discuss its computational complexity.

Theorem 1. B2B � PP always terminates either successfully byAccept or unsuccessfully by Stop.


When the protocol terminates, we define its soundness andcompleteness as follows:

Definition 18 (Soundness - Completeness). A persuasion protocolabout a wff p is sound and complete iff for some arguments a for oragainst p we have:

ARðRa [ RbÞ . a() ARð[CSÞ . a
E
Theorem 2. The protocol B2B-PP is sound and complete.


As discussed earlier, the agents are supposed to be truth tellingand cooperative. The following theorem gives the result if such anassumption is not considered.

Theorem 3. The soundness and completeness of the protocol B2B-PPdo not hold if agents are not truth telling.


This means if the agents are not truth telling, the interactionoutcome cannot be determined, as it could be anything.

The computational complexity of the protocol can be computedconsidering two issues: (1) the complexity of computing argu-ments, partial arguments, and their acceptability; and (2) the com-plexity of playing the games. An important issue in this complexityis the underlying logical language used to specify arguments. It hasbeen proved in [4] that when Horn clauses are used, the complex-ity of computing arguments and their acceptability is polynomial ifthe knowledge base is consistent or is under the form of definiteHorn. Because partial arguments are also arguments that miss gi-ven parts, the complexity of their computation along with theiracceptability is also polynomial in the case of Horn clauses. We no-tice that for the purpose of B2B applications, Horn clauses, whichare disjunction of literals (an elementary or atomic propositionor its negation) with at most one positive literal (also written asimplication), are sufficient to represent and reason about knowl-edge that the three businesses levels presented in Fig. 1 use duringargumentative conversations.

The complexity of playing the games can be reduced to thecomplexity of deciding about the next move given the previousmove and the content of the agent’s knowledge base and the



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Fig. 4. Specification of the purchase-order scenario.

Fig. 5. Scenario description.




Please cite this article in press as: J. Bentahar et al., Using argumentation to model and deploy agent-based B2B applications, Knowl. Based Syst. (2010),doi:10.1016/j.knosys.2010.01.005


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Fig. 6. Sample of interactions between A� AA of Inv-Mgmt-WS and A� AA of Shipper-WS.




shared commitment store. From the game specification, decidingthe next move is argumentation-based with a polynomial com-plexity. Combining the different games is clearly polynomial asthe last replied move decides about the game to be played. There-fore, given the fact that businesses/agents’ knowledge bases are fi-nite and repeated games with the same content is prohibited, thecomplexity of the protocol B2B-PP is polynomial.
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E5. Case study

5.1. Description and analysis

Our running example (provided by IBM Research Division) illus-trates an online purchase-order application using Web servicestechnology [24] (Fig. 4). This application, widely used in B2B set-tings and supply chain management, is inspired by SpendMap Pur-chase Order Software3. A customer places an order for products viaCustomer-WS (WS for Web service). Based on this order, Cus-tomer-WS obtains details on the customer’s purchase history fromCRM-WS (Customer Relationship Management) of Business B1. Next,Customer-WS forwards these details to B1’s Billing-WS, whichcalculates the customer’s bill based on these details (e.g., consideringif the customer is eligible for discounts) and sends the bill to CRM-

WS. This latter prepares the detailed purchase-order based on the billand sends Inv-Mgmt-WS (Inventory Management) of B1 this orderfor fulfillment. For those products that are in stock, Inv-Mgmt-WSsends Shipper-WS of B2 a shipment request. Shipper-WS is nowin charge of delivering the products to the customer. For those notin stock, Inv-Mgmt-WS sends Supplier-WS of B3 a supply messageto the requisite, which provides the products to Shipper-WS forsubsequent shipment to the customer.

From a B2B perspective, the above application shows how dif-ferent businesses need to collaborate in order to fulfill customers’needs, as per the three horizontal relations of Fig. 1. This applica-

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Bpurch.


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tion could be affected by several types of conflicts. For example,B2’s Shipper-WS may not deliver the products as agreed withB1’s Inv-Mgmt-WS, perhaps due to lack of trucks. This is an appli-cation level conflict that needs to be resolved using our B2B-PP bywhich, Shipper-WS tries to persuade Inv-Mgmt-WS about thenew shipment time and then, inform Customer-WS of the newdelivery time. If not, Shipper-WS may change its policies by can-celling its partnership agreements without prior notice. This is astrategic level conflict, that calls for either asking B2 to whichShipper-WS belongs to review its policies, or if that does notwork, selecting an alternate shipper.

Let aB1 be the A� AA of Inv-Mgmt-WS and bB2be the A� AA of

Shipper-WS. The resolution of the application level conflict alongwith the use of dialogue games are hereafter provided:

1. bB2identifies the conflict and plays the Initial game by asserting

an acceptable argument a about lack of trucks from its RbB2sup-

porting its position: AssertðbB2; aB1 ; aÞ.

2. aB1 has an argument b attacking bB2’s argument, which is about

the available trucks that can be borrowed from a company andcould be used to ship the products. aB1 plays then the Assertiongame by advancing the Attack move: AttackðaB1 ; bB2

; bÞ.3. bB2

replies by playing the Attack game. Because it does not havean argument to change the status of the persuasion topic, buthas a partial argument for that, which is about the high priceof these particular trucks that could be not accepted by aB1 , itadvances the move: QuestionðbB2

; aB1 ; xÞ where x representsaccepting or not the new prices. The idea here is that bB2

canattack aB1 , if it refuses the new prices that others have accepted.

4. aB1 plays the Question game and answers the question byasserting an argument c in favor of the increased shipmentcharges: AssertðaB1 ; bB2

; cÞ:5. bB2

plays the Assertion game, and from RbB2[ CSaB1

, it acceptsthe argument and agrees to deliver the products as per theagreed schedule with the new price, which is represented byd: AcceptðbB2

; aB1 ; dÞ. Consequently, the persuasion terminatessuccessfully by resolving the conflict.


http://www.spendmap.com









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Figs. 5 and 6 illustrate the scenario details with the exchangedarguments.

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5.2. Implementation

We have implemented a proof-of-concept prototype of our B2Bframework using Jadex Agent System (a Java-based programminglanguage for autonomous agents) and applied it to the case studyscenario. Fig. 7 depicts a screenshot of the prototype illustratingthe involved agents and computation of the arguments in the sce-nario. The two involved agents in this scenario (described in Fig. 6)are Inv Mgmt and Shipper. The console output shows the differentcomputed arguments and their extensions.

Computing the different argument extensions and acceptablearguments and partial arguments is an essential part of our frame-work and thus, the prototype. This process has been implementedusing InterProlog, an open source Java front-end and functionalenhancement for Prolog. Because both Jadex Agent System andInterProlog are Java-based, they are compatible and can communi-cate. The computed arguments and their extensions are then con-veyed by InterProlog to Jadex Agent System that implements the B2Bapplication. The Input Screen in Fig. 8-a is a Java Swing GUI used tospecify the agents’knowledge bases, their partial arguments, andthe conflicts between arguments. Then, the acceptable arguments

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Fig. 7. A screenshot from the prototype -invo


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and the way to resolve the conflict in the B2B setting is shown afterrunning the system as illustrated in Fig. 8-b. The arguments used inthe figure are taken from the case study where the meaning ofevery argument is defined in a separate text file, for example argu-ment 0a0 is about lack of trucks, which implies delayed delivery.

In this particular running example, agent Inventory (Inv Mgmt)has two arguments 0b0 and 0c0 in the knowledge base, which are notattacked. In addition, argument 0b0 attacks and argument 0e0 attacks0b0 (the symbol 0#n0 is used as a separator). The final text field is forsupport; for instance support for 0x0 is 0c0 (this is captured in theframework by the assertion in Question game). The process of com-puting the extensions and resolving the conflicts is illustrated inFig. 9. In this figure, (1) check partial, (2) check ques, (3)Find Extension, and (4) ques ans are Java methods having the fol-lowing respective purposes: (1) filter partial arguments to returnonly arguments; (2) ask for missing information; (3) find groundedor preferred extensions from the argumentation framework; and(4) find support for information asked.

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6. Related work

Recent years have seen a continuing surge of interest in design-ing and deploying B2B applications. Service-oriented architectureis the most widely methodology that have been used in this field

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lved agents and computing arguments-.



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Fig. 8. (a) Input screen, (b) Resolving conflict scenario.




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EC[15,19,26,28]. In Ref. [15] the author proposes the exploitation of

Web services and intelligent agent techniques for the design anddevelopment of a B2B eCommerce application. A multi-party mul-ti-issue negotiation mechanism is developed for this application.This negotiation is a Pareto optimal negotiation based on gametheory. This proposal aims at achieving an agreement by comput-ing concessions and generating offers in order to maximize theutility of the participating agents. However, unlike our argumenta-tion-based framework, this mechanism cannot be used to resolvegeneral conflicts as those discussed in Sections 2 and 3. In [19],the authors develop a methodology for B2B design applicationsusing Web-based data integration. The aim is the creation of adapt-able semantics oriented meta-models to facilitate the design ofmediators by considering several characteristics of interoperableinformation systems such as extensibility and composability. Themethodology is used to build cooperative environments involvingthe integration of Web data and services. Unlike our methodology,this proposal does not consider conflicts that can arise during thecooperation phase and only addresses the cooperation from tech-nological point of view.

On the other side, and from an argumentation viewpoint, someinteresting protocols for persuasion and inquiry have been pro-posed. [2] propose Persuasive Argument for Multiple Agents (PAR-MA) Protocol, which enables participants to propose, attack, anddefend an action or course of actions. This protocol is specifiedusing logical consequence and denotational semantics. The focusof this work is more on the semantics of the protocol rather thanthe dynamics of interactions. [7] propose a dialogue game inquiryprotocol that allows two agents to share knowledge in order toconstruct an argument for a specific claim. There are many funda-mental differences between this protocol and ours. Inquiry and


persuasion settings are completely different since the objectivesand dynamics of the two dialogues are different. In [7], argumenta-tion is captured only by the notion of argument with no attackrelation between arguments. This is because agents collaborateto establish joint proofs. However, in our system, agents can reasonabout conflicting assumptions, and they should compute differentacceptability semantics, not only to win the dispute, but also toreason internally in order to remove inconsistencies from theirassumptions. From the specification perspective, there are no sim-ilarities between the two protocols. Our protocol is specified as aset of rules about which agents can reason using argumentation,which captures the agents’ choices and strategies. However, in[7] the protocol is specified in a declarative manner and the strat-egy is only defined as a function without specifying how the agentscan use it. The adopted moves in the two proposals are also differ-ent. Another technical, but fundamental difference in the two pro-tocols is the possibility in our protocol of considering not only thelast uttered argument, but any previous argument which allowsagents to consider and try different ways of attacking each other.

7. Conclusions and future work

In this paper, a 3-level framework for B2B applications is pre-sented. The three levels namely strategic, application and resourceare populated with argumentative agents. The first contribution ofthis paper is the development of a framework to set-up collabora-tions among autonomous businesses (via strategic level), and exe-cute and manage these collaborations (via application level).Inevitably, given the autonomous and dynamic nature of busi-nesses, conflicts are bound to arise. The second contribution is



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Fig. 9. Process of computing the extensions and resolving the conflicts.




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COthe proposition of a sound and complete persuasion protocol for

resolving such conflicts. This protocol, that includes inquiry stagesis argumentation-based.

Future work would include considering a negotiation protocolduring argumentation and scaling up and demonstrating our argu-mentation-based model on larger examples. Additional researchvenues would be enriching this model with fuzzy concepts andnew criteria of acceptability and with contextual ontologies whenmodeling knowledge bases of individual agents. Promoting truthtelling in our argumentation-based framework and consideringnon-cooperative agents are other plans for future investigation.

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Acknowledgements

The first author is partially supported by Natural Sciences andEngineering Research Council of Canada (NSERC), Fonds québécoisde la recherche sur la nature et les technologies (NATEQ), andFonds québécois de la recherche sur la société et la culture(FQRSC). The authors would also like to thank the reviewers fortheir very helpful comments and suggestions.


Appendix. Proof of Proposition 3

Without loss of generality, let a; a1; . . . ; an be arguments in a gi-ven argumentation framework such that a1; . . . ; an are the onlyattackers of a and a is the only attacker of these arguments.According to Definition 6, the argument a is not acceptable sinceit is attacked and not defended, directly or indirectly by a non-at-tacked argument. Because it is defended, a belongs to some pre-ferred extensions. However, a does not belong to all of them. Forexample, a does not belong to the preferred extension to whichthe arguments a1; . . . ; an belong since these arguments belong alsoto some preferred extensions because they are defended. a is thensemi-acceptable. �

Proof of Proposition 4

We prove this proposition by a counter example usingExample 4. In this example fa; dg and fb; dg are completeextensions (preferred extensions). However, fdg is not a com-plete extension. �



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By Definition 5, the grounded extension is included in all pre-ferred extensions. Consequently, using Definition 8, an eliminatedargument is not acceptable. Also, according to Definition 7, aneliminated argument is not semi-acceptable and not preferredsemi-acceptable. �


Suppose that 9x 2 WF : apx is not acceptable. Therefore, a part of

the non-missing part of apx is not acceptable. Because this part is

also a part of a, then a is not acceptable. Contradiction! �


To prove this we should prove that Cas3 ) :Cas1 ^ :Cas2. Usingthe logical calculation, we can easily prove that :Cas1 ^ :Cas2 ¼:Cas1 ^ :Opqu1

as2^ :Opqu2

as2. Also, if an agent b can build an acceptable

argument a from Ab [ CSa, then it cannot build an acceptable or(preferred) semi-acceptable argument attacking a from the sameset. Therefore, ARðAb [ CSaÞ . a) :Cas1. Thus the result follows.�

Proof of Theorem 1

Agents’ knowledge bases are finite and repeating moves withthe same content is prohibited. Consequently, the number of Attackand Question moves that agents can play is finite. At a given mo-ment, agents will have two possibilities only: Accept if an accept-able argument can be built from CSa [ CSb, or Stop, otherwise.Therefore, the protocol terminates successfully by Accept, or unsuc-cessfully by Stop when Accept move cannot be played, whichmeans that only semi-acceptable arguments are included inCSa [ CSb. �

Proof of Theorem 2

For simplicity and without loss of generality, we suppose thatagent a starts the persuasion.

Let us first prove the ) direction: ARðAa [AbÞ . a)ARð[CSÞ . a.

In the protocol, the persuasion starts when a conflict over p oc-curs. Consequently, the case where Aa . a and Ab . a does not hold.The possible cases are limited to three:

1. Aa . a and Ab7a. In this case, agent a starts the persuasion overp by asserting a. Agent b can either play the Attack move or theQuestion move. Because ARðAa [Ab . aÞ all the b’s argumentswill be counter-attacked. For the same reason, b cannot play

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move. It follows that ARð[CS . aÞ.2. Aa7a and Ab . a. In this case, agent a starts the persuasion by

asserting an acceptable argument b in its knowledge baseagainst pðAa . bÞ. This argument will be attacked by agent b,and the rest is identical to case 1 by substituting agent roles.

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3. Aa7a and Ab7a. To construct argument a out of Aa [ Ab, twocases are possible. Either, (1) agent a has an acceptable partialargument aY

@ for p and agent b has the missing assumptions(or some parts of the missing assumptions, and agent a has

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the other parts), or (2) the opposite (i.e., agent b has an accept-able partial argument aY

@ for p and agent a has the missingassumptions (or some parts of the missing assumptions, andagent b has the other parts)). Only the second case is possiblesince the first one is excluded by hypothesis. For simplicity,


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we suppose that agent a has all the missing assumptions, other-wise the missing assumptions will be built by exchanging thedifferent partial arguments. Agent a starts the persuasion byasserting an acceptable argument b in its knowledge baseagainst p. Agent b can either play an Attack or a Question move.If attack is possible, then agent a can either counter-attack orplay the Stop move. The same scenario continues until agent aplays Stop, and then agent b plays a Question Move. Agent aanswers now the question by providing the missing assump-tions, after which agent b attacks and agent a can only acceptsince ARðAa [ Ab . aÞ. It follows that ARð[CS . aÞ.

Let us now prove the ( direction: ARð[CSÞ . a) ARðAa [ AbÞ . a.

In the protocol, to have ARð[CSÞ . a one of the two agents, sayagent a, puts forward the argument a and the other, agent b, ac-cepts it. On the one hand, to advance an argument, agent a playsthe Assert move (in the initial or question rules) or Attack move(in the assertion or attack rules). In all these cases, we have:ARðAa [ CSbÞ . a and there is no partial acceptable argumentattacking a from Aa [ SCb. On the other hand, to accept an argu-ment (in the assertion or attack rules), agent b should check thatARðAb [ CSaÞ . a, there is no other arguments changing the statusof the persuasion topic, and there is no partial acceptable argumentattacking a from Ab [ SCa. Therefore we obtain: ARðAa [ CSb[Ab [ CSaÞ . a. Because CSa #Aa and CSb #Ab we are done. �

EDProof of Theorem 3

Suppose for simplicity reasons that the agents’ knowledge basescontain directly arguments and partial arguments. The following isa counterexample proving that if the agents are not truth telling,the protocol will not be sound and complete. Suppose that agenta starts the protocol such that: Ra ¼ fb; c; xg; Rb ¼ fa; dp

xg;AT ða; bÞ; AT ðc; aÞ; AT ðd; cÞ; CSa ¼ fb; c; �xg; CSb ¼ fa; dp

xg. In thisexample, after playing the Question move about x by agent b, agenta answers by asserting �x, instead of x. We have thenARð[CSÞ . b ^ ARðRa [ RbÞ7b (the protocol is not sound) andARðRa [ RbÞ . a ÂRð[CSÞ7a (the protocol is not complete). �

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