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Argumentation and Dialogue in Artificial Intelligence Syllabus for Tutorial T12, IJCAI 2005 Trevor J.M. Bench-Capon and Paul E. Dunne Department of Computer Science, University of Liverpool Liverpool L69 7ZF, U.K. {tbc,ped}@csc.liv.ac.uk 1. Introduction and Overview Distinguishing the notions of “proof” and “argument”; practical rea- soning examples; concepts of argument status; argument frameworks. 2. Modelling Sets of Arguments Formal definition of “Argument System”; arguments and attacks; con- cept of “acceptable argument”; defining “admissible” sets of argu- ments; overview of assumption based argumentation frameworks. 3. Strengths of Arguments and Audiences Refining the concept of “successful attack”; Preference-based argu- ment frameworks; Value-based argument frameworks. 4. Dialogue Based on Argumentation Frameworks Introduction to dialogue in argumentation; dialogue types and proto- cols; two-party immediate response disputes (tpi) and properties. 5. Structure of Arguments Argument Schema and their motivation; Toulmin’s argument schema and developments of this; problems with argument schema. 6. Example Studies Analysis of some selected legal cases couched in terms of Value-based argument frameworks. 7. Summary

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Argumentation and Dialogue

in Artificial Intelligence

Syllabus for Tutorial T12, IJCAI 2005

Trevor J.M. Bench-Capon and Paul E. DunneDepartment of Computer Science, University of Liverpool

Liverpool L69 7ZF, U.K.{tbc,ped}@csc.liv.ac.uk

1. Introduction and OverviewDistinguishing the notions of “proof” and “argument”; practical rea-soning examples; concepts of argument status; argument frameworks.

2. Modelling Sets of ArgumentsFormal definition of “Argument System”; arguments and attacks; con-cept of “acceptable argument”; defining “admissible” sets of argu-ments; overview of assumption based argumentation frameworks.

3. Strengths of Arguments and AudiencesRefining the concept of “successful attack”; Preference-based argu-ment frameworks; Value-based argument frameworks.

4. Dialogue Based on Argumentation FrameworksIntroduction to dialogue in argumentation; dialogue types and proto-cols; two-party immediate response disputes (tpi) and properties.

5. Structure of ArgumentsArgument Schema and their motivation; Toulmin’s argument schemaand developments of this; problems with argument schema.

6. Example StudiesAnalysis of some selected legal cases couched in terms of Value-basedargument frameworks.

7. Summary

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Argumentation and Dialogue

in Artificial Intelligence

Introduction to Tutorial T12

IJCAI 2005, Edinburgh

Trevor J.M. Bench-Capon and Paul E. DunneDepartment of Computer Science

University of LiverpoolLiverpool L69 7ZF, U.K.{tbc,ped}@csc.liv.ac.uk

1 Argument and Proof

In Artificial Intelligence reasoning is often modelled on the presentation of aproof. In some domains and for some topics this is entirely appropriate, butif we look at the justifications of reasoning offered in practice, they oftenfall short of the standards required by proof.

Whereas a proof compels us to accept the conclusion if we accept thepremises, natural language justifications tend to be open to objections: theymay persuade, but they rarely compel. Such justifications are always de-feasible: they succeed if the objections that are made are met, but theprocess of objection is complete only when the party to whom the justifi-cation is presented is content. Such defeasible justifications may be termedarguments.

Objections can arise from a number of sources:

• arguments tend to leave some premises implicit, presupposing that theaudience will agree with the information. But it may be necessary tomake such premises explicit if these presuppositions are not satisfied.

• arguments tend to use vague, imprecise and open textured terms. Allof these need to be given precise definitions if they are to form part ofa proof.

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• arguments tend to be “open world”: they typically admit of objectionsarising from exceptional cases.

• arguments may be made even when we are uncertain of particularfacts.

So in domains where we have incomplete, uncertain, or imprecise informa-tion, or where too much background is presupposed to allow everything tobe explicit we must use arguments rather than proofs.

Arguments can be seen as prima facie justifications, which are acceptableso long as there is no objection which cannot be met satisfactorily.

These objections themselves take the form of arguments and may attacka number of points in the original justification:

• we may have an argument for the negation of the conclusion

• we may have an argument for negation of one of the premises

• we may have an argument that the rule is inapplicable.

These attacks apply to an argument with a modus ponens like structure.There are other structures for arguments each of which have their own char-acteristic ways of being attacked.

Practical reasoning – reasoning about action – provides an importantarea of reasoning in which proof is not possible, and we must rely on ar-guments. Whereas we cannot choose what we believe, we can choose whatwe will try to make the case. Given the scope for choice, there is room forrational disagreement, and demonstration that an action is correct is notpossible.

Practical reasoning comes with its own distinctive form of argument,which can be expressed as:

• I wish to bring about some state of affairs S

• I can bring about S by performing A

• Therefore, I should perform A

This can be attacked by arguments which

• show that S is not desirable

• show that A will not bring about S

• declare that S can be brought about in other ways

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• point to undesirable side effects of A

To use arguments to justify a belief or an action, we must propose an ar-gument, and then defend it against other arguments which attack it. Ar-guments must therefore be considered in the context of other related argu-ments.

This issue can be explored using the notion on argumentation framework,which consists of a set of arguments and the attack relations between them.Given such a framework, we can then attempt to determine the status ofthe arguments within it.

2 Argumentation Frameworks

Dung [25] defines an argumentation framework as follows.

Definition 1 An argumentation framework is a pair 〈X ,A〉 where X is aset of arguments and A is a binary relation on X , i.e. A ⊆ X × X .

For two arguments x and y, the meaning of 〈x, y〉 ∈ A is that x representsan attack on y. We also say that a set of arguments S attacks an argumenty if y is attacked by an argument in S. An argumentation framework is con-veniently represented as a directed graph H(X ,A) in which the argumentsare vertices and edges represent attacks between arguments. This picture ofunderlies much of our discussion.

The key question to ask about such a framework is whether a givenargument, x ∈ X , should be accepted. One reasonable view is that anargument should be accepted only if every attack on it is rebutted by anaccepted argument. This notion produces the following definitions:

Definition 2 An argument x ∈ X is acceptable with respect to the set ofarguments S, if:

∀y ∈ X 〈y, x〉 ∈ A ⇒ ∃z ∈ S such that 〈z, y〉 ∈ A

Here we can say that z defends x, and that S defends x, since an element ofS defends x.

Definition 3 A set S of arguments is conflict-free if

∀ x, y ∈ S 〈x, y〉 6∈ A and 〈y, x〉 6∈ A

A conflict-free set of arguments S is admissible if for each x in S, x isacceptable with respect to S. A set of arguments S in an argumentationframework H(X ,A) is a preferred extension if it is a maximal (with respectto set inclusion) admissible subset of X .

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The notion of a preferred extension is interesting because it represents aconsistent position which can defend itself against all attacks and whichcannot be further extended without introducing a conflict. We can nowview a credulous reasoner as one who accepts an argument if it is in atleast one preferred extension, and a sceptical reasoner as one who acceptsan argument only if it is in all preferred extensions.

From Dung [25] we know that a preferred extension always exists, (this,however, could be the empty set) and that it is not generally true that thereis a unique preferred extension. In the special case where there is a uniquepreferred extension we say the dispute is resoluble, since there is only oneset of arguments capable of rational acceptance.

Alternative definitions of acceptability are also possible: instead of thepreferred extension we may use the grounded extension, or the stable exten-sion.

Within such a framework, we can classify the complexity of a number ofproblems as has been summarised in Table 1.

Problem Description Complexityadm(H, S) Is S admissible? p

pref-ext(H, S) Is S preferred? co-np–completestab-ext(H, S) Is S stable? p

has-stab(H) Does H have a stable ext. np–completeca(H, x) Is x accepted credulously np–completesa(H, x) Is x accepted sceptically Πp

2–completecoherent(H) Is H coherent Πp

2–complete

Table 1: Complexity of Problems Relating to Argumentation Frameworks

An accessible introduction to complexity classes such as Πp2 is given in

Papadimitriou [51].To conclude we briefly mention the important assumption-based frame-

work of Bondarenko et.al [13] with which there are close links with Dung’sformalism. A central idea of the former is to treat “arguments” and “at-tacks” not as primitive, atomic elements (as they are within [25]), butrather as constructs derived from a set of assumptions. This view pro-vides a powerful general technique with which default reasoning and variousnon-monotonic logics can be modelled.

An assumption-based framework is defined with respect to some formaldeductive system 〈L,R〉 with L the well-formed sentences of some formallanguage, e.g. the set of propositional formulae; and R a set of inference

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rules defining how “new” sentences in L may be derived. Given such asystem an assumption-based framework is defined as a triple 〈T,Ab, 〉 withT a subset of L describing a given collection of beliefs and Ab ⊂ L a non-empty set of assumptions that are to be used to “extend” T . The component

maps assumptions α into sentences, α of L called the contrary (of α). Theconcepts of “conflict-free” and various admissibility semantics are definedwith respect to whether a subset, ∆ of assumptions can extend the startingbelief set T in such a way that the resulting theory T ∪ ∆ does not allowthe derivation of both an assumption α and its contrary α.

The formal deductive system is a significant element in such frameworks:in particular, as has been shown in Dimopoulos, Nebel, and Toni [19, 20, 21]the complexity of problems analogous to those given in Table 1 is linked tothe complexity of the “derivability” problem in the supporting logic.

3 Strengths of Arguments and Audiences

In Dung’s framework, an attack of one argument on another is assumedto succeed. But this is not always appropriate: sometimes we may choosewhich argument to accept.

Choice arises in particular when the argument is justifying an action:then choice may be determined by how we rank social values, attitude torisk, or other factors. Different people may make different choices: thismeans that an argument which is persuasive to one audience may fail topersuade another audience which makes different choices. The notion of anaudience is explored in the writings of Perelman, e.g. [55].

To accommodate the notion of audience we may extend the standardargument framework of Dung to include audiences. Two approaches thathave been considered are the Preference Based argumentation frameworksof Amgoud and Cayrol [2] and the Value Based argumentation frameworksof Bench-Capon [10].

The preference based scheme of [2] captures a concept of “audience”through a relationship over arguments. Formally,

Definition 4 A Preference Based argumentation framework (PAF) is atriple 〈X ,A, P ref〉 where 〈X ,A〉 is an argument framework and Pref ⊂X × X is a preference relation that is transitive and asymmetric.

Thus 〈x, y〉 ∈ Pref is interpreted as “the argument x is preferred to theargument y”. The key idea is that an attack 〈x, y〉 ∈ A may fail not onlybecause of the presence of a defender for y but also because 〈y, x〉 ∈ Pref ,

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i.e. 〈x, y〉 ∈ A is a successful attack (in the terminology of [2] x defeatsy) only if 〈y, x〉 6∈ Pref . In such terms the concepts of “conflict-free”,“acceptable”, and “admissible” are enriched via,

Definition 5 For a PAF 〈X ,A, P ref〉, and x, y ∈ X , x defeats y if 〈x, y〉 ∈A and 〈y, x〉 6∈ Pref . A subset S is conflict-free if for each x, y in S if〈x, y〉 ∈ A then 〈y, x〉 ∈ Pref . An argument x is acceptable to S if forevery y ∈ X if y defeats x then there is some z ∈ S such that z defeatsy. A conflict-free set, S, is admissible if every x ∈ S is acceptable to S.Finally, S, is a preferred extension if it is a maximal (with respect to setcontainment) admissible set.

Any preference relation Pref induces a standard argumentation frameworkby including only those 〈x, y〉 ∈ A for which 〈y, x〉 6∈ Pref , i.e. such that xdefeats y. Now, since Pref is asymmetric this induced framework is acyclicand its preferred extension (which corresponded to the grounded extension)is unique, non-empty, and efficiently computable.

While these properties are compelling indicators of the practical efficacyof “audience related” enhancements to Dung’s schema, there are, however,a number of issues that PAFs do not address. Thus, Bench-Capon [10]promotes the view of audiences being captured in the observation that ad-vancing an argument x is not only a statement of “belief” in the argumentitself but also of any “values” endorsed by x.

To record the values associated with arguments we need to add to thestandard argumentation framework a set of values, and a function to maparguments on to these values.

Definition 6 A value-based argumentation framework (VAF) is a 5-tuple:V AF = 〈X ,A, V, η, P 〉, where 〈X ,A〉 is an argument framework, V is anon-empty set of values, η is a function which maps from elements of Xto elements of V and P is the set of possible audiences. We say that anargument x relates to value v if accepting x promotes or defends v: the valuein question is given by η(x). For every x ∈ X , η(x) ∈ V .

The set P of audiences is introduced because, following Perelman, we want tobe able to make use of the notion of an audience. Audiences are individuatedby their preferences between values. We therefore have potentially as manyaudiences as there are orderings on V . We can therefore see the elements ofP as being names for the possible orderings on V . Any given argumentationwill be assessed by an audience in accordance with its preferred values.We therefore next define an audience specific value based argumentationframework, AVAF:

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Definition 7 An audience specific value-based argumentation framework(AVAF) is a 5-tuple: V AF (α) = 〈X ,A, V, η,�α〉, where X , A, V and ηare as for a VAF, α is an audience, and �α is a value-preference relation(transitive, irreflexive and asymmetric) over V ×V reflecting the value pref-erences of audience α. We write v1 is preferred to v2 as v1 �α v2. TheAVAF relates to the VAF in that X , A, V and η are identical, α ∈ P and�α is the set of preferences derivable from the ordering α in the VAF.

Our purpose in extending argumentation frameworks was to allow us todistinguish between one argument attacking another, and that attack suc-ceeding, so that the attacked argument is defeated. We therefore define thenotion of defeat for an audience:

Definition 8 An argument x defeats an argument y for audience α if andonly if both 〈x, y〉 ∈ A and ¬(η(y) �α η(x)).

It is useful to note the difference between the notion of defeat in PAFs andthat in VAFs. For 〈x, y〉 ∈ A, “x defeats y” in PAFs means “the argument yis not preferred to the argument x”; in VAFs, however, “x defeats y” means“the value promoted by the argument y is not superior (in the view of theaudience α) to the value promoted by the argument x”

Note that an attack succeeds if both arguments relate to the same value,or if no preference between the values has been defined. If V contains asingle value, or no preferences are expressed, the AVAF becomes a standardAF. If each argument can map to a different value, we have a PreferenceBased Argument Framework in the sense of Amgoud and Cayrol [2]. Inpractice we expect the number of values to be small relative to the numberof arguments. Many disputes can be naturally modelled using only twovalues. Note that defeat is only applicable to an AVAF: defeat is alwaysrelative to a particular audience.

Dung [25] introduces the important notions, described in section 2, ofacceptability, conflict free set, admissible set, and preferred extension forAFs. We next need to define these notions for an AVAF.

Definition 9 An argument x is acceptable to audience α with respect to aset of arguments S, if: for each y ∈ X if y defeats x for α then there is somez ∈ S that defeats y for α.

A set S is conflict-free for audience α if

∀x, y ∈ S 〈x, y〉 ∈ A ⇒ η(y) �α η(x)

A conflict-free for audience α set S is admissible for an audience α if everyx ∈ S is acceptable to audience α with respect to S.

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A set of arguments S in a value-based argumentation framework is apreferred extension for audience α if it is a maximal (with respect to setinclusion) admissible for audience α subset of X .

Now for a given choice of value preferences �α we are able to construct anargument framework equivalent to the AVAF, by removing from the set ofattacks A those attacks which fail because faced with a superior value.

Thus for any AVAF, V AF (α) = 〈X ,A, V, η,�α〉 there is a correspondingargument framework, AF (α) = 〈X ,D〉, such that an element 〈x, y〉 ∈ A isan element of D if and only if x defeats y for α. The preferred extension ofAF (α) will contain the same arguments as V AF (α), the preferred extensionfor audience α of the VAF. Note that if V AF (α) does not contain any cyclesin which all arguments pertain to the same value, AF (α) will contain nocycles, since the cycle will be broken at the point at which the attack isfrom an inferior value to a superior one. Hence both AF (α) and V AF (α)will have a unique, non-empty, preferred extension for such cases.

When we consider a range of audience, we may identify three new cat-egories of acceptability for arguments, according to whether they are ac-ceptable to all audiences (objective acceptance), some audiences (subjectiveacceptance) or no audiences (indefensible):

Definition 10 Given a VAF, 〈X ,A, V, η, P 〉, an argument x ∈ X is objec-tively acceptable if and only if for all α ∈ P , x is in the preferred extensionfor audience α.

An argument x ∈ X is subjectively acceptable if and only if for someα ∈ P , x is in the preferred extension for audience α.

An argument which is neither objectively nor subjectively acceptable (suchas one attacked by an objectively acceptable argument with the same value)is said to be indefensible.

Deciding into which of these categories a given argument falls is hard:

• Subjective Acceptance is np-complete.

• Objective Acceptance co-np-complete

• Deciding if a value ordering is critical is harder than either of these.

None the less there are some positive results. For example

• For a given audience, there is a unique, non-empty preferred extension,and an efficient algorithm to determine it.

• Given S there is an efficient algorithm to discover the class of audiencesfor which S is the preferred extension.

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4 Dialogue

Because argumentation, with its notions of attack and counterattack, is in-tuitively adversarial in nature, it is natural to relate argumentation to adialogue in which two parties attempt to persuade one another. Dialoguegames have been used for sometime (e.g. MacKenzie [46], who used themto characterise logical fallacies and Gordon [36] who used them to identifythe points of disagreement between parties to a legal case). Dialogue gameshave been related to argumentation frameworks also, such as Bench-Caponet al. [12], which bases the game on the Argument Schema of Toulmin [67]and Dunne and Bench-Capon [29] in which the game uses Dung’s argu-mentation framework. Kowalski et al. [42] observe that procedures suchas the TPI dialogue games introduced in Vreeswijk and Prakken [70] andanalysed in [29], as well as variants of this, e.g. Cayrol et al. [15], Doutreand Mengin [23], may be viewed as “forward-reasoning” proof search mech-anisms: they propose an alternative “backward-reasoning” technique withinthe assumption-based framework, proving its soundness and completenesswith respect to the credulous admissibility semantics. Other recent workincludes the concept of “graduality” in Cayrol and Lagasquie-Schiex [16];the dialogue scheme outlined in Doutre et al. [24] for “position analysis”in Value-based frameworks; and the preliminary study of so-called “Ex-amination Dialogues” (modelling, among other ideas, one of the classicaltechniques of Socratic dialogue) presented in Dunne et al. [33].

Typically a dialogue will begin with one party making a claim and pro-ceed with the other party attacking that claim and the original party defend-ing it. The moves available to attack and defend claims will vary accordingto the particular dialogue game, and different games will offer more or lessrich sets of moves. Typically the dialogue will terminate with a winner whenone of the parties has no move available to continue the dialogue.

Casting the argument as a formally constrained dialogue allows a numberof issues to be explored, such as: the complexity of the dispute; strategiesfor dispute; and the procedures under which disputes may be conducted.

5 Structure of Arguments

So far we have considered arguments as entirely abstract. There are, how-ever, situations in which it is helpful to consider the structure of arguments,for example if we wish to automate the generation of arguments, or to ex-plore the attack relation in more detail.

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The most general way to structure arguments is as deductions. Here anargument will be seen as a sequence of rule applications leading from knownpremises or assumptions to a conclusion.

This approach has a number of advantages:

1. It is uniform

2. Any desired logic may be used to guide the inference

3. Generation of arguments is straightforward

4. The notion of derivation is well defined and understood

There are, however, disadvantages. Not all arguments can be put into thisform without some distortion, and the uniformity of the approach can ob-scure some subtle differences between arguments. To meet these difficultiesa variety of argument schemes have been proposed.

One popular scheme is that proposed by Toulmin [67]. This scheme de-composes arguments into a number of components: claims whose truth weseek to establish by the argument, data that we appeal to as the grounds forthe claim, and warrants which provide the rules of inference that connectthe data and the claim. Warrants can, in Toulmin’s scheme, bestow varyingdegrees of support for the claim, and these degrees of support are indicatedby the use of a modal qualifier, such as “necessarily” or “possibly”. Theremay also be exceptional conditions which prevent the claim from being es-tablished: these are indicated by the rebuttal which contains circumstancesacknowledged as requiring the authority of the warrant to be put aside.Warrants also require some justification: this is the role of the backing.

This scheme, although entirely general, has proved popular, and hassome intuitive appeal in that it is able to distinguish different roles playedby various premises, and embodies ideas of defeasibility. It has been used asthe basis of dialogue games in Bench-Capon et al. [12] and Bench-Capon [7].

In addition a number of more specific, special purpose, arguments schemeshave been proposed, by e.g. Perelman and Olbrech-Tyteca [54] and Wal-ton [72]. One classic example is the Argument From Authority:

• X says that P

• X is an authority on matters relating to P

• Therefore, P

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Such argument schemes have their attractions, in that it is clear that, asa matter of fact, such arguments are advanced in practice. But there areproblems

• argument schemes often embody fallacious patterns of reasoning

• argument schemes are often ill-defined

For these reasons it is hard to formalise such schemes and to determine whatarguments represent acceptable uses of the schemes.

Despite these difficulties, argument schemes are widely employed in theanalysis of natural argument, and it appears that their understanding iscrucial to realizing the full potential of argument based approaches. Wemay therefore expect argument schemes to be receive an increasing degreeof attention in the future.

6 Examples

We conclude with two examples.One small example is the moral dilemma of a diabetic who loses his in-

sulin and considers taking the insulin of another diabetic in order to preservehis life. Can he take the insulin? And if he does take the insulin, must heprovide compensation?

The more extended example concerns of body of legal case law. Theparticular cases form an example widely used in training law students.

The facts of the chosen cases are:Keeble v Hickergill (1707). This was an English case in which Keeble

owned a duck pond, to which he lured ducks, which he shot and sold forconsumption. Hickergill, out of malice, scared the ducks away by firing guns.The court found for Keeble.

Pierson v Post (1805). In this New York case, Post was hunting a foxwith hounds. Pierson intercepted, killed and carried off the fox. The courtfound for Pierson.

Young v Hitchens (1844). In this English case, Young was a commercialfisherman who spread a net of 140 fathoms in open water. When the net wasalmost closed, Hitchens went through the gap, spread his net and caughtthe trapped fish. The case was decided for Hitchens.

Ghen v Rich (1881). In this Massachusetts case, Ghen was a whalehunter who harpooned a whale which subsequently was not reeled in, butwas washed ashore. It was found by a man called Ellis, who sold it to Rich.According to local custom, Ellis should have reported his find, whereupon

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Ghen would have identified his lance and paid Ellis a fee. The court foundfor Ghen.

Conti v ASPCA (1974). In this New York case, Chester, a parrot ownedby the ASPCA, escaped and was recaptured by Conti. The ASPCA foundthis out and reclaimed Chester from Conti. The court found that they werewithin their rights to do so.

New Mexico vs Morton (1975) and Kleepe vs New Mexico (1976). Thesecases concerned the ownership of unbranded burros normally present onpublic lands, which had temporarily strayed off them.

These have been represented as a Dung style argumentation frameworkin Bench-Capon [8]. In addition the arguments can be associated with theirpurposes to instantiate a value based argument framework. The argumentsidentified and their associated values are shown in Table 2.

This example shows both how case law can be described as an argumen-tation framework and how the use of values can explain

• different intuitions and dissenting opinions

• different decisions in different jurisdictions

• different decisions as culture changes

7 Summary

We may summarise as follows:

• Arguments are important when modelling reason, since proof is notpossible in a variety of domains.

• Arguments are defeasible: they are attacked by other arguments andmust defend themselves if they are to be acceptable.

• In consequences, arguments must be considered in the context of re-lated and conflicting arguments.

• Argumentation frameworks give us a means of analysing sets of argu-ments to determine their status.

• Arguments relating to action often offer a choice between alternatives,which the audience is free to resolve according to their preferences.

• Argumentation frameworks can be extended to accommodate the no-tion of audiences.

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ID Argument Attacks ValuesA Pursuer had right to animal ClaimB Pursuer not in possession A,T Clear lawC Owns the land so possesses animals C PropertyD Animals not confined by owner C Clear lawE Effort promising success made B,D Clear law

by pursuerto secure animal

F Pursuer has right to pursue livelihood B LivelihoodG Interferer was trespassing S PropertyH Pursuer was trespassing F PropertyI Pursuit not enough (JUSTINIAN) E Clear lawJ Animal was taken (JUSTINIAN) I Clear lawK Animal was mortally wounded (Puffendorf) I Clear lawL Bodily seizure is not necessary (Barbeyrac), I Clear law

interpreted as animal was broughtwithin certain control (TOMPKINS)

M Mere pursuit is not enough(TOMPKINS) E,O Clear lawN Justinian is too old J

an authority (LIVINGSTON)O Bodily seizure is not necessary (Barbeyrac) I,M Useful

interpreted as reasonable prospect Activityof capture is enough (LIVINGSTON)

Q The land was open G,H,C PropertyS Defendant in competition with the plaintiff E,F LivelihoodT Competition was unfair S LivelihoodU Not for courts to regulate competition T Role of

CourtV The iron holds the whale B,U Common

is an established convention of whaling. PracticeW Owners of domesticated animals have B Property

a right to regain possessionX Unbranded animals living on land D Property

belong to owner of landY Branding establishes title B PropertyZ Physical presence (straying) insufficient to C Clear law

confer title on owner

Table 2: Arguments in the Example Cases

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• Dialogue provides a natural way of modelling the process of argumentbetween disputing parties.

• We can analyse the structure of arguments using argumentation schemes,which may range from the entirely general to the very specific.

• We can apply the above notions to quite extensive disputes, such asan evolving body of legal case law.

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Annotated Selected Bibliography

It is noted that there is an extensive literature covering topics that arerelevant to the overview presented in this tutorial: reasons of space pre-clude presentation of a more detailed survey. A number of the articles andmonographs discussed below present excellent comparative surveys of re-lated work, thus providing a valuable source of further reading. Omissionof specific items should not be interpreted as a comment on their merits.

References

[1] A. Aleven. Teaching Case Based Argumentation Through an Exampleand Models. PhD Thesis, The University of Pittsburgh. (1997)

This describes CATO, a program designed to teach case based argu-mentation to law students. It is based in the domain of US Trade Secretslaw, extends the ideas of [3], and represents the factor based approachto reasoning with legal cases.

[2] L. Amgoud and C. Cayrol. A reasoning model based on the productionof acceptable arguments, Annals of Math. and Artificial Intelligence,34, 197–215, (2002)

Introduces the model of Preference-Based Argumentation Frameworks(PAF). These together with the VAF model of [9, 10] are one of themain mechanisms which seek to extend [25] by accounting for conceptsof attacks which only succeed if the position promoted is not outrankedby the position attacked.

[3] K. Ashley. Modeling Legal Argument: Reasoning with Cases and Hypo-theticals. Cambridge, MA: MIT Press, (1990)

Describes the influential HYPO system, developed with Edwina Riss-land, which models reasoning with legal cases in the domain of US TradeSecrets Law. It introduces several important notions, including dimen-sions for the representation of cases, the three-ply argument scheme forlegal argument, and argument moves using legal cases such as citation,distinguishing and counter examples.

[4] K. Atkinson, T. Bench-Capon, and P. McBurney. Computational Rep-resentation of Persuasive Argument. Technical Report ULCS-04-006,Department of Computer Science, Univ. of Liverpool, (2004) (submit-ted)

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Provides an account of persuasive action over argumentation based ona argument scheme and associated critical questions.

[5] K. Atkinson, T. Bench-Capon, and P. McBurney. A Dialogue GameProtocol for Multi-Agent Argument Over Proposals for Action. FirstInternational Workshop on Argumentation in Multi-Agent Systems(ArgMAS2004), LNAI 3366, Springer-Verlag, pages 149–161, (2004)(extended version, in press Jnl. of Autonomous Agents and Multi-AgentSystems

Provides denotational semantics for the account of persuasive argumentgiven in [4]

[6] T. J. M. Bench-Capon. Argument in Artificial Intelligence and LawArtificial Intelligence and Law, 5(4):249–61, (1997)

A survey of the uses made of argument in Artificial Intelligence in Lawup to 1996.

[7] T. J. M. Bench-Capon. Specification and Implementation of ToulminDialogue Game. In: J. C. Hage et al. (ed.): Legal Knowledge BasedSystems, pages 5–20. (1998)

A further extension of ideas initiated in [12]. This gives a completeset of moves for a game based on Toulmin’s schema, together with anoperational semantics for them, and describes an implementation of thegame in Prolog.

[8] T.J.M. Bench-Capon. Representation of Case Law as an ArgumentationFramework. In T. Bench-Capon, Daskalopoulu, A., and Winkels, R.,(eds) Legal Knowledge and Information Systems, Proceedings of Jurix2002. IOS Press: Amsterdam. pages 103–112. (2002).

This paper formalises the wild animals cases discussed in the tutorialas an Argumentation Framework in the style of [25]

[9] T. J. M. Bench-Capon. Agreeing to differ: modelling persuasive dia-logue between parties with different values, Informal Logic, 22(3):231–45 (2003).

Augments the Value Based Argumentation Framework described in[10], by describing a dialogue game based on the TPI game of [29].

[10] T. J. M. Bench-Capon. Persuasion in Practical Argument Using ValueBased Argumentation Frameworks, Journal of Logic and Computation,13(3):429–48 (2003).

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Introduces Value-based Argumentation Frameworks establishinguniqueness of preferred extension, efficient computational properties,and defining the ideas of Subjective and Objective Acceptance.

[11] T.J.M. Bench-Capon. Try To See It My Way: Modelling Persuasion inLegal Discourse. Artificial Intelligence and Law, 11(4):271–87 (2003)

Gives a full account of the wild animals cases discussed in the tutorial.

[12] T. J. M. Bench-Capon, P. E. Dunne, and P. H. Leng. A dialogue gamefor dialectical interaction with expert systems. In Proc. 12th AnnualConf. Expert Systems and their Applications, pages 105–113, (1992).

One of the first formalisations combining dialogue style techniques witha precisely defined argument scheme - that of Toulmin [67].

[13] A. Bondarenko, P. M. Dung, R. A. Kowalski, and F. Toni. An abstract,argumentation-theoretic approach to default reasoning, Artificial Intel-ligence, 93(1–2):63–101, (1997).

Dung’s argument systems described in [25] have concepts of “argument”and “attack” as atomic concepts. This article takes “assumptions” asatomic illustrating various approaches to deriving arguments and at-tacks (in the sense of [25]) from sets of these.

[14] C. Cayrol, S. Doutre, and J. Mengin. Dialectical proof theories forthe credulous preferred semantics of argumentation frameworks. InSixth European Conference on Symbolic and Quantitative Approaches toReasoning with Uncertainty (ECSQARU-2001), pages 668–679. LNAI,2143, Springer-Verlag, (2001).

[15] C. Cayrol, S. Doutre, and J. Mengin. On decision problems relatedto the preferred semantics for argumentation frameworks. Journal ofLogic and Computation, 13(3):377–403 (2003).

These articles (and [23]) address algorithms for computing preferredextensions via a dialogue game. This game is couched in terms of thegeneral classification presented in [41].

[16] C. Cayrol and M.C. Lagasquie-Schiex. Graduality in Argumentation.Jnl. of A.I. Research, 23:245-297, (2005)

Describes a view of argumentation as based on the exchange and val-uation of interacting arguments followed by the selection of the mostacceptable. Introduces “graduality” in the selection of the best argu-ments to partition the set of the arguments into more than the two usual

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subsets of “selected” and “non-selected” arguments. Proposes new ac-ceptability classes and a refinement of existing classes taking advantageof an available “gradual” valuation.

[17] G. Christie. The Notion of an Ideal Audience in Legal Argument.Kluwer Academic, Dordrecht, (2000).

This applies the idea of an audience proposed in [54] to law, and inparticular provides an account of how and why there are differencesbetween jurisdictions.

[18] F. Dignum (Editor). Advances in Agent Communication. LNAI, 2922,Springer-Verlag, 2004

Section IV includes a number of recent papers on dialogue in the settingof multi-agent system applications. For other multi-agent system basedanalyses of dialogue, the articles [47, 48, 49, 50, 52, 53, 61] provide agood overview of current approaches.

[19] Y. Dimopoulos, B. Nebel, and F. Toni. Preferred arguments are harderto compute than stable extensions. In Proceedings of the 16th Inter-national Joint Conference on Artificial Intelligence (IJCAI99), (Ed.,T. Dean), pages 36–43, San Francisco, Morgan Kaufmann (1999)

See [21].

[20] Y. Dimopoulos, B. Nebel, and F. Toni. Finding admissible and preferredarguments can be very hard. In KR2000: Principles of KnowledgeRepresentation and Reasoning, eds., A. G. Cohn, F. Giunchiglia, andB. Selman, pp. 53–61, San Francisco, (2000). Morgan Kaufmann.

See [21].

[21] Y. Dimopoulos, B. Nebel, and F. Toni. On the compuational complex-ity of assumption-based argumentation by default reasoning. ArtificialIntelligence, 141, 57–78, (2002).

The basis provided in [13] allows concepts of credulous and scepticalreasoning, preferred and stable extensions to be developed for a numberof non-classical logics. In studying the complexity of these problemsa significant element is shown to be the complexity of “derivability”in the associated logic. One consequence is that sceptical reasoningunder some logics can be shown complete for rather higher levels of thepolynomial-time hierarchy.

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[22] Y. Dimopoulos and A. Torres. Graph theoretical structures in logicprograms and default theories. Theoretical Computer Science, 170,209–244, (1996).

The results for the decision problems ca, pref-ext, has-stab given inTable 1 above, all derive from this paper. The terminology differs quitenoticeably from that of [25], however, these are not difficult to relate.A more detailed discussion of the contribution of [22] expressed in theterminology of [25] may be found in [28].

[23] S. Doutre and J. Mengin. Preferred extensions of argumentation frame-works: Query answering and computation. In First Intern. JointConf. Automated Reasoning (IJCAR 2001), pages 272–288. LNAI,2083, Springer-Verlag, June 2001.

See [15]

[24] S. Doutre, T.J.M. Bench-Capon, and P.E. Dunne Explaining prefer-ences with argument positions. Proc. IJCAI05, (to appear)

Presents a “TPI-style” dialogue game for validating that a subset ofarguments within a value-based argument framework has (at least) oneaudience for which this set is admissible.

[25] P. M. Dung. On the acceptability of arguments and its fundamental rolein nonmonotonic reasoning, logic programming, and N -person games.Artificial Intelligence, 77, 321–357, (1995).

Seminal article introducing the concept of argument framework andacceptability semantics that underpin the ideas and developments pre-sented in this tutorial.

[26] P. E. Dunne. On Concise Encodings of Preferred Extensions. Proc.9th Non-monotonic Reasoning Workshop (NMR’2002), Toulouse, April2002, pages 393-398

Complexity-based consideration of whether the set of all preferred ex-tensions of an argument system can be represented by a descriptionwhich is both length efficient and admits efficient testing as to whethera set of arguments is a preferred extension: motivation is to determineto what extent precomputation of all preferred extensions once is afeasible approach.

[27] P.E. Dunne. Prevarication in dispute protocols. In Proc. Ninth Interna-tional Conference on A.I. and Law (ICAIL’03), Edinburgh, June 2003,ACM Press, pages 12–21

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Examines to what extent the “loser” of a dispute can exploit dialoguerules and their opponent’s strategy in order to delay having to concededefeat.

[28] P.E. Dunne and T.J.M. Bench-Capon. Coherence in finite argumentsystems. Artificial Intelligence, 141, 187–203, (2002).

Technical complexity classification proving the problem of deciding ifH is coherent, i.e. every preferred extension is also stable, to be Πp

2-complete. A similar classification of sa follows from this result.

[29] P.E. Dunne and T.J.M. Bench-Capon. Two party immediate responsedisputes: properties and efficiency. Artificial Intelligence, 149, 221–250,(2003).

Detailed study and formalisation of the tpi-dispute protocol introducedin [70]. Introduces the concept of dispute complexity as the number ofmoves needed to win an argument. Main technical contribution showstpi dialogues establishing an argument is not credulously accepted canbe viewed as a very weak propositional proof calculus and thus mayrequire exponentially many (in the number of arguments) rounds toreach a conclusion.

[30] P.E. Dunne and T.J.M. Bench-Capon. Complexity in value-based ar-gument systems. Proc. 9th European Conf. on Logics in Artificial In-telligence. (JELIA’04), LNAI, 3229, Springer-Verlag, pages 360–371,2004

Classifies the complexity of deciding Subjective and Objective Accep-tance that were left open in [10]. Also introduces the problem “criticalpair” concerned with deciding whether a given argument is subjectivelyaccepted with one specific ordering of a pair of values but indefensiblewhen this order is reversed. This problem being demonstrated to be“harder” than deciding Subjective or Objective Acceptance.

[31] P.E. Dunne and T.J.M. Bench-Capon. Identifying Audience Preferencesin Legal and Social Domains. Proc. DEXA’04, LNCS 3180, Springer-Verlag, pages 518–527, 2004

Presents an efficient algorithm by which the set of audiences consistentwith a given S being a preferred extension in a VAF can be recovered.

[32] P.E. Dunne and T.J.M. Bench-Capon (Editors) Argumentation in Ar-tificial Intelligence and Law. Wolf Legal Publishing, (2005), (in press)

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Collection of papers presenting recent developments in the specific fieldof argumentation techniques as applied in legal contexts.

[33] P.E. Dunne, S. Doutre, and T.J.M. Bench-Capon. Discovering incon-sistency through examination dialogues. Proc. IJCAI05 (to appear)

Introduces a class of dialogue scheme aimed at modelling question pro-cesses seeking to expose inconsistencies in argument.

[34] P.E. Dunne and P.J. McBurney. Optimal Utterances in Dialogue Pro-tocols. Proc. Second International joint Conference on AutonomousAgents and Multiagent Systems (AAMAS’03), July 2003, ACM Press,pages 608-615

Considers the question of “move selection” for participants in a di-alogue, reviewing notions of what can be said to consitute a “best”move. Extended version appears in the collection [18].

[35] J. Glazer and A. Rubinstein. Debates and decisions: on a rationale ofargumentation rules. Games and Economic Behavior, 36(2):158–173,2001.

Good representative article presenting argument and dialogue from thegame-theoretic perspective favoured within economics.

[36] T. F. Gordon. The Pleadings Game: An Artificial Intelligence Modelof Procedural Justice. Dordrecht: Kluwer Academic Publishers. (1995)

An account of how dialogue and argumentation can be used to modellegal process. The idea is that parties use a dialectical exchange toidentify the points of agreement and disagreement between them sothat the issues which need to be decided before a judge can be agreed.

[37] K. Greenwood, T. Bench-Capon, and P. McBurney. Towards a Compu-tational Account of Persuasion in Law. In Proc. of the Ninth Interna-tional Conf. on AI and Law (ICAIL’03), ACM press, New York, pages22–31, 2003

An application of the theory of persuasive argument of [4] to legal casebased reasoning, illustrated from the domain of US Trade Secrets Law.

[38] J.C. Hage. Reasoning With Rules. Kluwer Academic Publishers; Dor-drecht (1997).

A book describing Hage’s Rule Based Logic, a logic targeted at explain-ing defeasible argument in Law.

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[39] A. Hunter. Making argumentation more believable. Proc. of the 19thAmerican National Conference on Artificial Intelligence (AAAI’2004),pages 269–274, MIT Press, 2004

[40] A. Hunter. Towards higher impact argumentation. Proc. of the 19thAmerican National Conference on Artificial Intelligence (AAAI’2004),pages 275-280, MIT Press, 2004

These two papers give a formal account of audiences, to explain howdifferent perspectives can affect what people believe.

[41] H. Jakobovits and D. Vermeir. Dialectic semantics for argumentationframeworks. In Proceedings of the Seventh International Conference onArtificial Intelligence and Law (ICAIL’99), pages 53–62, N.Y., (June1999). ACM Press.

Describes a uniform approach to defining dialogue games within argu-ment systems. The schemes presented in [14, 15] are couched in termsof this approach.

[42] R. Kowalski, P.M. Dung and F. Toni. Dialectic proof procedures forassumption-based, admissible argumentation (to appear Artificial In-telligence, 2005)

Presents dialogue style proof procedures for credulous reasoning inassumption-based frameworks, introducing backward reasoning as amechanism for guiding the dialogue development.

[43] A. R. Lodder. Dialaw: On legal justification and Dialogue Games.Ph.D. thesis, Univ.of Maastricht. (1998)

Description of a simple dialogue game based on the Reason Based Logicof [38].

[44] P. Lorenzen and K. Lorenz. Dialogische Logik. Darmstadt: Wis-senschaftliche Buchgesellschaft. 1978

A monograph presenting the view of propositional proof theory as adialogue mechanism.

[45] R. P. Loui. Process and Policy: Resource-Bounded NondemonstrativeReasoning. COMPINT: Computational Intelligence: An InternationalJournal 14, 1–38. 1998

This paper investigates the appropriateness of formal dialectics as a ba-sis for nonmonotonic and defeasible reasoning that takes computational

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limits seriously. Dialectical protocols are shown to be appropriate forsuch deliberations when resources are bounded and search is serial.

[46] J. D. MacKenzie. Question-Begging in Non-Cumulative Systems. Jour-nal of Philosophical Logic 8(1), 117–133. 1978

One of the first dialogue games, introducing important notions such ascommitment stores. Based on standard propositional logic, it is par-ticularly intended to explain certain fallacies, especially begging thequestion.

[47] P. McBurney and S. Parsons. Representing epistemic uncertainty bymeans of dialectical argumentation. Annals of Mathematics and AI,32(1–4):125–169, 2001.

See comments following Dignum [18].

[48] P. McBurney and S. Parsons. Games that agents play: A formal frame-work for dialogues between autonomous agents. J. Logic, Language andInformation, 11:315–334, 2002.

See comments following Dignum [18].

[49] P. McBurney and S. Parsons. Chance Discovery using dialectical ar-gumentation. In T. Terano et al., editors, New Frontiers in ArtificialIntelligence, pages 414–424. LNAI, 2253, Springer-Verlag, 2001.

See comments following Dignum [18].

[50] P. McBurney, S. Parsons, and M. J. Wooldridge. Desiderata for agentargumentation protocols. In Proc. First Intern. Joint Conf. on Au-tonomous Agents and Multiagent Systems (AAMAS’02), pages 402–409. ACM Press, 2002.

See comments following Dignum [18].

[51] C. H. Papadimitriou. Computational Complexity. Addison-Wesley:Reading, MA, 1994.

[52] S. Parsons, C. A. Sierra, and N. R. Jennings. Agents that reason andnegotiate by arguing. J. Logic and Computation, 8(3):261–292, 1998.

See comments following Dignum [18].

[53] S. Parsons, M. J. Wooldridge, and L. Amgoud. An analysis of formalinter-agent dialogues. In Proc. First Intern. Joint Conf. AutonomousAgents and Multiagent Systems, pages 394–401. ACM Press, 2002.

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See comments following Dignum [18].

[54] C. Perelman and L. Olbrechts-Tyteca. The New Rhetoric: A Treatise onArgumentation. University of Notre Dame Press, Notre Dame (1969).

The definitive presentation of Perelman’s ideas relating to the role ofaudience and the role of values in determining the persuasiveness ofarguments. It also contains a systematic exploration of a large numberof argument schemes.

[55] C. Perelman. Justice, Law and Argument. Reidel: Dordrecht, 1980.

A collection of essays providing an accessible introduction to Perelman’sideas.

[56] J.L. Pollock. How to reason defeasibly. Artificial Intelligence, 57(1):1–42. (1992)

This paper describes the construction of a general-purpose defeasiblereasoner that is complete for first-order logic and provably adequate forPollock’s argument-based conception of defeasible reasoning.

[57] J.L. Pollock. Defeasible reasoning with variable degrees of justification.Artificial Intelligence, 133(1–2):233–282. (2001).

Considers how the degree of justification of a belief is determined, whereconclusions are supported by several different arguments, the argumentstypically being defeasible, and there may also be arguments of varyingstrengths for defeaters for some of the supporting arguments.

[58] H. Prakken. Logical Tools for Modelling Legal Argument. Kluwer Aca-demic Publishers, 1997.

This book surveys the use of logic in describing conflicts between legalnorms, and discusses logical approaches to resolving such conflicts.

[59] H. Prakken and G. Sartor. A Dialectical Model of Assessing ConflictingArguments in Legal Reasoning. Artificial Intelligence and Law, 4(3–4):331–68 (1996).

Gives a formal description of arguments as deductions and provides aproof theory based on grounded semantics and expressed as a dialogueprocedure.

[60] H. Prakken and G. Sartor. Argument-Based Extended Logic Program-ming with Defeasible Priorities. Journal of Applied Non-classical Logics,7:25–75. 1997

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This paper discusses non-monotonic reasoning in terms of argumentsrepresented as logic programs, and in particular offers a formalisationof how priorities between conflicting arguments can themselves be thesubject of argument.

[61] C. Reed. Dialogue frames in agent communications. In: Y. De-mazeau (ed.): Proc. 3rd International Conference on Multi-agent sys-tems (ICMAS-98), pages 246–253. 1998

See comments following Dignum [18].

[62] C. Reed and T. Norman. Argumentation Machines. Kluwer AcademicPublishers: Dordrecht. (2003).

A book surveying argument in AI from a variety of perspectives, includ-ing multi-agent systems, decision support, persuasion, law and rhetoric.

[63] C.A. Reed and G.W.A Rowe. Araucaria: Software for Puzzles in Ar-gument Diagramming and XML. Department of Applied Computing,University of Dundee, Technical Report. (2001).

Describes Araucaria, a program supporting the graphical analysis ofarguments in terms of argument schemes.

[64] J.R. Searle. Rationality in Action. MIT Press, Cambridge Mass., 2001

A recent monograph giving an account of practical reasoning. In partic-ular it addresses the problems with the practical syllogism, and arguesthat a deductive theory of practical reason is inappropriate.

[65] G.R. Simari and R.P. Loui. A mathematical treatment of defeasiblereasoning and its implementation. Artificial Intelligence, 53(2–3):125–157 (1992).

An early and influential presentation of a formal approach to defeasiblereasoning based on argumentation.

[66] D.B. Skalak and E.L. Rissland. Arguments and cases: an inevitableintertwining. Artificial Intelligence and Law 1:3–44 (1992).

Develops a number of strategies for argument and the moves to realisein the context of legal case based reasoning.

[67] S. Toulmin. The uses of argument. Cambridge University Press. 1959

This book introduces a popular scheme for the analysis of argument.

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[68] H.B. Verheij. Automated argument assistance for lawyers. Proceedingsof the Seventh International Conference of Artificial Intelligence andLaw. New York: ACM Press, pages 43–52. (1999).

Describes Argu-Med, which provides a graphical interface to an argu-mentation framework based on the Reason Based Logic of [38]

[69] G. Vreeswijk. Abstract Argumentation Systems. Artificial Intelligence,90:225–279, 1997

Presents a theory of argumentation systems modelling these as collec-tions of “defeasible proofs”. The introduction, additionally, provides auseful comparative survey of formal argumentation systems up to andincluding [25].

[70] G. Vreeswijk and H. Prakken. Credulous and sceptical argument gamesfor preferred semantics. In: Proceedings of JELIA’2000, The 7th Euro-pean Workshop on Logic for Artificial Intelligence, Berlin, pages 224–238, 2000

Presents the elements of the Two party immediate response (TPI) dial-goue game studied and analysed in [29], showing this to be sound andcomplete for credulous reasoning in any system, and sound and com-plete for sceptical reasoning in coherent argument systems. Presentsexamples of where the sceptical reasoning method may fail in systemswhich are not coherent.

[71] D. N. Walton and E. C. W. Krabbe Committment in Dialogue: BasicConcepts of Interpersonal Reasoning. Univ. of New York Press. 1995

Presents one of the first systematic attempts to construct a taxonomyof dialogue types and aims.

[72] D.N. Walton, Argumentation Schemes for Presumptive Reasoning. Er-baum: Mahwah, NJ. 1996

An account of presumptive or defeasible argument in the informal logictradition. Its approach makes use of argument schemes and criticalquestions. It describes some sixteen schemes for presumptive reasoningand their associated critical questions in detail.

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B4: So why do you think he should not get the benefit? (-B)Now there is no reason to think that L is a reason for -B, a different reason is sought.A5: He is f it for wor k (F)Another reason is supplied.B5: Suppose he is. Why should that matter?Here player B does not immediately accept the truth of the data, but wishes to deferconsideration of it, while exploring the connection between F and -BA6: I f someone is f it for wor k, they should not get sickness benefit.The relevant rule is suppliedB6: Any wor k at all?Player B suspects that the rule is not always applicable and seeks the elements of the context which make it applicable to this caseA7: Wor k that someone would pay to have done. (P)The background assumption is givenB7: True, but what's your author ity?Player B accepts that P is true, but now wishes to know the authority for the ruleA8: Social Secur ity Act 1984, section 32(1).This time player A has an authority, in the form of a statutory provisionB8: Why do you say John is fit for wor k? (F)Player B accepts the rule but questions the premise, asking for grounds that support it.A9: I saw him gardening. (G)A supplies the groundsB9: I can accept that. But gardening is unsuitable wor k for John(G, U -> B)B accepts the truth of the grounds, and that there is a rule entailing F. On the face of it this would establish -B. But Player B is aware of an exceptional circumstance which can defeat the argument.

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IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 15

A10: What's that got to do with it?Player A now wishes to know the authority for the rule implicit in B's rebuttal. Note that it is now B who is the proponent of the claimB10: Fit for work means fit for suitable work. Toogood, Commisssioner, RS3/58.B supplies an authority from case lawA11: Why do you say gardening is not suitable work?Player A is forced to accept the rule, but can question the premiseB11: John is a University Lecturer. (J)B supplies his data for UA12: OK, OK. John should get the benefit. (B)Player accepts the truth of J, and that J implies U, and so is constrained to accept that B

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IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 16

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