Argumentation in the semantic web

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Abstract In this article, we define ArgSciFF, a prototype operational argumentation framework to support dialogic argument exchange between Semantic Web services. ArgSciFF is based on the Sciff abductive-logic programming (ALP) framework.(Sciff is an
  66 1541-1672/07/$25.00 © 2007 IEEE IEEE INTELLIGENTSYSTEMS Published by the IEEE Computer Society A r g u m e n t a t i o n T e c h n o l o g y  Argumentationin the Semantic Web Paolo Torroni and Federico Chesani, University of Bologna Marco Gavanelli, University of Ferrara T he Semantic Web vision looks toward a universal medium for data exchange. Thisvision has motivated significant research in classifying,packaging,and semanti-cally enriching information to support data automation,integration,and reuse across vari-ous applications. A large share of current research on these topics addresses new logics for concept description and knowledge representation;new languages for defining ontologies,taxonomies,and behavior; and new cooperation models,inter-change formats,and open standards. If these effortssucceed,Web pages will eventually include descrip-tions of their content that can leverage Semantic Webapplications and foster their growth. Search engineswill be able to respond to semantic queries,and Webservices will reason from semantically rich informa-tion and act accordingly.We believe the reasoning enabled by machine-understandable,semantically rich information isessential to the Semantic Web vision. Our work focuses on making this reasoning more visible topotential users by using dialogues for service inter-action. As currently understood,interaction amongSemantic Web services is essentially a point-to-pointservice request followed by a server response. Wedon’t propose modifying the way Web services inter-act. Instead,we suggest using argumentation tech-nology to drive the interaction at a higher level,wherehuman users can perceive message exchanges andservice-request sequences as high-level dialogues thatthey can understand better than current modalities.In this article,we define ArgS CIFF ,a prototypeoperational argumentation framework to support dia-logic argument exchange between Semantic Webservices. ArgS CIFF is based on the S CIFF abductive-logic programming (ALP) framework. 1 (S CIFF is anabbreviation for “  IFF  with c onstraints for agent s oci-eties,”referring to the “if and only if”proof proce-dure developed by Tze Ho Fung and Robert Kowal-ski. 2 ) In ArgS CIFF ,an intelligent agent can interactwith a Web service and reason from the interactionresult. The reasoning semantics is an argumentationsemantics that views the interaction as a dialogue.The dialogue lets two parties exchange argumentsand attack,challenge,and justify them on the basisof their knowledge. This format has the potential toovercome a well-known barrier to human users’adoption of IT solutions because it permits interac-tion that includes justified answers that can be rea-soned about and rebutted. Semantic Web interaction We begin with a scenario to use as a runningexample of a Semantic Web interaction and a gen-eral discussion of how argumentation can support it. A scenario: Scientists,departments, and trips In our scenario,Sarah is a Computer ScienceDepartment research scientist who often travels to con-ferences. Before traveling,CSD researchers must haveformal approval for their trip. To this end,they sendCSD a request. CSD checks its rules and regulationsand answers accordingly. The CSD regulations areoften cryptic and subject to change. CSD researchers The ArgS CIFF  architecture supports high-level reasoning and argumentation- driven interaction among Semantic Web services. A prototypeimplementation is based on a concrete operational model.  often have obsolete information about administration regulations and lit-tle interest in them generally. However,they must abide by them. Howcan we help this situation? Solution 1. CSD publishes all regulations and relevant forms on itsWeb site. Every time Sarah needs to travel,she reads the most recentregulations,downloads the relevant forms from the Web,does the nec-essary paperwork,and delivers the filled-in forms to CSD administra-tion. She solves any problems by direct interaction with the adminis-tration staff.This solution has many drawbacks. Employees don’t necessarilywant to keep up-to-date with new regulations,nor is it their job to doso. Furthermore,technology is helping provide information in thissolution,but it isn’t helping use it properly. All the paperwork andinteraction with the administration are still there and represent poten-tial sources of mistakes and misunderstandings. Moreover,the require-ment for direct interaction to solve problems means Sarah has to coor-dinate her time with administration officehours. Solving problems can become alengthy and frustrating process on both sides. Solution 2. The administration feeds alldepartment regulations into a server,whichpublishes them on the CSD Web site using asemantically rich,machine-understandable,Web-friendly format. Sarah has a PDA,whichruns an intelligent agent that can automati-cally download information from the CSDWeb service,parse it,and reason from it.Whenever Sarah needs to travel,she queriesher PDA to know if her trip is approved.This solution solves some of solution 1’sproblems. When Sarah needs to obtain aCSD service,she doesn’t have to read thedepartment’s regulations but can instead let her PDA do the job onher behalf. Sarah interacts with her PDA by simply assigning goalsto it—for example,“attend conference.”Because the rules are pub-lished in a machine-understandable format and a semantically richlanguage,the intelligent PDA agent can understand their meaning,reason from them,and determine whether Sarah’s goal can be accom-plished given the current regulations. Her PDA can access the CSDWeb service even when she’s away,so this is an “anywhere-anytime”solution that eliminates interaction problems due to misunderstand-ings and limited office hours.However,this solution presents a serious drawback:the exchangebetween Sarah and CSD has lost its interactive,dialogical character.Why is this a problem? Consider solution 1 again. If Sarah’s requestis rejected,Sarah can interact with the administration staff and findout why. Solution 2 doesn’t permit this interaction. Indeed,a well-known barrier to human adoption of IT solutions is that IT tends toprovide definitional answers rather than informed justifications thatusers could argue with and,possibly,eventually understand andaccept. Even an elegant and efficient solution such as this one,basedon a Semantic Web service,would hardly prevent Sarah from goingand talking directly to the administration to challenge every nega-tive answer her PDA obtains. Solution 3. The CSD’s service and Sarah’s PDA agent interact byexchanging arguments in a dialogical fashion. Sarah’s PDA not onlyposts requests to the CSD service and obtains replies but also rea-sons from such replies. When the replies are negative,the agent chal-lenges them and tries to understand ways to obtain alternative,pos-itive replies. If necessary,the agent can provide fresh informationthat could inhibit some regulations and activate others.This solution combines the benefits of the previous two. It dele-gates most of the reasoning and interaction to the machine by rely-ing on Semantic Web service technology,and it gives Sarah and CSDunderstandable,justified answers and decisions. The whole processis a machine-supported,collaborative problem-solving activity ratherthan a flat client-server,query-answer interaction. Reasoning and argumentation Reasoning occurs at different levels. For example,Loredana Laeraand her colleagues propose an argumentation framework for reachingagreements over ontology alignments. 3 Agreement over ontologiesand,more generally,over service descriptionsand semantics is one part of Semantic Webservice interactions. Another part is the high-level reasoning that supports message ex-changes among services. To the best of ourknowledge,the only research addressing thelatter is in the context of argumentation-baseddialogues for multiagent systems. In the mul-tiagent literature,we typically find rich inter-action protocols aimed at supporting per-suasion,negotiation,and so on,as well asdedicated architectural components,such ascommitment stores. We can nevertheless con-sider Semantic Web services as a concreteinstantiation of multiagent systems,in whichthe type of messages exchanged is generallyrestricted to request-response patterns.Argumentation is a natural way of conceptualizing nonmonotonicreasoning,appropriately reflecting its defeasible nature. The Seman-tic Web is a source of defeasible knowledge:it’s open by nature andsubject to inconsistencies deriving from multiple sources and incom-pleteness. So,the Semantic Web appears to be an extremely suitabledomain for applying argumentation theories,especially when the ser-vices interact with each other on the basis of different and possiblyinconsistent knowledge.Interaction can occur to request services and to coordinate andexchange information. In the Semantic Web,such information willalso include rules and logical constructs. The exchange requires suit-able reasoning tools that can consider logical constructs as first-classentities and suitable interaction models that can provide the meansto exchange rules,implications,conclusions,assumptions,and soon. Argumentation theories suit this task perfectly at both the rea-soning and the interaction levels. Abductive-logic programming Our research builds on Phan Minh Dung’s work on the acceptabil-ity of arguments. 4 S CIFF is both an ALP language and a proof proce-dure for generating grounded sets of arguments starting from a knowl-edge base. 1 Using the S CIFF ALP framework to construct arguments,we can map the arguments onto ALP abducibles —that is,unknownfacts that S CIFF can hypothesize and reason about as if they were true. NOVEMBER/DECEMBER 2007 67 We can consider Semantic Webservices as a concreteinstantiation of multiagentsystems, in which the typeof messages is restrictedto request-response patterns.  A r g u m e n t a t i o n T e c h n o l o g y 68 IEEE INTELLIGENTSYSTEMS Using S CIFF to construct arguments has some important advan-tages. S CIFF programs consist of rules,definitions,known facts,andevents that can occur dynamically. Such elements can contain vari-ables,quantified in various ways and possibly subject to constraintsand quantifier restrictions. It’s therefore an expressive language. Tothe best of our knowledge,most existing frameworks implementingargumentation are propositional and presume static knowledge. WithS CIFF ,however,you can use terms to encode data structures whose sizeisn’t known a priori. You can also represent events in a parametric way(“Employee  X  has been authorized by Y  at time T  ”) and reason fromsuch parameters.Moreover,S CIFF distinguishes between events that are known tohave happened and events that are expected either to happen or notto happen. All these elements together make it easy to represent inter-action protocols, 1 norms and regulations, 5 Web service specifica-tions, 6 and situations such as those we described in our scenario.Expected events represent future actions (Sarah traveling),whereashappened events represent facts that can become known to Web ser-vices as a dialogue develops (for example,when Sarah notifies CSDthat she holds a trip authorization from the CSD head,the CSDknowledge increases by one fact).We have developedArgS CIFF as an integrated suite of extensionsand tools developed on top of S CIFF . The extensions address Web ser-vice discovery and contracting, 6 and the tools address formal verifi-cation—both a priori (for example,abductive-logic Web service spec-ification and verification) and at runtime (for example,monitoringinteraction-protocol execution). So,after an argumentation-baseddialogue leads to an agreement (“Sarah can travel and is entitled toask for reimbursement”),ArgS CIFF and theS CIFF procedure can eas-ily verify that the actual behavior of the parties involved conforms tosuch an agreement.All material,including tools,is available from the S CIFF Web site,  ArgS CIFF :Extendingthe Semantic Web architecture We can view the Semantic Web as a lay-ered architecture. At the bottom are standardsfor unique resource identification,text encod-ing,message and resource descriptions,andontologies. On the top layer,the SemanticWeb emerges as a trusted convergence pointof core technologies based on semantic des-criptions,security technologies,logical mod-els,and automated reasoning procedures. Thecentral layers mediate between the bottom(ontology) layer and the top (logic and proof)layers. This is where reasoning about Seman-tic Web resources takes place.Machine-to-machine interaction over thenetwork occurs via Semantic Web services.Web services are an instance of the service-oriented-computing paradigm. They are state-less servers,implemented by software agents,interacting with each other through simplerequest-response message exchanges. Serviceprovidersuse WSDL to specify Web servicedescriptions—specifically,XML descriptionsof the service’s methods and the concrete net-work protocols and message formats needed to access them.The World Wide Web Consortium has a recommendation that sup-ports semantic descriptions of Web services ( sawsdl). Such descriptions could take the form of rules. More specif-ically,the Semantic Web Services Language is a general-purpose lan-guage to formally characterize service concepts and descriptions. Itssponsors have submitted SWSL to the W3C for consideration as arec-ommendation ( SWSL contains sev-eral sublanguages,including SWSL-Rules,which is based onRuleML-serialized logic programming and aims to support the useof the service ontology in reasoning and execution environments.Figure 1 shows the ArgS CIFF architecture as an extension of theWeb service architecture. On the left side of the figure is an agent, s ,which could be the intelligent agent running on Sarah’s PDA. On theright side,we have a Semantic Web service, d  ,which could be theCSD’s Web service. s and d  interact with each other using SemanticWeb technologies. From the Semantic Web’s ontology layer down-ward, s and d  will adopt some agreed-upon standard. In the currentprototype,they exchange SOAP messages,which can contain S CIFF rules. Messages are passed using an Internet transfer protocol suchas HTTP. s and d  will adopt some common domain-related ontology,such as one provided by the CSD for inquiries about regulations. Atthe logiclevel, s and d  use knowledge expressed by S CIFF programs.At the proof level,they use the ArgS CIFF proof procedure to evaluatequeries and replies,according to the abductivesemantics we definein the next section.The exchanged messages follow a simple request-reply protocol,but at a high level,we can view the way d  interacts with s as a dia-logue,in which s argues for its case against d  . From d  ’s standpoint,no dialogue occurs. d  simply provides two methods: request  and chal-lenge . The two different views of the ongoing interaction neverthe-less generate a decoupling,and this decoupling makes it possible tomarry stateless Web services with argumentation dialogues. WebservicedescriptionWebservicedescriptionopenRuleML/OWL/SOAP/HTTPInteractionRequesteragentProvideragentdeny challengeclose“dialogue” “services”agreejustifyrequestdeny request challenge request  agree challenge  justify s d  ArgS CIFF ArgS CIFF Figure 1. The ArgS CIFF architecture extends the Semantic Web service architecture withargumentation technology implemented through request and challenge methods. TheArgS CIFF argumentation protocol is asymmetric: the requester agent sees a dialogue,and the provider agent sees service requests.  S CIFF abductive semantics “Argument”is a semantically overloaded term. 7 We’ll define it for-mally later,but in the general context of argumentation frameworks,we use “argument”and “argumentation”in the sense that Dung usesthem in his seminal work. 4 Specifically,an argument is an abstractentity whose role is solely determined by its relation to other argu-ments. We pay no special attention to an argument’s internal struc-ture. An argumentation framework is defined as a pair  AF  = á  AR , attacks ñ ,where  AR is a set of arguments and attacks is a binary rela-tion on  AR —that is, attacks Í  AR ´  AR . Related to this notion of attacks is that of  defense :an argument can defend itself from an attack-ing argument by having a set S  of arguments that attack the attackingargument in turn. Accordingly, S  supports the first argument.Dung gives a model-theoretic semantics to abstract argumentationframeworks via the notion of  admissibility . In particular,an AF’sadmissible models are sets of arguments that don’t attack each otherand can defend each other from attacks srcinating from the outside.We can map Dung’s AF onto the S CIFF ALP framework and show thatthe sets of arguments S CIFF produces are admissible in Dung’s sense. The S CIFF ALP proof procedure ALP is a computational paradigm aimed at introducing hypothet-ical reasoning in the context of logic programming. 8 A logic program P  is a collection of clauses with an associated notion of entailmentindicated by |=. In ALP,the abductive reasoner can assume somepredicates—namely, abducibles ,belonging to a special set A  —tobe true,if need be. To prevent unconstrained hypothesis-making,ALP programs typically contain expressions that must be true at alltimes,called integrity constraints (IC). IC  indicates a set of such ICs,whereas ic indicates a singleton integrity constraint (an ic in S CIFF isan implication written as  Body ®  Head  ). An abductive-logic pro-gram is the triplet á P  , A  , IC  ñ ,with an associated notion of abduc-tive entailment.S CIFF provides the reference-logic framework for ArgS CIFF . A dis-tinguishing feature of S CIFF is its notion of expectations about events.Events are denoted as  H  atoms. Expectations are abducibles denotedas  E  (  X  ) (positive expectations) and  EN  (  X  ) (negative expectations),where  E  (  X  )/   EN  (  X  ) stands for “  X  is expected/expected not to hap-pen.”For example,we can express the expectation that Sarah won’tattend a conference by the atom  EN  ( action ( attend  ( sarah,conf  ))).Variables in events,expectations,and other atoms can be subject toconstraint-logic programming (CLP) constraints and quantifierrestrictions (intuitively,quantifier restrictions are constraints on uni-versally quantified variables). The following example IC not H  ( tell ( csd,X,authorization )) ®  EN  ( action ( attend  (  X,C  ))) (1)means,“If an (individual)  X  does not hold authorization from csd  ,  X  is expected not to attend (any conference) C  .”We use the functor tell to represent communicative actions,and the functor action to repre-sent all other actions.In equation 1,failure to hold authorization is mapped onto a nega-tive  H  literal. In the S CIFF language,  H  denotes events or facts that canbecome known in a dynamic fashion,and it supports S CIFF ’s ability toreason about them.Two fundamental S CIFF concepts are hypothesis consistency andgoal entailment,where a goal G reflects a logic-programming con- junction of literals and possibly constraints.D EFINITION 1.  A set of hypotheses ⌬ is consistent if and only if  ᭙ (ground atom)  p,p Î ⌬® not p Ï ⌬ and  ᭙ (ground term) t,E  ( t  ) Î ⌬®  EN  ( t  ) Ï ⌬ . Definition 2 summarizes S CIFF ’s abductive semantics. It’s based onKenneth Kunen’s 3-valued completion semantics; 9 as such,it relieson Clark’s Equality Theory (CET).D EFINITION 2.  A S  CIFF   ALP S = á P   , A   , IC  ñ entails a goal G ( writtenS|= ⌬ G ), if and only if  ͕⌬ ⊆  A such that  ⌬ is consistent and where Comp stands for completion,T   x  is the constraints theory,and  HAP is the set of known events. To exemplify,consider the following ALP:(2)The abductive program á P  , A  , IC  ñ entails the goal  p by a set ⌬ ={  E  ( t  ),  E  ( s ),  E  ( r  )}.S CIFF operates by considering G together with IC  and by calcu-lating a  frontier  as a disjunction of formula conjunctions. Each stepin this process uses one of the inference rules defined in the S CIFF framework. 1 Given the frontier,a selection function can pick oneamong the equally true disjuncts at any step; we call this selection an abductive answer  to G . When no inference rule applies ( termina-tion ),if there exists one disjunct that isn’t false,then S CIFF succeedsand the frontier contains at least one abductive answer ( ⌬ ) to G .To exemplify,let’s consider the following IC,which could belongto Sarah:  H  ( tell ( csd  , sarah , deny (  E  ( action (  A ))))) ®  EN  ( action (  A )) Ú challenge ( csd  ,  EN  ( action (  A )))Let its head elements be abducible predicates,and let  HAP contain  H  ( tell ( csd  , sarah , deny (  E  ( action ( attend  ( conf  ))))))The frontier will then eventually contain at least two disjuncts:• ⌬ 1 ,holding  EN  ( action ( attend  ( conf  ))),and• ⌬ 2 ,holding challenge ( csd  ,  EN  ( action ( attend  ( conf  )))).The intuitive reading is that once CSD has told Sarah that it deniesher request to attend the conference,the world can evolve in two pos-sible ways: ⌬ 1 ,by which Sarah accepts that she can’t attend the con-ference (and possibly tries to satisfy her goal in other ways),or ⌬ 2 ,by which she challenges CSD’s denial of authorization. ArgS CIFF argumentation Following the work of Antonis Kakas and Francesca Toni, 10 ArgS CIFF maps arguments to abducibles. In particular,arguments can IC   = ← { } = → ∨ { }  p E t E s E t EN s E r  ( ), ( )( ) ( ) ( ) Comp HAP CET T GComp HAP CET T   x x ( ) |( ) P  ∪ ∪ ∪ ∪ =∪ ∪ ∪ ∪ΔΔ P   || =⎧⎨⎪⎩⎪ IC   NOVEMBER/DECEMBER 2007 69  be generic abducibles or expectations. As we noted earlier,expecta-tions about events are particularly suited to representing actions,which leads to smooth modeling of regulations and norms. 5 So,asdefinition 3 specifies,ArgS CIFF lets the involved parties consideractions and other normative elements as arguments that they can pro-pose and the system can reason about.D EFINITION 3 . An Argument is a literal p or not p of an abducible pred-icate p,where p could be any element of  A   ,including expectations inthe form E  ( t  )  /EN  ( t  )  ,where t is a term .From now on,if not explicitly stated otherwise,we’ll refer to anarbitrary but fixed instance S  = á P  , A  , IC  ñ of a S CIFF program. Wealso use the terms “hypotheses”and “arguments”interchangeably.We can now recast Dung’s notion of attacks as a binary relation sothat it fits the ALP semantics of the S CIFF framework.D EFINITION 4 . A set of arguments A attacksanother set  ⌬ if and only if at least one of the following expressions is true:S |=  A not p,for some p Î ⌬ , S |=  A  E  ( t  )  ,for some EN  ( t  ) Î ⌬ ,or S |=  A  EN  ( t  )  ,for some E  ( t  ) Î ⌬ .In the example of equation 2,  A = {  E  ( t  ),  E  ( s ),  E  ( r  )} attacks ⌬ 1 = {  EN  ( s )} and ⌬ 2 ={ not p }.We can prove that ArgS CIFF has the prop-erties that Kakas and Toni considered fun-damental of an attacking relation: 10 •No set of arguments attacks the empty setof arguments  .• attacks is monotonic—that is,for all (consistent)  A ,  A ¢  , ⌬ ,and ⌬ ¢  ⊆A  ,if   Aattacks ⌬ ,then(i) if   A ⊆  A ¢  then  A ¢  attacks ⌬ ,and(ii) if  ⌬ ⊆ ⌬ ¢  then  A attacks ⌬ ¢  .• attacks is compact—that is, ᭙  A , ⌬ ⊆A  ,if   A attacks ⌬ then thereexists a finite  A ¢  ⊆  A such that  A ¢  attacks ⌬ .The notion of  attacks in definition 4is symmetric,which makesArgS CIFF a symmetric argumentation framework. Moreover, attacks is irreflexive and,in all nontrivial cases,nonempty. This leads to theagreement of several semantics and makes ArgS CIFF a coherent,grounded framework. 11 However,we’ll focus on the admissible setssemantics,which suffices for our purposes here.For a set of arguments  A such that S | =  A  p for some  p ,it follows fromS CIFF ’s declarative semantics that  A is consistent and that if a set of argu-ments ⌬ is attacked by  A ,  A È ⌬ isn’t consistent in the S CIFF sense.In the following definition,we extend Dung’s abstract argumen-tation framework: 4 D EFINITION 5.  A set  ⌬ of arguments is said to be conflict-free if thereare no sets of arguments A and B ⊆ ⌬ such that A attacks B. For example,the set ⌬ = {  E  ( t  ),  E  ( s ),  E  ( r  ),  EN  ( s )} isn’t conflict-free because it contains  A = {  E  ( s )} and  B = {  EN  ( s )} and  A attacks B .It follows from definition 5 that all consistent argument sets in theS CIFF sense are conflict-free and therefore that all arguments  A suchthat S| =  A  p are conflict-free.Finally,we define admissible sets of arguments according to thework of Dung 4 and Kakas and Toni. 10 D EFINITION 6.  A (conflict-free) set of arguments ⌬ is admissible if and only if for all sets of arguments A,if A attacks ⌬  ,then ⌬ attacks A \  ⌬ . Dung’s Fundamental Lemma, 4 together with the fact that the emptyset is always admissible,implies that all arguments  A such that S  | =  A  p are admissible sets of arguments for S  . This result determines anArgS CIFF semantics based on admissible sets. In other words,Webservices using ArgS CIFF will produce requests and responses that con-tain only consistent argument sets and that can therefore defend eachother against attacks of external defeaters.Dung defines preferred extensions as maximal sets of admissiblesets of arguments, 4 but we focus here insteadon admissible sets of arguments. In fact,asKakas and Toni stress, 10 because every admis-sible set of arguments is contained in somepreferred extension,determining that a givenquery holds with respect to the semantics of admissible sets is sufficient for determiningthat the query holds with respect to the pre-ferred extension and partial stable-modelsemantics.The attacks relation can apply to all argu-ments,including elements of an  IC  ’s body.For example,if we consider ic = Body ®  Head  and  p Î  Body ,then not p represents anattack to ic ’s body. The reasoning Web ser-vice agent can use such an attack to inhibit ic .This corresponds to the concept of  undercut  ,which appears in the argumentation literature. We can now show howArgS CIFF implements this feature for use inside dialogues.  ArgS CIFF proof theory  ArgS CIFF ’s proof-theoretic semantics is based on the S CIFF proof procedure. 2 The S CIFF procedure is a rewriting system that transformsone node into other nodes and,starting from an initial node,definesa proof tree. A node can be either the special node  false or a nodedefined by the tuple T  ºá  R , CS  , PSIC,HAP, ⌬ñ (3)where  R is the resolvent—  that is,a conjunction of literals; CS  is theconstraint store,containing CLP constraints and quantifier restric-tions; PSIC  is a set of implications;  HAP is the history of happenedevents,represented by a set of events; and ⌬ is the set of hypothesesgenerated by S CIFF (corresponding to a set of arguments in ArgS CIFF ).If one element of the tuple is  false ,then the tuple is the specialnode  false ,without successors. A derivation  D is a sequence of nodes T  0 ® T  1 ® … ® T  n –1 ® T  n .Given a goal G ,a set of integrity constraints IC  ,and an initial his-tory  HAP i ,the first node is T  0 ºá { G },  , IC   ,HAP i  ,  ñ . We obtainthe other nodes by applying transitions until no further transition canbe applied. A r g u m e n t a t i o n T e c h n o l o g y 70 IEEE INTELLIGENTSYSTEMS ArgS CIFF lets the involvedparties consider actionsand other normative elementsas arguments that theycan propose and the systemcan reason about.
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