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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 reasoning examples; concepts of argument status; argument frameworks. 2. Modelling Sets of Arguments Formal definition of “Argument System”; arguments and attacks; concept of “acceptable argument”; defining “admissible” sets of arguments; overview of assumption based argumentation frameworks. 3. Strengths of Arguments and Audiences Refining the concept of “successful attack”; Preference-based argument frameworks; Value-based argument frameworks. 4. Dialogue Based on Argumentation Frameworks Introduction to dialogue in argumentation; dialogue types and protocols; 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 Argumentation and Dialogue in Artificial Intelligence Introduction to Tutorial T12 IJCAI 2005, Edinburgh 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 Argument and Proof In Artificial Intelligence reasoning is often modelled on the presentation of a proof. In some domains and for some topics this is entirely appropriate, but if we look at the justifications of reasoning offered in practice, they often fall short of the standards required by proof. Whereas a proof compels us to accept the conclusion if we accept the premises, natural language justifications tend to be open to objections: they may persuade, but they rarely compel. Such justifications are always defeasible: they succeed if the objections that are made are met, but the process of objection is complete only when the party to whom the justification is presented is content. Such defeasible justifications may be termed arguments. Objections can arise from a number of sources: • arguments tend to leave some premises implicit, presupposing that the audience will agree with the information. But it may be necessary to make such premises explicit if these presuppositions are not satisfied. • arguments tend to use vague, imprecise and open textured terms. All of these need to be given precise definitions if they are to form part of a proof. 1 • arguments tend to be “open world”: they typically admit of objections arising from exceptional cases. • arguments may be made even when we are uncertain of particular facts. So in domains where we have incomplete, uncertain, or imprecise information, or where too much background is presupposed to allow everything to be explicit we must use arguments rather than proofs. Arguments can be seen as prima facie justifications, which are acceptable so long as there is no objection which cannot be met satisfactorily. These objections themselves take the form of arguments and may attack a 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 characteristic ways of being attacked. Practical reasoning – reasoning about action – provides an important area of reasoning in which proof is not possible, and we must rely on arguments. Whereas we cannot choose what we believe, we can choose what we will try to make the case. Given the scope for choice, there is room for rational disagreement, and demonstration that an action is correct is not possible. 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 2 • point to undesirable side effects of A To use arguments to justify a belief or an action, we must propose an argument, and then defend it against other arguments which attack it. Arguments must therefore be considered in the context of other related arguments. 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 of the arguments within it. 2 Argumentation Frameworks Dung [25] defines an argumentation framework as follows. Definition 1 An argumentation framework is a pair hX , Ai where X is a set of arguments and A is a binary relation on X , i.e. A ⊆ X × X . For two arguments x and y, the meaning of hx, yi ∈ A is that x represents an attack on y. We also say that a set of arguments S attacks an argument y if y is attacked by an argument in S. An argumentation framework is conveniently represented as a directed graph H(X , A) in which the arguments are vertices and edges represent attacks between arguments. This picture of underlies much of our discussion. The key question to ask about such a framework is whether a given argument, x ∈ X , should be accepted. One reasonable view is that an argument should be accepted only if every attack on it is rebutted by an accepted argument. This notion produces the following definitions: Definition 2 An argument x ∈ X is acceptable with respect to the set of arguments S, if: ∀y ∈ X hy, xi ∈ A ⇒ ∃z ∈ S such that hz, yi ∈ A Here we can say that z defends x, and that S defends x, since an element of S defends x. Definition 3 A set S of arguments is conflict-free if ∀ x, y ∈ S hx, yi 6∈ A and hy, xi 6∈ A A conflict-free set of arguments S is admissible if for each x in S, x is acceptable with respect to S. A set of arguments S in an argumentation framework H(X , A) is a preferred extension if it is a maximal (with respect to set inclusion) admissible subset of X . 3 The notion of a preferred extension is interesting because it represents a consistent position which can defend itself against all attacks and which cannot be further extended without introducing a conflict. We can now view a credulous reasoner as one who accepts an argument if it is in at least one preferred extension, and a sceptical reasoner as one who accepts an 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 there is a unique preferred extension. In the special case where there is a unique preferred extension we say the dispute is resoluble, since there is only one set of arguments capable of rational acceptance. Alternative definitions of acceptability are also possible: instead of the preferred extension we may use the grounded extension, or the stable extension. Within such a framework, we can classify the complexity of a number of problems as has been summarised in Table 1. Problem adm(H, S) pref-ext(H, S) stab-ext(H, S) has-stab(H) ca(H, x) sa(H, x) coherent(H) Description Is S admissible? Is S preferred? Is S stable? Does H have a stable ext. Is x accepted credulously Is x accepted sceptically Is H coherent Complexity p co-np–complete p np–complete np–complete Πp2 –complete Πp2 –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 framework of Bondarenko et.al [13] with which there are close links with Dung’s formalism. A central idea of the former is to treat “arguments” and “attacks” not as primitive, atomic elements (as they are within [25]), but rather as constructs derived from a set of assumptions. This view provides a powerful general technique with which default reasoning and various non-monotonic logics can be modelled. An assumption-based framework is defined with respect to some formal deductive system hL, Ri with L the well-formed sentences of some formal language, e.g. the set of propositional formulae; and R a set of inference 4 rules defining how “new” sentences in L may be derived. Given such a system an assumption-based framework is defined as a triple hT, Ab, i with T a subset of L describing a given collection of beliefs and Ab ⊂ L a nonempty 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). The concepts of “conflict-free” and various admissibility semantics are defined with respect to whether a subset, ∆ of assumptions can extend the starting belief set T in such a way that the resulting theory T ∪ ∆ does not allow the 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 to the 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 assumed to succeed. But this is not always appropriate: sometimes we may choose which 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 to risk, or other factors. Different people may make different choices: this means that an argument which is persuasive to one audience may fail to persuade another audience which makes different choices. The notion of an audience is explored in the writings of Perelman, e.g. [55]. To accommodate the notion of audience we may extend the standard argument framework of Dung to include audiences. Two approaches that have been considered are the Preference Based argumentation frameworks of Amgoud and Cayrol [2] and the Value Based argumentation frameworks of 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 a triple hX , A, P ref i where hX , Ai is an argument framework and P ref ⊂ X × X is a preference relation that is transitive and asymmetric. Thus hx, yi ∈ P ref is interpreted as “the argument x is preferred to the argument y”. The key idea is that an attack hx, yi ∈ A may fail not only because of the presence of a defender for y but also because hy, xi ∈ P ref , 5 i.e. hx, yi ∈ A is a successful attack (in the terminology of [2] x defeats y) only if hy, xi 6∈ P ref . In such terms the concepts of “conflict-free”, “acceptable”, and “admissible” are enriched via, Definition 5 For a PAF hX , A, P ref i, and x, y ∈ X , x defeats y if hx, yi ∈ A and hy, xi 6∈ P ref . A subset S is conflict-free if for each x, y in S if hx, yi ∈ A then hy, xi ∈ P ref . An argument x is acceptable to S if for every y ∈ X if y defeats x then there is some z ∈ S such that z defeats y. 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 set containment) admissible set. Any preference relation P ref induces a standard argumentation framework by including only those hx, yi ∈ A for which hy, xi 6∈ P ref , i.e. such that x defeats y. Now, since P ref is asymmetric this induced framework is acyclic and 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 efficacy of “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 advancing an argument x is not only a statement of “belief” in the argument itself but also of any “values” endorsed by x. To record the values associated with arguments we need to add to the standard argumentation framework a set of values, and a function to map arguments on to these values. Definition 6 A value-based argumentation framework (VAF) is a 5-tuple: V AF = hX , A, V, η, P i, where hX , Ai is an argument framework, V is a non-empty set of values, η is a function which maps from elements of X to elements of V and P is the set of possible audiences. We say that an argument x relates to value v if accepting x promotes or defends v: the value in 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 to be able to make use of the notion of an audience. Audiences are individuated by their preferences between values. We therefore have potentially as many audiences as there are orderings on V . We can therefore see the elements of P as being names for the possible orderings on V . Any given argumentation will be assessed by an audience in accordance with its preferred values. We therefore next define an audience specific value based argumentation framework, AVAF: 6 Definition 7 An audience specific value-based argumentation framework (AVAF) is a 5-tuple: V AF (α) = hX , A, V, η, α i, where X , A, V and η are 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 preferences of audience α. We write v1 is preferred to v2 as v1 α v2 . The AVAF 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 to distinguish between one argument attacking another, and that attack succeeding, so that the attacked argument is defeated. We therefore define the notion of defeat for an audience: Definition 8 An argument x defeats an argument y for audience α if and only if both hx, yi ∈ A and ¬(η(y) α η(x)). It is useful to note the difference between the notion of defeat in PAFs and that in VAFs. For hx, yi ∈ A, “x defeats y” in PAFs means “the argument y is 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 the audience 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 a single value, or no preferences are expressed, the AVAF becomes a standard AF. If each argument can map to a different value, we have a Preference Based Argument Framework in the sense of Amgoud and Cayrol [2]. In practice we expect the number of values to be small relative to the number of arguments. Many disputes can be naturally modelled using only two values. Note that defeat is only applicable to an AVAF: defeat is always relative to a particular audience. Dung [25] introduces the important notions, described in section 2, of acceptability, conflict free set, admissible set, and preferred extension for AFs. We next need to define these notions for an AVAF. Definition 9 An argument x is acceptable to audience α with respect to a set of arguments S, if: for each y ∈ X if y defeats x for α then there is some z ∈ S that defeats y for α. A set S is conflict-free for audience α if ∀x, y ∈ S hx, yi ∈ A ⇒ η(y) α η(x) A conflict-free for audience α set S is admissible for an audience α if every x ∈ S is acceptable to audience α with respect to S. 7 A set of arguments S in a value-based argumentation framework is a preferred extension for audience α if it is a maximal (with respect to set inclusion) admissible for audience α subset of X . Now for a given choice of value preferences α we are able to construct an argument framework equivalent to the AVAF, by removing from the set of attacks A those attacks which fail because faced with a superior value. Thus for any AVAF, V AF (α) = hX , A, V, η, α i there is a corresponding argument framework, AF (α) = hX , Di, such that an element hx, yi ∈ A is an element of D if and only if x defeats y for α. The preferred extension of AF (α) will contain the same arguments as V AF (α), the preferred extension for audience α of the VAF. Note that if V AF (α) does not contain any cycles in which all arguments pertain to the same value, AF (α) will contain no cycles, since the cycle will be broken at the point at which the attack is from 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 categories of acceptability for arguments, according to whether they are acceptable to all audiences (objective acceptance), some audiences (subjective acceptance) or no audiences (indefensible): Definition 10 Given a VAF, hX , A, V, η, P i, an argument x ∈ X is objectively acceptable if and only if for all α ∈ P , x is in the preferred extension for audience α. An argument x ∈ X is subjectively acceptable if and only if for some α ∈ P , x is in the preferred extension for audience α. An argument which is neither objectively nor subjectively acceptable (such as 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 audiences for which S is the preferred extension. 8 4 Dialogue Because argumentation, with its notions of attack and counterattack, is intuitively adversarial in nature, it is natural to relate argumentation to a dialogue in which two parties attempt to persuade one another. Dialogue games have been used for sometime (e.g. MacKenzie [46], who used them to characterise logical fallacies and Gordon [36] who used them to identify the points of disagreement between parties to a legal case). Dialogue games have been related to argumentation frameworks also, such as Bench-Capon et 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 argumentation framework. Kowalski et al. [42] observe that procedures such as the TPI dialogue games introduced in Vreeswijk and Prakken [70] and analysed in [29], as well as variants of this, e.g. Cayrol et al. [15], Doutre and Mengin [23], may be viewed as “forward-reasoning” proof search mechanisms: they propose an alternative “backward-reasoning” technique within the assumption-based framework, proving its soundness and completeness with respect to the credulous admissibility semantics. Other recent work includes 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 “Examination Dialogues” (modelling, among other ideas, one of the classical techniques of Socratic dialogue) presented in Dunne et al. [33]. Typically a dialogue will begin with one party making a claim and proceed with the other party attacking that claim and the original party defending it. The moves available to attack and defend claims will vary according to the particular dialogue game, and different games will offer more or less rich sets of moves. Typically the dialogue will terminate with a winner when one of the parties has no move available to continue the dialogue. Casting the argument as a formally constrained dialogue allows a number of issues to be explored, such as: the complexity of the dispute; strategies for 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, however, 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 explore the attack relation in more detail. 9 The most general way to structure arguments is as deductions. Here an argument will be seen as a sequence of rule applications leading from known premises 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 this form without some distortion, and the uniformity of the approach can obscure some subtle differences between arguments. To meet these difficulties a variety of argument schemes have been proposed. One popular scheme is that proposed by Toulmin [67]. This scheme decomposes arguments into a number of components: claims whose truth we seek to establish by the argument, data that we appeal to as the grounds for the claim, and warrants which provide the rules of inference that connect the data and the claim. Warrants can, in Toulmin’s scheme, bestow varying degrees of support for the claim, and these degrees of support are indicated by the use of a modal qualifier, such as “necessarily” or “possibly”. There may also be exceptional conditions which prevent the claim from being established: these are indicated by the rebuttal which contains circumstances acknowledged 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 has some intuitive appeal in that it is able to distinguish different roles played by various premises, and embodies ideas of defeasibility. It has been used as the basis of dialogue games in Bench-Capon et al. [12] and Bench-Capon [7]. In addition a number of more specific, special purpose, arguments schemes have been proposed, by e.g. Perelman and Olbrech-Tyteca [54] and Walton [72]. One classic example is the Argument From Authority: • X says that P • X is an authority on matters relating to P • Therefore, P 10 Such argument schemes have their attractions, in that it is clear that, as a matter of fact, such arguments are advanced in practice. But there are problems • 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 what arguments represent acceptable uses of the schemes. Despite these difficulties, argument schemes are widely employed in the analysis of natural argument, and it appears that their understanding is crucial to realizing the full potential of argument based approaches. We may therefore expect argument schemes to be receive an increasing degree of attention in the future. 6 Examples We conclude with two examples. One small example is the moral dilemma of a diabetic who loses his insulin and considers taking the insulin of another diabetic in order to preserve his life. Can he take the insulin? And if he does take the insulin, must he provide compensation? The more extended example concerns of body of legal case law. The particular 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 for consumption. 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 fox with hounds. Pierson intercepted, killed and carried off the fox. The court found for Pierson. Young v Hitchens (1844). In this English case, Young was a commercial fisherman who spread a net of 140 fathoms in open water. When the net was almost closed, Hitchens went through the gap, spread his net and caught the trapped fish. The case was decided for Hitchens. Ghen v Rich (1881). In this Massachusetts case, Ghen was a whale hunter who harpooned a whale which subsequently was not reeled in, but was 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 11 Ghen would have identified his lance and paid Ellis a fee. The court found for Ghen. Conti v ASPCA (1974). In this New York case, Chester, a parrot owned by the ASPCA, escaped and was recaptured by Conti. The ASPCA found this out and reclaimed Chester from Conti. The court found that they were within their rights to do so. New Mexico vs Morton (1975) and Kleepe vs New Mexico (1976). These cases concerned the ownership of unbranded burros normally present on public lands, which had temporarily strayed off them. These have been represented as a Dung style argumentation framework in Bench-Capon [8]. In addition the arguments can be associated with their purposes to instantiate a value based argument framework. The arguments identified and their associated values are shown in Table 2. This example shows both how case law can be described as an argumentation 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 not possible in a variety of domains. • Arguments are defeasible: they are attacked by other arguments and must defend themselves if they are to be acceptable. • In consequences, arguments must be considered in the context of related and conflicting arguments. • Argumentation frameworks give us a means of analysing sets of arguments 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 notion of audiences. 12 ID A B C D E F G H I J K L M N O Q S T U V W X Y Z Argument Pursuer had right to animal Pursuer not in possession Owns the land so possesses animals Animals not confined by owner Effort promising success made by pursuer to secure animal Pursuer has right to pursue livelihood Interferer was trespassing Pursuer was trespassing Pursuit not enough (JUSTINIAN) Animal was taken (JUSTINIAN) Animal was mortally wounded (Puffendorf) Bodily seizure is not necessary (Barbeyrac), interpreted as animal was brought within certain control (TOMPKINS) Mere pursuit is not enough(TOMPKINS) Justinian is too old an authority (LIVINGSTON) Bodily seizure is not necessary (Barbeyrac) interpreted as reasonable prospect of capture is enough (LIVINGSTON) The land was open Defendant in competition with the plaintiff Competition was unfair Not for courts to regulate competition Attacks A,T C C B,D Values Claim Clear law Property Clear law Clear law B S F E I I I Livelihood Property Property Clear law Clear law Clear law Clear law E,O J Clear law I,M Useful Activity G,H,C E,F S T B Property Livelihood Livelihood Role of Court Common Practice Property The iron holds the whale is an established convention of whaling. Owners of domesticated animals have a right to regain possession Unbranded animals living on land belong to owner of land Branding establishes title Physical presence (straying) insufficient to confer title on owner B,U D Property B C Property Clear law Table 2: Arguments in the Example Cases 13 • Dialogue provides a natural way of modelling the process of argument between 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 as an evolving body of legal case law. 14 Annotated Selected Bibliography It is noted that there is an extensive literature covering topics that are relevant to the overview presented in this tutorial: reasons of space preclude presentation of a more detailed survey. A number of the articles and monographs discussed below present excellent comparative surveys of related work, thus providing a valuable source of further reading. Omission of specific items should not be interpreted as a comment on their merits. References [1] A. Aleven. Teaching Case Based Argumentation Through an Example and Models. PhD Thesis, The University of Pittsburgh. (1997) This describes CATO, a program designed to teach case based argumentation to law students. It is based in the domain of US Trade Secrets law, extends the ideas of [3], and represents the factor based approach to reasoning with legal cases. [2] L. Amgoud and C. Cayrol. A reasoning model based on the production of 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 the main mechanisms which seek to extend [25] by accounting for concepts of attacks which only succeed if the position promoted is not outranked by the position attacked. [3] K. Ashley. Modeling Legal Argument: Reasoning with Cases and Hypotheticals. Cambridge, MA: MIT Press, (1990) Describes the influential HYPO system, developed with Edwina Rissland, which models reasoning with legal cases in the domain of US Trade Secrets Law. It introduces several important notions, including dimensions for the representation of cases, the three-ply argument scheme for legal argument, and argument moves using legal cases such as citation, distinguishing and counter examples. [4] K. Atkinson, T. Bench-Capon, and P. McBurney. Computational Representation of Persuasive Argument. Technical Report ULCS-04-006, Department of Computer Science, Univ. of Liverpool, (2004) (submitted) 15 Provides an account of persuasive action over argumentation based on a argument scheme and associated critical questions. [5] K. Atkinson, T. Bench-Capon, and P. McBurney. A Dialogue Game Protocol for Multi-Agent Argument Over Proposals for Action. First International 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-Agent Systems Provides denotational semantics for the account of persuasive argument given in [4] [6] T. J. M. Bench-Capon. Argument in Artificial Intelligence and Law Artificial Intelligence and Law, 5(4):249–61, (1997) A survey of the uses made of argument in Artificial Intelligence in Law up to 1996. [7] T. J. M. Bench-Capon. Specification and Implementation of Toulmin Dialogue Game. In: J. C. Hage et al. (ed.): Legal Knowledge Based Systems, pages 5–20. (1998) A further extension of ideas initiated in [12]. This gives a complete set of moves for a game based on Toulmin’s schema, together with an operational semantics for them, and describes an implementation of the game in Prolog. [8] T.J.M. Bench-Capon. Representation of Case Law as an Argumentation Framework. In T. Bench-Capon, Daskalopoulu, A., and Winkels, R., (eds) Legal Knowledge and Information Systems, Proceedings of Jurix 2002. IOS Press: Amsterdam. pages 103–112. (2002). This paper formalises the wild animals cases discussed in the tutorial as an Argumentation Framework in the style of [25] [9] T. J. M. Bench-Capon. Agreeing to differ: modelling persuasive dialogue 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 Value Based Argumentation Frameworks, Journal of Logic and Computation, 13(3):429–48 (2003). 16 Introduces Value-based Argumentation Frameworks establishing uniqueness 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 in Legal 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 game for dialectical interaction with expert systems. In Proc. 12th Annual Conf. Expert Systems and their Applications, pages 105–113, (1992). One of the first formalisations combining dialogue style techniques with a 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 Intelligence, 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” as atomic illustrating various approaches to deriving arguments and attacks (in the sense of [25]) from sets of these. [14] C. Cayrol, S. Doutre, and J. Mengin. Dialectical proof theories for the credulous preferred semantics of argumentation frameworks. In Sixth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU-2001), pages 668–679. LNAI, 2143, Springer-Verlag, (2001). [15] C. Cayrol, S. Doutre, and J. Mengin. On decision problems related to the preferred semantics for argumentation frameworks. Journal of Logic and Computation, 13(3):377–403 (2003). These articles (and [23]) address algorithms for computing preferred extensions via a dialogue game. This game is couched in terms of the general 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 valuation of interacting arguments followed by the selection of the most acceptable. Introduces “graduality” in the selection of the best arguments to partition the set of the arguments into more than the two usual 17 subsets of “selected” and “non-selected” arguments. Proposes new acceptability classes and a refinement of existing classes taking advantage of 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 in particular provides an account of how and why there are differences between 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 setting of multi-agent system applications. For other multi-agent system based analyses of dialogue, the articles [47, 48, 49, 50, 52, 53, 61] provide a good overview of current approaches. [19] Y. Dimopoulos, B. Nebel, and F. Toni. Preferred arguments are harder to compute than stable extensions. In Proceedings of the 16th International 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 preferred arguments can be very hard. In KR2000: Principles of Knowledge Representation and Reasoning, eds., A. G. Cohn, F. Giunchiglia, and B. Selman, pp. 53–61, San Francisco, (2000). Morgan Kaufmann. See [21]. [21] Y. Dimopoulos, B. Nebel, and F. Toni. On the compuational complexity of assumption-based argumentation by default reasoning. Artificial Intelligence, 141, 57–78, (2002). The basis provided in [13] allows concepts of credulous and sceptical reasoning, preferred and stable extensions to be developed for a number of non-classical logics. In studying the complexity of these problems a significant element is shown to be the complexity of “derivability” in the associated logic. One consequence is that sceptical reasoning under some logics can be shown complete for rather higher levels of the polynomial-time hierarchy. 18 [22] Y. Dimopoulos and A. Torres. Graph theoretical structures in logic programs and default theories. Theoretical Computer Science, 170, 209–244, (1996). The results for the decision problems ca, pref-ext, has-stab given in Table 1 above, all derive from this paper. The terminology differs quite noticeably from that of [25], however, these are not difficult to relate. A more detailed discussion of the contribution of [22] expressed in the terminology of [25] may be found in [28]. [23] S. Doutre and J. Mengin. Preferred extensions of argumentation frameworks: Query answering and computation. In First Intern. Joint Conf. 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 preferences with argument positions. Proc. IJCAI05, (to appear) Presents a “TPI-style” dialogue game for validating that a subset of arguments within a value-based argument framework has (at least) one audience for which this set is admissible. [25] P. M. Dung. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming, and N -person games. Artificial Intelligence, 77, 321–357, (1995). Seminal article introducing the concept of argument framework and acceptability semantics that underpin the ideas and developments presented in this tutorial. [26] P. E. Dunne. On Concise Encodings of Preferred Extensions. Proc. 9th Non-monotonic Reasoning Workshop (NMR’2002), Toulouse, April 2002, pages 393-398 Complexity-based consideration of whether the set of all preferred extensions of an argument system can be represented by a description which is both length efficient and admits efficient testing as to whether a set of arguments is a preferred extension: motivation is to determine to what extent precomputation of all preferred extensions once is a feasible approach. [27] P.E. Dunne. Prevarication in dispute protocols. In Proc. Ninth International Conference on A.I. and Law (ICAIL’03), Edinburgh, June 2003, ACM Press, pages 12–21 19 Examines to what extent the “loser” of a dispute can exploit dialogue rules and their opponent’s strategy in order to delay having to concede defeat. [28] P.E. Dunne and T.J.M. Bench-Capon. Coherence in finite argument systems. Artificial Intelligence, 141, 187–203, (2002). Technical complexity classification proving the problem of deciding if H is coherent, i.e. every preferred extension is also stable, to be Πp2 complete. A similar classification of sa follows from this result. [29] P.E. Dunne and T.J.M. Bench-Capon. Two party immediate response disputes: properties and efficiency. Artificial Intelligence, 149, 221–250, (2003). Detailed study and formalisation of the tpi-dispute protocol introduced in [70]. Introduces the concept of dispute complexity as the number of moves needed to win an argument. Main technical contribution shows tpi dialogues establishing an argument is not credulously accepted can be viewed as a very weak propositional proof calculus and thus may require exponentially many (in the number of arguments) rounds to reach a conclusion. [30] P.E. Dunne and T.J.M. Bench-Capon. Complexity in value-based argument systems. Proc. 9th European Conf. on Logics in Artificial Intelligence. (JELIA’04), LNAI, 3229, Springer-Verlag, pages 360–371, 2004 Classifies the complexity of deciding Subjective and Objective Acceptance that were left open in [10]. Also introduces the problem “critical pair” concerned with deciding whether a given argument is subjectively accepted with one specific ordering of a pair of values but indefensible when 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 Preferences in Legal and Social Domains. Proc. DEXA’04, LNCS 3180, SpringerVerlag, pages 518–527, 2004 Presents an efficient algorithm by which the set of audiences consistent with 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 Artificial Intelligence and Law. Wolf Legal Publishing, (2005), (in press) 20 Collection of papers presenting recent developments in the specific field of argumentation techniques as applied in legal contexts. [33] P.E. Dunne, S. Doutre, and T.J.M. Bench-Capon. Discovering inconsistency through examination dialogues. Proc. IJCAI05 (to appear) Introduces a class of dialogue scheme aimed at modelling question processes seeking to expose inconsistencies in argument. [34] P.E. Dunne and P.J. McBurney. Optimal Utterances in Dialogue Protocols. Proc. Second International joint Conference on Autonomous Agents and Multiagent Systems (AAMAS’03), July 2003, ACM Press, pages 608-615 Considers the question of “move selection” for participants in a dialogue, 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 of argumentation rules. Games and Economic Behavior, 36(2):158–173, 2001. Good representative article presenting argument and dialogue from the game-theoretic perspective favoured within economics. [36] T. F. Gordon. The Pleadings Game: An Artificial Intelligence Model of Procedural Justice. Dordrecht: Kluwer Academic Publishers. (1995) An account of how dialogue and argumentation can be used to model legal process. The idea is that parties use a dialectical exchange to identify the points of agreement and disagreement between them so that the issues which need to be decided before a judge can be agreed. [37] K. Greenwood, T. Bench-Capon, and P. McBurney. Towards a Computational Account of Persuasion in Law. In Proc. of the Ninth International Conf. on AI and Law (ICAIL’03), ACM press, New York, pages 22–31, 2003 An application of the theory of persuasive argument of [4] to legal case based reasoning, illustrated from the domain of US Trade Secrets Law. [38] J.C. Hage. Reasoning With Rules. Kluwer Academic Publishers; Dordrecht (1997). A book describing Hage’s Rule Based Logic, a logic targeted at explaining defeasible argument in Law. 21 [39] A. Hunter. Making argumentation more believable. Proc. of the 19th American National Conference on Artificial Intelligence (AAAI’2004), pages 269–274, MIT Press, 2004 [40] A. Hunter. Towards higher impact argumentation. Proc. of the 19th American National Conference on Artificial Intelligence (AAAI’2004), pages 275-280, MIT Press, 2004 These two papers give a formal account of audiences, to explain how different perspectives can affect what people believe. [41] H. Jakobovits and D. Vermeir. Dialectic semantics for argumentation frameworks. In Proceedings of the Seventh International Conference on Artificial Intelligence and Law (ICAIL’99), pages 53–62, N.Y., (June 1999). ACM Press. Describes a uniform approach to defining dialogue games within argument systems. The schemes presented in [14, 15] are couched in terms of this approach. [42] R. Kowalski, P.M. Dung and F. Toni. Dialectic proof procedures for assumption-based, admissible argumentation (to appear Artificial Intelligence, 2005) Presents dialogue style proof procedures for credulous reasoning in assumption-based frameworks, introducing backward reasoning as a mechanism 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 Logic of [38]. [44] P. Lorenzen and K. Lorenz. Dialogische Logik. Darmstadt: Wissenschaftliche Buchgesellschaft. 1978 A monograph presenting the view of propositional proof theory as a dialogue mechanism. [45] R. P. Loui. Process and Policy: Resource-Bounded Nondemonstrative Reasoning. COMPINT: Computational Intelligence: An International Journal 14, 1–38. 1998 This paper investigates the appropriateness of formal dialectics as a basis for nonmonotonic and defeasible reasoning that takes computational 22 limits seriously. Dialectical protocols are shown to be appropriate for such deliberations when resources are bounded and search is serial. [46] J. D. MacKenzie. Question-Begging in Non-Cumulative Systems. Journal of Philosophical Logic 8(1), 117–133. 1978 One of the first dialogue games, introducing important notions such as commitment stores. Based on standard propositional logic, it is particularly intended to explain certain fallacies, especially begging the question. [47] P. McBurney and S. Parsons. Representing epistemic uncertainty by means 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 framework for dialogues between autonomous agents. J. Logic, Language and Information, 11:315–334, 2002. See comments following Dignum [18]. [49] P. McBurney and S. Parsons. Chance Discovery using dialectical argumentation. In T. Terano et al., editors, New Frontiers in Artificial Intelligence, pages 414–424. LNAI, 2253, Springer-Verlag, 2001. See comments following Dignum [18]. [50] P. McBurney, S. Parsons, and M. J. Wooldridge. Desiderata for agent argumentation protocols. In Proc. First Intern. Joint Conf. on Autonomous 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 and negotiate 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 formal inter-agent dialogues. In Proc. First Intern. Joint Conf. Autonomous Agents and Multiagent Systems, pages 394–401. ACM Press, 2002. 23 See comments following Dignum [18]. [54] C. Perelman and L. Olbrechts-Tyteca. The New Rhetoric: A Treatise on Argumentation. University of Notre Dame Press, Notre Dame (1969). The definitive presentation of Perelman’s ideas relating to the role of audience and the role of values in determining the persuasiveness of arguments. It also contains a systematic exploration of a large number of argument schemes. [55] C. Perelman. Justice, Law and Argument. Reidel: Dordrecht, 1980. A collection of essays providing an accessible introduction to Perelman’s ideas. [56] J.L. Pollock. How to reason defeasibly. Artificial Intelligence, 57(1):1– 42. (1992) This paper describes the construction of a general-purpose defeasible reasoner that is complete for first-order logic and provably adequate for Pollock’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, where conclusions are supported by several different arguments, the arguments typically being defeasible, and there may also be arguments of varying strengths for defeaters for some of the supporting arguments. [58] H. Prakken. Logical Tools for Modelling Legal Argument. Kluwer Academic Publishers, 1997. This book surveys the use of logic in describing conflicts between legal norms, and discusses logical approaches to resolving such conflicts. [59] H. Prakken and G. Sartor. A Dialectical Model of Assessing Conflicting Arguments in Legal Reasoning. Artificial Intelligence and Law, 4(3– 4):331–68 (1996). Gives a formal description of arguments as deductions and provides a proof theory based on grounded semantics and expressed as a dialogue procedure. [60] H. Prakken and G. Sartor. Argument-Based Extended Logic Programming with Defeasible Priorities. Journal of Applied Non-classical Logics, 7:25–75. 1997 24 This paper discusses non-monotonic reasoning in terms of arguments represented as logic programs, and in particular offers a formalisation of how priorities between conflicting arguments can themselves be the subject of argument. [61] C. Reed. Dialogue frames in agent communications. In: Y. Demazeau (ed.): Proc. 3rd International Conference on Multi-agent systems (ICMAS-98), pages 246–253. 1998 See comments following Dignum [18]. [62] C. Reed and T. Norman. Argumentation Machines. Kluwer Academic Publishers: Dordrecht. (2003). A book surveying argument in AI from a variety of perspectives, including multi-agent systems, decision support, persuasion, law and rhetoric. [63] C.A. Reed and G.W.A Rowe. Araucaria: Software for Puzzles in Argument Diagramming and XML. Department of Applied Computing, University of Dundee, Technical Report. (2001). Describes Araucaria, a program supporting the graphical analysis of arguments 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 particular it addresses the problems with the practical syllogism, and argues that a deductive theory of practical reason is inappropriate. [65] G.R. Simari and R.P. Loui. A mathematical treatment of defeasible reasoning and its implementation. Artificial Intelligence, 53(2–3):125– 157 (1992). An early and influential presentation of a formal approach to defeasible reasoning based on argumentation. [66] D.B. Skalak and E.L. Rissland. Arguments and cases: an inevitable intertwining. Artificial Intelligence and Law 1:3–44 (1992). Develops a number of strategies for argument and the moves to realise in 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. 25 [68] H.B. Verheij. Automated argument assistance for lawyers. Proceedings of the Seventh International Conference of Artificial Intelligence and Law. New York: ACM Press, pages 43–52. (1999). Describes Argu-Med, which provides a graphical interface to an argumentation 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 collections of “defeasible proofs”. The introduction, additionally, provides a useful comparative survey of formal argumentation systems up to and including [25]. [70] G. Vreeswijk and H. Prakken. Credulous and sceptical argument games for preferred semantics. In: Proceedings of JELIA’2000, The 7th European Workshop on Logic for Artificial Intelligence, Berlin, pages 224– 238, 2000 Presents the elements of the Two party immediate response (TPI) dialgoue game studied and analysed in [29], showing this to be sound and complete for credulous reasoning in any system, and sound and complete for sceptical reasoning in coherent argument systems. Presents examples of where the sceptical reasoning method may fail in systems which are not coherent. [71] D. N. Walton and E. C. W. Krabbe Committment in Dialogue: Basic Concepts of Interpersonal Reasoning. Univ. of New York Press. 1995 Presents one of the first systematic attempts to construct a taxonomy of dialogue types and aims. [72] D.N. Walton, Argumentation Schemes for Presumptive Reasoning. Erbaum: Mahwah, NJ. 1996 An account of presumptive or defeasible argument in the informal logic tradition. Its approach makes use of argument schemes and critical questions. It describes some sixteen schemes for presumptive reasoning and their associated critical questions in detail. 26 !"#%$&'()# (*,+-).%#,+/01 , 2%1 43%1 +657-"8%1 9%$ 2)1 +:<;01 =. 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F.)0 * IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 16 JI `)Q)RZjZ[ h+P)QY)j,+O)XT\ R0g%OD[WP)X+PG[W[TO0T\)P)X P)QY)j,+O)XT\=T_ acbGdGdGe LK d Ff]f V \G\^` V \ R PZ\]\^PG[ U O)Q R ) NKO XZOGO/+\^`7/)V R \-V XZY)jGV RZh7=ZOZ\ g0O2O)X aM0P)X/ ) Gf]f@ URZjZ[W[TOARWR>J2 jc PZ\]\^PG[ U'V ) NKO ZX OGO/DPg0PZ_i\^` QO0GQOARTO)XT\G\-hZO0GQO32O)QO)XZ[WOAR ) R ` QO0GQOARTO)XT\)P)j/)V OXZ[WOAR%g0O XZOGO4/DPg%PZ_i\^` QO PZ\^OSR _ R \^O+ , PZ\-V [WP _AG0 QO32 O)Q^OXZ[WOGR IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 17 ' = .;(JJ(*FF, &'"<ON 4 > <",?(-(1 PF,CD @ M * = R \-QPG[c\)O)XZ`)jZY)h'\^`DP- `)V /L)jAOAR \-V `)X R'`32Gg'hZPZ\ [T`)jGXT\ R'PAR'P)X+P)QY)j ,+O)XT\)`)QPZ\]\^PG[ZU = $$ )(JE(F1 4 (JI1 # " (F1 4 *)# " E"1 2 M Q3O 2O)QO)XZ[WO PAR O / * QY)j ,+O)XT\^PZ\-V `)X I QP ,+O g0`)QJU R M Q7P jZO PARTO / * Q^Y)j ,+O)XT\^PZ\-V `)X I Q-P ,+O g%`)QJU R IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 18 6 (- = $$ )(J?* , @ = ⊂ × 1 4 (+ ?,?4 = ∈ 6 ( ?1 4 *8E(- 9 ( ; ! F J * G F # ( 1 4 E , " G 4 ( H 1 = *F1 1 < ( 4 $ ( ! i.e. without IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 19 $ % p r q #"$%&(' &')9 *,+.- # 1 / ( #"$%# 1 / ' &')9 0 * +1 IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 20 =?> 1 <KF*-F24 ,?4 (F( (-(J@ H5 K,?5%4 (- 4"22 ,E"4G(# ∉ 1 4 # 4 ( F ( 1 * 44( 4 6 & = * 4 ∈ ∉ = .0IH(J1 EC * 1 1 (F1 * 4 ' % 4 " ' 2 3 2 4) 5 ) 6) 5 7 8 8 5 5# :9; < IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 21 7 ( ( + )/ &9 / 6 + *J , = 1 (F1 FG(J " $ ?⊂* × /(( 2(-1 4 # % 5 4(4 4 6 &' = 1 4B<)(1 4IA5# 4 "1 L" F,E(5E*-FFI)(-41 ∴1 41 (J4B< ")(J41 IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 22 ! F*JGI42,?4 H42I = ; H4G(FG(F# (1 41 ?$9 ( I 2 4 4 " E , F ( 1 4 * ? J * G4 = 81 <1 (- E(5?,?5)< = $7?1 *-*-F(F*-G F# (F1 I,E"42( HI42 1 I1 42# (F1 )?(J"<(F ,?5EHI42,?I" # 51 <I2G(1 4 1 IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 23 ) * (- @ ' η " $ * 1 1 (JI42(*3 .( = * = η → ,?4 F<",?(-4 (J?# "4 =?> - > PK1 41 4G(-(1 (J?C (8)( & (( ?81 <* (α 1 4F@ZI H?(F ( 7H5 (FI"1 G = $$)(J?* , α IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne α 24 8 ) * = I241 4G(JG5 )1 (1 2-5A5# 1 2(1 4B(# 4G(1 4G(1 G(F# 5 # " EF<",?(J4 ( 4( =?> (-(-@A4B4"2) # (1 (J% + ) ( * 4 " 2 ) 2 4 A 4 F * " A # ( ( @ H5 = 1 4C # ( & ∈ / )/ η+ η+ ! 2 α IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 25 ) * 2 4"224 1 * 5& %. $3 +" %2 +" ( ( 1 &( 4 α I4"H <FE* + // (F(2(-1 4 # 54")2424A* "#Z(-(J@A4 C ] (8 4 = = I((-@ A5# 4 "1 L" ,E(5Eα* F (-41 <")(J41 ≡ IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 26 p s q r IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 27 9 p s Y={p,r} ; B={s,q} q r Y {p,s} B IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne p s 28 Y={p,r} ; B={s,q} q r {s,q} B Y IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 29 ' . =?> F <",?( (DK()<?*J 1 *-*JF("1 G4 = &4 *# "4 4 5 =?> EF<",(,?5HE)2(JIH% "1 2 ">' 44 4 5 "1 G4 '" ' = # 5EH% = H5 ("1 G ( " # / + % / + < + / IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 30 10 ' & 1 1 < 1 (-EC 1 *(4GE2(-< 1 4 = % I<1 ?<",(*-# # 4 1 4 < " " >>'' : 44 4%# 9<9<27&& &%1 1 < 1 *?)# "F 1 <I1 4 21 4 = (E1 (*(4G IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 31 ( + < = 1 (FK1 4BE** 1 1 (# < 1 (, -( 1 422(FE# 4)4 *"1 24 * C 1 1 4 (IF* F()(41 = I2,E# 1 (5 # 4)41 * 1 2(F1 I,?5EH ,1 4# 1 < 2(FKF4"# (J4B"4)E4A54G(-,4 C 1 F( ",H* (( G,EJH# ((F ",EH*$6 ($ # 2 ) 4 4 ( ( -K"42*C # "4 = < 3, ) ! 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V ,)(P /, * V 3 B 53"$)62 #RJ ; C OX DU2 51Y 0EDUEEDU72*J I C ))=)=Z 5K3$# 75H"53J $ C )X $6/)2 5+YROX $$52 <I$# Y J IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 9 3 !" N 6# ,<6-HDFZ 5U,/352 $<2 A B P 5" ) % P '-. +L6A"$-) 5 75R)=-H5HOI$$6$53$; B$# # )/$G-H$# 5H$$# )DU2 )# 535 I5R)6$R)5+)8)2 A$5[+; AL+;"$# -.2 Y 5 A"$-)5+-L BC DU2 # # 352 $O/)2 "$# 2 5R)/)2 $)62 W&% $(' '" IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 10 B*) 2 D 65"$52 E2 # $A"5K2 -H$) $53)=I# 2 5$2 A53-6A"-H)[ [2 5 >4('1,'% !*,P J 2 L3)O2 5K $-E2 5352 I$# .5+)3)=2 $2 AG2 )* B Q# 53352 $ P ">P, (^ $)62 A.)6)$)63-.$# 2 3)2 5H2 )$2 5P+$53L IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 11 B -.$# )=$535 2 ,G33)/$.) )O2 5K2 # $A"GX DFYI7 ,+ 2 ,& ) $+3)/$.)66G2 5P2 # $A"EDFI7 B 01"$5+5 =7H2 # $A"G$$"35 )53-G6$5"# )* B ;-E2 )2 =7H2 # $A"O6$"3$5 53-HG65"$# ))6"# # 7 IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 12 4 8?A= GRCIHJ8G>\c= : ∈ 3"$)= W+20 ! L ! + X # $53)/YR6A"$-) ∈ I$ZWI0 ! 1L 5R)//)/5KOX D YR$)8)/$ZU ! "52 A 22 ! ∈ 6)6R)W ,/3$.)/.$)X D YR$,/3L IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 2 13 ' * IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 2 ' 14 IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne * "! 15 5 B 72 3# # 7H536#3$5352 I$# .2 # $A"$5 E6A"$-H)2 7HA2 E5 75R)/-G B ")/3-G2 5H2 $)2 +#32 679+$53LW 2 ) # DF75UDU2 5K# D 75H# $5+$5 BMV , DU2 5P)6.5+),6A"$-)/5H"53$G2 $,/2 A 2 5KE$-.2 5352 I$# 53)* B 1! V <2 5$")=$5K53"$.+-E# )/ ,6$"$# "5H6$53$2 AL IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 16 B 1! 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B Q $ "$-.I,# A<2 )6-E2 H2 535"$5K2 53G2 )=)/-E)62 A.)=")=-)/2 # $A" $$3$5+53$5K,).)7")# 2 $LW % - E *> JJ% I2 A <"5R)$)8DF-.$# $5 IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 19 B $# $-),G2 # $A"G-)$$5 ,6 ) Q ! 5H2 5P)IR6$R),"$)DFZ B Q2 -E/)/),6$)"$6,)/$2 5H2 5P)/. $# 2 ) )/$$2 "$5U,/L$3<2 A"2 +$5 ))6352 5R)/)$D 2 )# # A$L) $+3)2 A.A2 EA"$-)* IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 20 7 !"$#%&$'("$ '&)*+,-.$")/012 3 4($2 652 )879,;:2 <$# 4($2 )=?>@2 A$IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 1 B 01C,6DEF352 $6$A"$-)/5 2 )6G5H)6$H) B @"))65H)<"H)6"6,A"$-)/5I+G 2 -C/)/) JLK MHN&OPNRQ SUT(VWYXHO+Z[O+\][VOY]+\8X+^H_OZ[V`S1M/\8W+_a] b Z[WcNRd OHeHXHOgf[]UShO JLK MHN&OPNRQ SUT(VWYO+ZH^H_O+\][VOV=T[OVjiHkUOUS(WcM][VjV]Hl b IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 2 Bm 2 C53),n2 ,63o<"# $5.p Jq]+rts+uFsh]Hv ] Bw $$"H)62 x,<6-y.)$/79z2 5{ 53|"+FG}~~GxDL2 )65" ≥ )),6# #3{ Jf[ ∈ W+\ JV=T[O+\8OgQ SP]g\=^Hd OY] r s+uFsh] v f ∈ SU^[lcT V=T[][V+OH]Hl[T]+r*s+uFsh]Hv ∈ f3r*s+uos[f[/ r/ IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 3 1 Z]+\8X+^H_O+ZhVUNRQ d d l W+_YkH\/Q ShO !" ∈ #%$ &&' (!") * + ,* $ -' . (*. /* + ,!" $ Z][VjV]Hl b Q SPW+Z[OYWcM * + , +(0 . /1 * + , +(0 . /&&' # /* '2 +' IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 4 HT Q S(]+\8X+^H_O+ZhV3S V=\/^[l V=^H\8OgT[]US(]gZ+^H_Yf[O+\+WcM ]H4e 3c]+ZhV]HXHOUS 56/' 0 &..6/!(* 87 9 9 / 0/ :; 0 <9* # *- , 9 1 < ' '2*+ */ * * ; * K V+]+d ScWgT[]USRShW+_OYe+Q Sh]He4[3 ]+ZhV]HXHOUS >=? ' '2 0 / 1 ' 6/ *1 ** &; A@/6 : /& / /9 94& IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 5 B ;3)6"$53-.,)6$53o"+$5~ 0@)/$x;"$# -.2 .653$ A"$-)5+-.)6$)DE"$# 2 5H)2 A"$2 5C2 ,=,66)6# $5x$# 7FG7 $-.2 535 BCB )$5{o$2 3A6$$2 3#3$$53)=)2 BCB )$3+-C-$$$)=$5x*-)/$2 2 )7 BCB )# # DY5{|"# 2 ,<2 3$)62 C,3# "52 5 BCB )$5xG"53$F2 > w B IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 6 2 Data Modal Claim Rebuttal Warrant Backing IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 7 John is 78 Normally Over 78 Is old John is old 9+' * !+0 John is a Demographic Data IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 8 To Other To Other Data Claim Arguments Arguments Presupposition Warrant Rebuttal To Other Arguments Backing IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 9 3 B 2 "5x-x$5{$5E,/t~+5"$$$# 7~ /)2 "# $2 )62 5I)/C)A"$-) A$ .2 +,/-x$)62 B ;A$)/$) $# )2 5"$$# 2 $$5x$$$ IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 10 A1: John should not get sickness benefit (-B) This is the initial claim B1: Why? The first question simply seeks the grounds for the claim, the data in our schema A2: He is a lazy person (L) Some grounds are advanced B2: OK, but so what? Here two moves are made. The truth of the data is accepted, but its relevance to the argument is questioned A3: Lazy people should not get sickness benefit (L -> -B) A rule which would licence the conclusion is advanced B3: Is there a law to that effect? Here a justification for the rule is sought. Note that here we do not seek a justification in terms of a logical argument for the rule, but rather in terms the authority from which the rule derives - making use of the backing in our schema. Moreover we seek a legal, not a moral authority A4: Not as such. IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 11 ! " No backing can be supplied so the warrant must be withdrawn and the data does not support the claim IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 12 4 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 fit for work (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 defer consideration of it, while exploring the connection between F and -B A6: If someone is fit for work, they should not get sickness benefit. The relevant rule is supplied B6: Any work 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 case A7: Work that someone would pay to have done. (P) The background assumption is given B7: True, but what's your authority? Player B accepts that P is true, but now wishes to know the authority for the rule A8: Social Security Act 1984, section 32(1). This time player A has an authority, in the form of a statutory provision B8: Why do you say John is fit for work? (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 grounds B9: I can accept that. But gardening is unsuitable work 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. IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 13 # ! $ % & Argument for Data Presupposition Statute gives backing IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne Rebuttal 14 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 claim B10: Fit for work means fit for suitable work. Toogood, Commisssioner, RS3/58. B supplies an authority from case law A11: Why do you say gardening is not suitable work? Player A is forced to accept the rule, but can question the premise B11: John is a University Lecturer. (J) B supplies his data for U A12: 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 IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 15 5 ' ( ! 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" / 00 / /0 0/ 24 8 * W A Y Z F B C X G H D M O E Q I N S T J K U V L IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne Blue: Need clear law Orange: Encourage useful activity 25 2 ! 3 ! 2 4 " 2 W A ' " Y Z F B C X G H D &2 O E Q #2 M 5 6 I N S J K U V L 7 T $2 " 8 ! IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 26 2 Green: Protect property rights # + " ! 2 ! W A Y Z F B C X G H D M O E Q I 9 2) ! : N S T J K U V L IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 4 ) ) 2 27 9 Red: Promote economic activity 2, # ++ " 7 W A Y Z F B C X G H D M O E Q I N S T J K U V L IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne 28 Purple: Restrictive view of role of courts 2 !" $ 2 !" ) 4 + W A Y 2 Z F !" B C ; X G # H D M [P] E Q ) 24 O [R] I !" 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