Logical Tools for Modelling Legal Argument. A Study of Defeasible Reasoning in Law

Henry Prakken

An overview of formal models of argumentation and their application in philosophy

Henry Prakken

Studies in Logic, vol 4, no 1 (2011): 65-86. (A shorter version has been submitted to the Handbook of Formal Philosophy, eds. V.F. Hendrickx & S.O. Hansson.)

Argumentation is the process of supporting claims with grounds and defending them against attack. In the last decades argumentation has become an important topic in philosophy and artificial intelligence. In philosophy, the criticisms of Toulmin and Perelman of formal logic in the 1950s and 1960s gave rise to the field of informal logic, which studies informal models of reasoning and argumentation. In artificial intelligence, formal models of argumentation have been proposed as models of commonsense reasoning and multi-agent conflict resolution. This paper discusses how the formal models resulting from this research can clarify philosophical problems and issues, including those raised in the field of informal logic. An important point will be that while formal logic in the days of Toulmin and Perelman only focused on mathematical reasoning, non-mathematical forms of reasoning can still be formalised.

Reconstructing Popov v. Hayashi in a framework for argumentation with structured arguments and Dungean semantics

Henry Prakken

The Knowledge Engineering Review (2011 or 2012), to appear.

In this article the argumentation structure of the court's decision in the Popov v. Hayashi case is formalised in Prakken's (2010) abstract framework for argument-based inference with structured arguments. In this framework, arguments are inference trees formed by applying two kinds of inference rules, strict and defeasible rules. Arguments can be attacked in three ways: attacking a premisse, attacking a conclusion and attacking an inference. To resolve such conflicts, preferences may be used, which leads to three corresponding kinds of defeat, after which Dung's (1995) abstract acceptability semantics can be used to evaluate the arguments. In the present paper the abstract framework is instantiated with strict inference rules corresponding to first-order logic and with defeasible inference rules for defeasible modus ponens and various argument schemes. The main techniques used in the formal reconstruction of the case are rule-exception structures and arguments about rule validity. Arguments about socio-legal values and the use of precedent cases are reduced to arguments about rule validity. The tree structure of arguments, with explicit subargument relations between arguments, is used to capture the dependency relations between the elements of the court's decision.

Using argument Schemes for hypothetical reasoning in law

T.J.M. Bench-Capon & H. Prakken

Artificial Intelligence and Law 18 (2010): 153-174.

This paper studies the use of hypothetical and value-based reasoning in US Supreme-Court cases concerning the United States Fourth Amendment. Drawing upon formal AI & Law models of legal argument a semi-formal reconstruction is given of parts of the Carney case, which has been studied previously in AI & law research on case-based reasoning. As part of the reconstruction, a semi-formal proposal is made for extending the formal AI & Law models with forms of metalevel reasoning in several argument schemes. The result is compared with Rissland's (1989) analysis in terms of dimensions and Ashley's (2008) analysis in terms of his process model of legal argument with hypotheticals.

A hybrid formal theory of arguments, stories and criminal evidence

F.J. Bex, P.J. van Koppen, H. Prakken & B. Verheij

Artificial Intelligence and Law 18 (2010): 123-152.

This paper presents a theory of reasoning with evidence in order to determine the facts in a criminal case. The focus is on the process of proof, in which the facts of the case are determined, rather than on related legal issues, such as the admissibility of evidence. In the literature, two approaches to reasoning with evidence can be distinguished, one argument-based and one story-based. In an argument-based approach to reasoning with evidence, the reasons for and against the occurrence of an event, e.g., based on witness testimony, are central. In a story-based approach, evidence is evaluated and interpreted from the perspective of the factual stories as they may have occurred in a case, e.g., as they are defended by the prosecution. In this paper, we argue that both arguments and narratives are relevant and useful in the reasoning with and interpretation of evidence. Therefore a hybrid approach is proposed and formally developed, doing justice to both the argument-based and the narrative-based perspective. By the formalization of the theory and the associated graphical representations, our proposal is the basis for the design of software developed as a tool to make sense of the evidence in complex cases.

An abstract framework for argumentation with structured arguments

Henry Prakken

Argument and Computation 1 (2010): 93-124.

An abstract framework for structured arguments is presented that instantiates Dung's (1995) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeat. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified.

The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat, and extends it in several respects. Various rationality postulates are proven to be satisfied by the framework, and several existing approaches are proven to be a special case of the framework, including assumption-based argumentation and DefLog.

Formalising ordinary legal disputes: a case study.

Henry Prakken

Artificial Intelligence and Law 16 (2008): 333-359.

This paper presents a formal reconstruction of a Dutch civil legal case in Prakken's formal model of adjudication dialogues. The object of formalisation is the argumentative speech acts exchanged during the dispute by the adversaries and the judge. The goal of this formalisation is twofold: to test whether AI \& law models of legal dialogues in general, and Prakken's model in particular, are suitable for modelling particular legal procedures; and to learn about the process of formalising an actual legal dispute.

A Formal Model of Adjudication Dialogues.

Henry Prakken

Artificial Intelligence and Law 16 (2008): 305-328.

This article presents a formal dialogue game for adjudication dialogues. Existing AI & law models of legal dialogues and argumentation-theoretic models of persuasion are extended with a neutral third party, to give a more realistic account of the adjudicator's role in legal procedures. The main feature of the model is a division into an argumentation phase, where the adversaries plea their case and the adjudicator has a largely mediating role, and a decision phase, where the adjudicator decides the dispute on the basis of the claims, arguments and evidence put forward in the argumentation phase. The model allows for explicit decisions on admissibility of evidence and burden of proof by the adjudicator in the argumentation phase. Adjudication is modelled as putting forward arguments, in particular undercutting and priority arguments, in the decision phase. The model reconciles logical aspects of burden of proof induced by the defeasible nature of arguments with dialogical aspects of burden of proof as something that can be allocated by explicit decisions on legal grounds.

The Carneades model of argument and burden of proof

Tom Gordon, Henry Prakken & Doug Walton

Artificial Intelligence 171 (2007): 875-896.

We present a formal, mathematical model of argument structure and evaluation, taking seriously the procedural and dialogical aspects of argumentation. The model applies proof standards to determine the acceptability of statements on an issue-by-issue basis. The model uses different types of premises (ordinary premises, assumptions and exceptions) and information about the dialectical status of statements (stated, questioned, accepted or rejected) to allow the burden of proof to be allocated to the proponent or the respondent, as appropriate, for each premise separately. Our approach allows the burden of proof for a premise to be assigned to a different party than the one who has the burden of proving the conclusion of the argument, and also to change the burden of proof or applicable proof standard as the dialogue progresses from stage to stage. Useful for modeling legal dialogues, the burden of production and burden of persuasion can be handled separately, with a different responsible party and applicable proof standard for each. Carneades enables critical questions of argumentation schemes to be modeled as additional premises, using premise types to capture the varying effect on the burden of proof of different kinds of questions

Introducing the Logic and Law Corner

Trevor Bench-Capon & Henry Prakken

Journal of Logic and Computation 18 (2008): 1-12.

In this paper we introduce the Logic and Law corner of this journal. We will discuss a number of ways in which logic has been used in AI and Law, and give some of the key references to previous work on these topics. We will also list some important questions which we see as ready for further exploration. We encourage contributions on these, and other, Logic and Law issues.

Sense-making software for crime investigation: how to combine stories and arguments?

F.J. Bex, S.W. van den Braak, H. van Oostendorp, H. Prakken, H.B. Verheij & G.A.W. Vreeswijk

Formal systems for persuasion dialogue

Henry Prakken

The Knowledge Engineering Review 21 (2006): 163-188.

This article reviews formal systems that regulate persuasion dialogues. In such dialogues two or more participants aim to resolve a difference of opinion, each trying to persuade the other participants to adopt their point of view. Systems for persuasion dialogue have found application in various fields of computer science, such as nonmonotonic logic, artificial intelligence and law, multi-agent systems, intelligent tutoring and computer-supported collaborative argumentation. Taking a game-theoretic view on dialogue systems, this review proposes a formal specification of the main elements of dialogue systems for persuasion and then uses it to critically review some of the main formal systems for persuasion. The focus of this review will be on regulating the interaction between agents rather than on the design and behaviour of individual agents within a dialogue.

Coherence and flexibility in dialogue games for argumentation.

Henry Prakken

Journal of Logic and Computation 15 (2005): 1009-1040.

This article carries out a formal study of dialogue games for argumentation. A formal framework for such games is proposed which imposes an explicit reply structure on dialogues, where each dialogue move either attacks or surrenders to some earlier move of the other participant. The framework is flexible in several respects. It allows for different underlying logics, alternative sets of locutions and more or less strict rules for when they are allowed. In particular, it allows for varying degrees of coherence and flexibility when it comes to maintaining the focus of a dialogue. Its formal nature supports the study of formal properties of specific dialogue protocols, especially on how they respect the underlying logic.

Towards a multi-agent system for regulated information exchange in crime investigations

Pieter Dijkstra, Floris Bex, Henry Prakken & Kees De Vey Mestdagh

Artificial Intelligence and Law 13 (2005): 133-151.

This paper outlines a multi-agent architecture for regulated information exchange of crime investigation data between police forces. Interactions between police officers about information exchange are analysed as negotiation dialogues with embedded persuasion dialogues. An architecture is then proposed consisting of two agents, a requesting agent and a responding agent, and a communication language and protocol with which these agents can interact to promote optimal information exchange while respecting the law. Finally, dialogue policies are defined for the individual agents, specifying their behaviour within a negotiation. Essentially, when deciding to accept or reject an offer or to make a counteroffer, an agent first determines whether it is obligatory or permitted to perform the actions specified in the offer. If permitted but not obligatory, the agent next determines whether it is in his interest to accept the offer..

AI & Law, logic and argument schemes.

Henry Prakken

Argumentation 19 (2005): 303-320. (special issue on The Toulmin model today)

This paper reviews the history of AI & Law research from the perspective of argument schemes. It starts with the observation that logic, although very well applicable to legal reasoning when there is uncertainty, vagueness and disagreement, is too abstract to give a fully satisfactory classification of legal argument types. It therefore needs to be supplemented with an argument-scheme approach, which classifies arguments not according to their logical form but according to their content, in particular, according to the roles that the various elements of an argument can play. This approach is then applied to legal reasoning, to identify some of the main legal argument schemes. It is also argued that much AI & Law research in fact employs the argument-scheme approach, although it usually is not presented as such. Finally, it is argued that the argument-scheme approach and the way it has been employed in AI & Law respects some of the main lessons to be learnt from Toulmin’s The Uses of Argument.

Henry Prakken

The three faces of defeasibility in the law.

Henry Prakken and Giovanni Sartor

Ratio Juris 17:1 (2004), 118-139.

In this paper we will analyse the issue of defeasibility in the law, taking into account research carried out in philosophy, artificial intelligence and legal theory. We will adopt a very general idea of legal defeasibility, in which we will include all different ways in which certain legal conclusions may need to be abandoned, though no mistake was made in deriving them. We will argue that defeasibility in the law involves three different aspects, which we will call inference-based defeasibility, process-based defeasibility, and theory-based defeasibility. Only the integration of these three perspectives allows us to provide a satisfactory account of the role of defeasibility in legal reasoning.

Towards a formal account of reasoning about evidence: argumentation schemes and generalisations

Floris Bex, Henry Prakken, Chris Reed & Douglas Walton

An exercise in formalising teleological case-based reasoning

Henry Prakken

Modelling defeasibility in law: logic or procedure?

Henry Prakken

Relating Protocols for Dynamic Dispute with Logics for Defeasible Argumentation

Henry Prakken

Modelling Reasoning with Precedents in a Formal Dialogue Game

Henry Prakken and Giovanni Sartor

Argument-based logic programming with defeasible priorities

Henry Prakken and Giovanni Sartor

A dialectical model of assessing conflicting arguments in legal reasoning

Henry Prakken and Giovanni Sartor

Two Approaches to the Formalisation of Defeasible Deontic Reasoning

Henry Prakken

Contrary-to-duty Obligations

Henry Prakken and Marek Sergot

An Argumentation Framework in Default Logic

Henry Prakken

Annals of Mathematics and Artificial Intelligence, 9 (1993) 91-132.

This article presents a formal theory about nontrivial reasoning with inconsistent information, applicable, among other things, to defeasible reasoning. The theory, which is inspired by a formal analysis of legal argument, is based on the idea that inconsistency tolerant reasoning is more than revising an unstructured set of premises; rather, it should be regarded as constructing and comparing arguments for incompatible conclusions. This point of view gives rise to two important observations, both pointing at some flaws of other theories. The first is that arguments should be compared as they are constructed, viz. step-by-step, while the second observation is that a knowledge representation language is needed with a defeasible conditional, since the material implication gives rise to arguments which are not constructed in actual reasoning. Accordingly, a nonmonotonic logic, default logic, is chosen as the formalism underlying the argumentation framework. The general structure of the framework allows for any standard for comparing pairs of arguments; in this study two such standards are investigated, based on specificity and on orderings of the premises.

A logical analysis of burdens of proof

Henry Prakken & Giovanni Sartor

In H. Kaptein, H. Prakken & B. Verheij (eds.) Legal Evidence and Proof: Statistics, Stories, Logic, pp. 223-253. Farnham: Ashgate Publishing, Applied Legal Philosophy Series, 2009.

The starting point of this article is the claim that logics for defeasible argumentation provide the means to logically characterise the difference between several kinds of proof burdens, but only if they are embedded in a dynamic setting that captures the various stages of a legal proceeding. It is also argued that ‘standard’ argumentation logics for AI must be adapted in order to model shifts in burdens of proof. Thus this analysis illustrates in two ways that logics cannot be simply imposed on the law but that features of legal systems must be taken into account. First there is the claim that the burden of persuasion, which legally is the burden to prove a statement to a specified degree (the standard of proof) on the penalty of losing on the issue, can be verified by applying an argumentation logic to the evidence available at the final stage of a proceeding. Then a precise distinction is made between two burdens that are sometimes confused, namely the burden of production and the tactical burden. In this analysis, the tactical burden of proof is automatically induced by the defeasible nature of the reasoning. The burden of production, by contrast, concerns the legal question whether an issue can be submitted to trial or must be decided as a matter of law against the one who fails to produce any evidence. Finally the issue is raised to what extent this account can be generalised to statistical and story-based approaches.

On the nature of argument schemes.

Henry Prakken

In C.A. Reed & C. Tindale (eds.) Dialectics, Dialogue and Argumentation. An Examination of Douglas Walton's Theories of Reasoning and Argument, pp. 167-185. London: College Publications, 2010.

Since the 1980s, computer science, especially artificial intelligence (AI) has developed formal models of many aspects of argumentation that since the work of Toulmin and Perelman were thought of as belonging to informal logic. Doug Walton is one of the argumentation theorists who has recognised the relevance of this body of work for argumentation theory. One of the concepts on which recent work in AI has shed more light is that of argument schemes (sometimes also called `argumentation schemes'), which features prominently in Walton's work. A study of argument schemes from the perspective of AI is therefore very appropriate for this volume in honour of his work. More precisely, the aim of this paper is to use insights from AI to propose an understanding of the nature of argument schemes as a means to evaluate arguments, and to compare this understanding with Walton's own account of argument schemes.

De logica van bewijslastverdeling (en wat het recht daar aan heeft).

Henry Prakken

Alles Afwegende .... Bijdragen aan het Vijfde Symposium Juridische Argumentatie, Rotterdam 22 Juni 2007. Nijmegen: Ars Aequi Libri, 2007, pp. 321-326.

Juridische claims moeten berusten op juridische gronden en die juridische gronden moeten toepasbaar zijn op grond van feiten. Dit klinkt eenvoudig maar iedere jurist weet dat de uitkomst van een rechtsgeding vaak afhangt van wie wat moet bewijzen. Het recht regelt dit middels de bewijslastverdeling. Doorgaans zegt men dat in het strafproces de bewijslast steeds bij het Openbaar Ministerie (OM) ligt vanwege het principe dat de verdachte is onschuldig tot tegendeel bewezen is, terwijl in het civiele geding de bewijslast over de partijen verdeeld kan worden. In dit artikel zal ik betogen dat de zaak subtieler ligt. Ook in het strafproces kan de bewijslast in bepaalde zin omkeren, en in het civiele proces kan de bewijslast op meerdere manieren verdeeld zijn over de partijen. Ik zal dit laten zien door een onderscheid tussen drie vormen van bewijslast uit het Anglo-Amerikaanse recht, namelijk ‘burden of persuasion’, ‘burden of production’ en ‘tactical burden’, op het Nederlandse recht toe te passen. Op het eerste gezicht lijkt dit vreemd omdat het Anglo-Amerikaanse procesrecht immers sterk verschilt van het Nederlandse. Toch zal ik betogen dat zo’n toepassing mogelijk is omdat het in essentie om een logisch onderscheid gaat. Ik zal met name laten zien dat met de Anglo-Amerikaanse begrippen bewijssituaties kunnen worden onderscheiden die niet door de Nederlandse wet onderscheiden worden terwijl dat logisch gezien wel zou moeten.

Argumentation

T.J.M. Bench-Capon & H. Prakken

In A.R. Lodder & A. Oskamp (eds.): Information Technology & Lawyers: Advanced technology in the legal domain, from challenges to daily routine. Dordrecht: Springer Verlag, 2006, 61-80.

A popular view of what Artificial Intelligence can do for lawyers is that it can do no more than deduce the consequences from a precisely stated set of facts and legal rules. This immediately makes many lawyers sceptical about the usefulness of such systems: this mechanical approach seems to leave out most of what is important in legal reasoning. We will review systems that can store conflicting interpretations and that can propose alternative solutions to a case based on these interpretations. We will also describe systems that can use legal precedents to generate arguments by drawing analogies to or distinguishing precedents. We will discuss systems that can argue why a rule should not be applied to a case even though all its conditions are met. Then there are systems that can act as a mediator between disputing parties by structuring and recording their arguments and responses. Finally we look at systems that suggest mechanisms and tactics for forming arguments.

Computational models, argumentation theories and legal practice.

T.J.M. Bench-Capon, J.B. Freeman, H. Hohmann and H. Prakken

In C. Reed and T.J. Norman (eds.): Argumentation Machines. New Frontiers in Argument and Computation. Kluwer Argumentation Library, Kluwer Academic Publishers, Boston/Dordrecht/London 2004, 85-120.

The role of logic in computational models of legal argument - a critical survey

Henry Prakken and Giovanni Sartor

In A. Kakas and F. Sadri (eds.), Computational Logic: Logic Programming and Beyond. Essays In Honour of Robert A. Kowalski, Part II. Springer Lecture Notes in Computer Science 2048, Berlin 2002, 342-380.

This article surveys the use of logic in computational models of legal reasoning, against the background of a four-layered view on legal argument. This view comprises a logical layer (constructing an argument); a dialectical layer (comparing and assessing conflicting arguments); a procedural layer (regulating the process of argumentation); and a strategic, or heuristic layer (arguing persuasively). Each further layer presupposes, and is built around the previous layers. At the first two layers the information base is fixed, while at the third and fourth layer it is constructed dynamically, during a dialogue or dispute.

Dyadic Deontic Logic and Contrary-to-duty Obligations

Henry Prakken and Marek Sergot

Relating Carneades with abstract argumentation

Bas van Gijzel & Henry Prakken

Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011), ***-***. Barcelona (Spain), 2011.

Carneades is a recently proposed formalism for structured argumentation with varying proof standards. An open question is its relation with Dung's seminal abstract approach to argumentation. In this paper the two formalisms are formally related by translating Carneades into ASPIC+, another recently proposed formalism for structured argumentation. Since ASPIC+ is defined to generate Dung-style abstract argumentation frameworks, this in effect translates Carneades graphs into abstract argumentation frameworks. It is proven that Carneades always induces a unique Dung extension, which is the same in all of Dung's semantics.

Multi-criteria argument selection in persuasion dialogues

T. van der Weide, F. Dignum, J.-J.Ch. Meyer, H. Prakken & G. Vreeswijk

Proceedings of the 10th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2011), ***-***. Taipeh (Taiwan), 2011.

The main goal of a persuasion dialogue is to persuade, but agents may have a number of additional goals concerning the dialogue duration, how much and what information is shared or how aggressive the agent is. Several criteria have been proposed in the literature covering di erent aspects of what may matter to an agent, but it is not clear how to combine these criteria that are often incommensurable and partial. This paper is inspired by multi-attribute decision theory and considers argument selection as decision-making where multiple criteria matter. A meta-level argumentation system is proposed to argue about what argument an agent should select in a given persuasion dialogue. The criteria and sub-criteria that matter to an agent are structured hierar- chically into a value tree and meta-level argument schemes are formalized that use a value tree to justify what argument the agent should select. In this way, incommensurable and partial criteria can be combined.

Visualising the argumentation structure of an expert witness report with Rationale (extended abstract).

Steven van Driel & Henry Prakken

In In A. Wyner (ed.), Proceedings of the Workshop on Modelling Legal Cases and Legal Rules, in conjunction with JURIX-10, Liverpool 2010, pp. 1-8.

This paper reports on a case study in which the use of the Rationale software was investigated to analyse the argumentation structure of a Dutch expert witness report in a criminal case. The underlying motivation of the case study was to explore the usefulness of argumentation visualisation software for increasing a judge's understanding of expert reports and for assisting him or her in asking the proper critical questions to the expert. By way of an initial exploration of this usefulness, an expert report was analysed with the Rationale software. The visualisation was informally discussed with a legal expert, who was generally positive but also expressed some concerns and expected that the main usefulness of the tool is in training and education of judges.

A lightweight formal model of two-phase democratic deliberation.

Trevor Bench-Capon & Henry Prakken

In R.G.F. Winkels (ed.), Legal Knowledge and Information Systems. JURIX 2010: The 23rd Annual Conference. Amsterdam etc, IOS Press (2010), 27-36.

A formal two-phase model of democratic policy deliberation is presented, in which in the first phase sufficient and necessary criteria for proposals to be accepted are determined (the `admissible' criteria') and in the second phase proposals are made and evaluated in light of the admissible criteria resulting from the first phase. Argument schemes for both phases are defined and formalised in a logical framework for structured argumentation. The process of deliberation is abstracted from and it is assumed that both deliberation phases result in a set of arguments and attack and defeat relations between them. Then preferred semantics is used to evaluate the acceptability status of criteria and proposals.

A formal analysis of the AIF in terms of the ASPIC framework.

F.J. Bex, H. Prakken & C.A. Reed

In P. Baroni, F. Cerutti, M. Giacomin & G.R. Simari (eds.): Computational Models of Argument. Proceedings of COMMA 2010. Amsterdam etc, IOS Press 2010, 99-110.

In order to support the interchange of ideas and data between different projects and applications in the area of computational argumentation, a common ontology for computational argument, the Argument Interchange Format (AIF), has been devised. One of the criticisms levelled at the AIF has been that it does not take into account formal argumentation systems and their associated argumentation-theoretic semantics, which are part of the main focus of the field of computational argumentation. This paper aims to meet those criticisms by analysing the core AIF ontology in terms of the recently developed ASPIC argumentation framework.

Reasoning about preferences in structured extended argumentation frameworks.

S. Modgil & H. Prakken

This paper combines two recent extensions of Dung's abstract argumentation frameworks in order to define an abstract formalism for reasoning about preferences in structured argumentation frameworks. First, extended argumentation frameworks extend Dung frameworks with attacks on attacks, thus providing an abstract dialectical semantics that accommodates argumentation-based reasoning about preferences over arguments. Second, a recent extension of the ASPIC framework (ASPIC+) instantiates Dung frameworks with accounts of the structure of arguments, the nature of attack and the use of preferences to resolve attacks. In this paper, ASPIC+ is further developed in order to define attacks on attacks, resulting in a dialectical semantics that accommodates argumentation based reasoning about preferences in structured argumentation. Then, some recently proposed rationality postulates for structured extended argumentation are proven to hold.

Argumentation without arguments.

Henry Prakken

I>Proceedings of the Seventh Conference of the International Society for the Study of Argumentation (ISSA 2010). Amsterdam: SicSat, 2011. Also to appear in Argumentation.

A well-known ambiguity in the term ‘argument’ is that of argument as an inferential structure and argument as a kind of dialogue. In the first sense, an argument is a structure with a conclusion supported by one or more grounds, which may or may not be supported by further grounds. Rules for the construction and criteria for the quality of arguments in this sense are a matter of logic. In the second sense, arguments have been studied as a form of dialogical interaction, in which human or artificial agents aim to resolve a conflict of opinion by verbal means. Rules for conducting such dialogues and criteria for their quality are part of dialogue theory.

Usually, formal accounts of argumentation dialogues in logic and artificial intelligence presuppose an argument-based logic. That is, the ways in which dialogue participants support and attack claims are modelled as the construction of explicit arguments and counterarguments (in the inferential sense). However, in this paper formal models of argumentation dialogues are discussed that do not presuppose arguments as inferential structures. The motivation for such models is that there are forms of inference that are not most naturally cast in the form of arguments (such as abduction, statistical reasoning and coherence-based reasoning) but that can still be the subject of argumentative dialogue. Some recent work in artificial intelligence is discussed which embeds non-argumentative inference in an argumentative dialogue system, and some general observations are drawn from this discussion.

A Formal argumentation framework for deliberation Dialogues.

E. Kok, J.-J.Ch. Meyer, H. Prakken & G. Vreeswijk

Proceedings of the 7th International Workshop on Argumentation in Multi-Agent Systems, 73-90. Toronto (Canada), 2010.

Agents engage in deliberation dialogues to collectively decide on a course of action. To solve conflicts of opinion that arise, they can question claims and supply arguments. Existing models fail to capture the interplay between the provided arguments as well as successively selecting a winner from the proposals. This paper introduces a general framework for agent deliberation dialogues that uses an explicit reply structure to produce coherent dialogues, guides in outcome selection and provide pointers for agent strategies.

Arguing about preferences and decisions.

T. van der Weide, F. Dignum, J.-J.Ch. Meyer, H. Prakken & G. Vreeswijk

Proceedings of the 7th International Workshop on Argumentation in Multi-Agent Systems, 229-246. Toronto (Canada), 2010.

Complex decisions involve many aspects that need to be considered, which complicates determining what decision has the most preferred outcome. Artificial agents may be required to justify and discuss their decisions to others. Designers must communicate their wishes to artificial agents. Research in argumentation theory has examined how agents can argue about what decision is best using goals and values. Decisions can be justified with the goals they achieve, and goals can be justified by the values they promote. Agents may agree on having a value, but disagree about what constitutes that value. In existing work, however, it is not possible to discuss what constitutes a specific value, whether a goal promotes a value, why an agent has a value and why an agent has specific priorities over goals. This paper introduces several argument schemes, formalised in an argumentation system, to overcome these problems. The techniques presented in this paper are inspired by multi attribute decision theory.

Coherence-driven argumentation to norm consensus

Sindhu Joseph & Henry Prakken

Practical reasoning using values. Giving meaning to values.

T. van der Weide, F. Dignum, J.-J.Ch. Meyer, H. Prakken & G. Vreeswijk

Proceedings of the 6th International Workshop on Argumentation in Multi-Agent Systems, 225-240. Budapest (Hungary), 2009.

Each person holds numerous values that represent what is believed to be important. As a result, our values inuence our behavior and play a role in practical reasoning. Various argumentation approaches use values to justify actions, but they assume a function that determines what values a state or action promotes and demotes. However, this is often open for debate, since values are abstract and can be interpreted in many ways. After giving an overview of how values are dened in social psychology, this paper denes values as preferences and introduces several argument schemes to reason about preferences. These schemes are used to give meaning to values and to determine whether values are promoted or demoted. Furthermore, value systems are used for practical reasoning and allow resolving conicts when pursuing your values. An example is given of how the new argument schemes can be used to do practical reasoning using values.

A case study of hypothetical and value-based reasoning in US Supreme-Court cases.

Trevor Bench-Capon & Henry Prakken

In G. Governatori (ed.), Legal Knowledge and Information Systems. JURIX 2009: The 22nd Annual Conference. Amsterdam etc, IOS Press (2009), 11-20.

This paper studies the use of hypothetical and value-based reasoning in US Supreme-Court cases concerning the United States Fourth Amendment. Drawing upon formal AI & Law models of legal argument a semi-formal reconstruction is given of parts of the Carney case, which has been studied previously in AI & law research on case-based reasoning. The result is compared with Rissland's (1989) analysis in terms of dimensions and Ashley's (2008) analysis in terms of his process model of legal argument with hypotheticals.

More on presumptions and burdens of proof.

Henry Prakken & Giovanni Sartor

In E. Francesconi, G. Sartor & D. Tiscornia (eds.), Legal Knowledge and Information Systems. JURIX 2008: The 21st Annual Conference. Amsterdam etc, IOS Press (2008), 176-185.

This paper extends our previous logical analysis of presumptions and burden of proof by studying the force of a presumption once counterevidence has been offered. In the jurisprudential literature different accounts of this issue have been given: some have argued that a presumption is nullified by counterarguments while others have maintained that this gives presumptions a force that is too slight. We argue that these differences largely are not a matter of logic but of legal policy, and we show how the various accounts can be logically formalised.

Representing narrative and testimonial knowledge in sense-making software for crime analysis.

Susan van den Braak, Herre van Oostendorp, Henry Prakken & Gerard Vreeswijk

In G. Sartor (ed.), Legal Knowledge and Information Systems. JURIX 2008: The 21st Annual Conference. Amsterdam etc, IOS Press (2008), 160-169.

In the AVERs sense-making tool for crime analysis different types of information are represented in different ways. More precisely, narrative knowledge is represented in an explanatory direction and testimonial knowledge in an indicative direction. This paper shows that this distinction agrees with the preference of potential users and reduces the number of interpretation errors made by them.

Combining modes of reasoning: an application of abstract argumentation.

Henry Prakken

Utilizing compression and refinement to handle large cases in crime analysis.

S.W. Van den Braak, H. Van Oostendorp, G. Vreeswijk & H. Prakken

Workshop Notes of the ECAI-08 Workshop on Computational Models of Natural Argument
Patras (Greece), 21 July, 2008.

When large arguments are produced graph visualizations are often hard to read. Argument visualization software should therefore offer features that allow users to display their graphs in a readable way. More specialized software for crime analysts should also offer the ability to elaborate on graphs and to hide redundant nodes. While doing so, it should be easy to unfold all hidden information about a certain node if desired. Therefore, refinement and compression methods are implemented in the AVERs software for crime analysts. This paper presents the results of a study that tested the effect of compression and refinement on the quality of the users’ analysis of a simple crime case and their understanding of this case. In this study professional crime analysts and students who used these methods outperformed users that were only allowed to use conventional methods to handle large graphs.

Investigating stories in a formal dialogue game.

Floris Bex & Henry Prakken

In Ph. Besnard, S. Doutre & A. Hunter (ed.), Computational Models of Argument. Proceedings of COMMA 2008. Amsterdam etc, IOS Press 2008, 73-84.

In this paper we propose a formal dialogue game in which two players aim to determine the best explanation for a set of observations. By assuming an adversarial setting, we force the players to advance and improve their own explanations as well as criticize their opponent’s explanations, thus hopefully preventing the well-known problem of ‘tunnel vision’. A main novelty of our approach is that the game supports the combination of argumentation with abductive inference to the best explanation.

Applying preferences to dialogue graphs.

Sanjay Modgil & Henry Prakken

In Ph. Besnard, S. Doutre & A. Hunter (ed.), Computational Models of Argument. Proceedings of COMMA 2008. Amsterdam etc, IOS Press 2008, 252-263.

An abstract framework for formalising persuasion dialogues has recently been proposed. The framework provides for a range of speech acts, and protocols of varying levels of flexibility. However, the framework assumes the availability of preference information relevant to determining whether arguments moved in a dialogue defeat each other. However, preference information may only become available after the dialogue has terminated. Hence, in this paper, we describe dialogues conducted under the assumption of an attack relation that does not account for preferences. We then describe how the resultant dialogue graph can be pruned by a preference relation in order to determine whether the winner of the dialogue is still the winner given the newly available preference information. We also describe a class of protocols that account for subsequent pruning by a preference relation, and show that under a restriction on the pruning, if the player defending the dialogue's main topic is winning the dialogue, then (s)he remains the winner irrespective of the preference relation applied.

Heuristics in argumentation: a game-theoretical investigation.

R. Riveret, H. Prakken, A. Rotolo & G. Sartor

In Ph. Besnard, S. Doutre & A. Hunter (ed.), Computational Models of Argument. Proceedings of COMMA 2008. Amsterdam etc, IOS Press 2008, 324-335.

This paper provides a game-theoretical investigation on how to determine optimal strategies in dialogue games for argumentation. To make our ideas as widely applicable as possible, we adopt an abstract dialectical setting and model dialogues as extensive games with perfect information where optimal strategies are determined by preferences over outcomes of the disputes. In turn, preferences are specified in terms of expected utility combining the probability of success of arguments with the costs and benefits associated to arguments.

Personality-based practical reasoning.

T. van der Weide, F. Dignum, J.-J.Ch. Meyer, H. Prakken & G. Vreeswijk

Success chances in argument games: a probabilistic approach to legal disputes.

R. Riveret, A. Rotolo, G. Sartor, H. Prakken & B. Roth

The outcome of a legal dispute, namely, the decision of its adjudicator, is uncertain, and both parties develop their strategies on the basis of their appreciation of the probability that the adjudicator will accept their arguments or the arguments of their adversary. Costs and gains have to be balanced in light of this uncertainty in order to identify the most convenient strategies. This paper provides a probabilistic approach embedded into an argumentation framework to capture this uncertainty and its use to determine the expected utility to engage in a legal dispute.

Formalising arguments about the burden of persuasion

Henry Prakken & Giovanni Sartor

Formalising argumentative story-based analysis of evidence.

Floris Bex, Henry Prakken & Bart Verheij

AVERs: An argument visualization tool for representing stories about evidence.

Susan van den Braak, Gerard Vreeswijk & Henry Prakken

An implementation of norm-based agent negotiation.

Pieter Dijkstra, Henry Prakken & Kees De Vey Mestdagh

Argumentation structures in legal dossiers.

J. Sombekke, T.M. van Engers & H. Prakken

Presumptions and burdens of proof.

Henry Prakken & Giovanni Sartor

In T.M. van Engers (ed.), Legal Knowledge and Information Systems. JURIX 2006: The Nineteenth Annual Conference. Amsterdam etc, IOS Press (2006), 21-30.

This paper studies the logical modelling of presumptions and their effects on the burden of proof. Presumptions are modelled as default rules and their effect on the burden of proof is defined in terms of a distinction between the burden of production, the burden of persuasion and the tactical burden of proof. These notions are logically characterised in such a way that presumptions enable a party to fulfil a burden of production or persuasion while shifting a tactical burden to the other party. Finally, it is shown how debates about what can be presumed can be modelled as debates about the backings of default rules.

Anchored narratives in reasoning about evidence.

F.J. Bex, H. Prakken & B. Verheij

In T.M. van Engers (ed.), Legal Knowledge and Information Systems. JURIX 2006: The Nineteenth Annual Conference. Amsterdam etc, IOS Press (2006), 11-20.

This paper concerns the reasoning with stories, evidence and generali-sations in a legal context. We will make some notions from the existing Anchored Narratives theory more clear by making use of two formal techniques from AI, namely causal-abductive reasoning and default-style argumentation. We will propose a combination of these two formalisms which solves some of the problems of the causal-abductive approach

Justifying actions by accruing arguments.

Trevor Bench-Capon & Henry Prakken

In P.E. Dunne and T.J.M. Bench-Capon (eds.), Computational Models of Argument. Proceedings of COMMA-06. Amsterdam etc, IOS Press 2006, 247-258.

This paper offers a logical formalisation of an argument-based account of reasoning about action, taking seriously the abductive nature of this form of reasoning. The particular question addressed is what is the best way to achieve a specified goal? Given a set of final goals and a set of rules on the effects of actions, the formation of subgoals for a goal is formalised as the application of an inference rule corresponding to the practical syllogism well-known from practical philosophy. Positive and negative applications of the practical syllogism are then accrued as a way to capture the positive and negative side effects of an action. Positive accruals can be attacked by negative accruals and by arguments for alternative ways to achieve the same goal. Defeat relations between accrued action arguments are determined in terms of the values promoted and demoted by the actions considered in the arguments. Applying preferred semantics to the result then yields the admissible ways to achieve the desired goal.

Combining sceptical epistemic reasoning with practical reasoning.

Henry Prakken

In P.E. Dunne and T.J.M. Bench-Capon (eds.), Computational Models of Argument. Proceedings of COMMA-06. Amsterdam etc, IOS Press 2006, 311-322.

Corrected version, put online May 14, 2007.

This paper proposes an argument-based semantics for combined epistemic and practical reasoning, taking seriously the idea that in certain contexts epistemic reasoning is sceptical while practical reasoning is credulous. The new semantics combines grounded and preferred semantics. A dialectical proof theory is defined which is sound and complete with respect to this semantics and which combines existing argument games for sceptical reasoning in grounded semantics and credulous reasoning with preferred semantics.

A critical review of argument visualization tools: Do users become better reasoners?

Susan van den Braak, Herre van Oostendorp, Henry Prakken and Gerard Vreeswijk

In Workshop Notes of the ECAI-06 Workshop on Computational Models of Natural Argument
Riva del Garda (Italy), 28-29 August, 2006.

This paper provides an assessment of the most recent empirical research into the effectiveness of argument visualization tools. In particular, the methodological quality of the reported experiments and the conclusions drawn from them are critically examined. Their validity is determined and the methodological differences between them are clarified. The discrepancies in intended effects of use especially are investigated. Subsequently, methodological recommendations for future experiments are given.

On formalising dialogue systems for argumentation in the event calculus.

Lianne Bodenstaff, Henry Prakken & Gerard Vreeswijk

Proceedings of the Eleventh International Workshop on Nonmonotonic Reasoning, Windermere (UK), 2006, 374-382.

This paper studies the logical formalisation and implementation of dialogue systems for argumentation, motivated by the claim that this benefits their formal investigation and implementation. A case study is described in which a dialogue system of Prakken is formalised in Shanahan's version of the `full' Event Calculus and then implemented as a Prolog program. Then a second case study is briefly summarised in which a dialogue system of Parsons, Wooldridge and Amgoud is formalised in the same way. From the case studies some conclusions are drawn on the usefulness of the formalisation method.

A protocol for arguing about rejections in negotiation.

Jelle van Veenen & Henry Prakken

One form of argument-based negotiation is when agents argue about why an offer was rejected. If an agent can state a reason for a rejection of an offer, the negotiation process may become more efficient since the other agent can take this reason into account when making new offers. Also, if a reason for rejection can be disputed, the negotiation process may be of higher quality since flawed reasons may be revised as a result. This paper presents a formal protocol for negotiation in which reasons can be asked and given for rejections and in which agents can try to persuade each other that a reason is or is not acceptable. The protocol is modelled as a persuasion dialogue game embedded in a negotiation protocol. It has a social semantics since the protocol does not refer to the internal state of negotiating agents.

A study of accrual of arguments, with applications to evidential reasoning

Henry Prakken

Dialogues about the burden of proof

Henry Prakken, Chris Reed and Douglas Walton

Reinterpreting arguments in dialogue: an application to evidential reasoning.

Floris Bex & Henry Prakken

In T.F. Gordon (ed.), Legal Knowledge and Information Systems. JURIX 2004: The Seventeenth Annual Conference. Amsterdam etc, IOS Press (2004), 119-129.

This paper presents a formalisation of two typical legal dialogue moves in a formal dialogue game for argumentation. The moves concern two ways of reinterpreting a general rule used in an argument, viz. by 'unpacking' and 'refining' the rule. The moves can be made not only by the user but also by the attacker of the rule, in order to reveal new ways to attack it. The new dialogue game is illustrated with examples from legal evidential reasoning, in which these types of moves are particularly common.

Argumentation schemes and burden of proof

Henry Prakken, Chris Reed and Douglas Walton

Argumentation schemes and generalisations in reasoning about evidence

Henry Prakken, Chris Reed and Douglas Walton

Incomplete arguments in legal discourse: a case study.

Henry Prakken

The use of legal knowledge-based systems in public administration: what can go wrong?

Hugo de Bruin, Henry Prakken & Jorgen Svensson

Logical dialectics: the missing link between deductivism and pragma-dialectics.

Henry Prakken

Proceedings of the Fifth Conference of the International Society for the Study of Argumentation. Amsterdam: Sic Sat 2003, 857-860.

This paper discusses a long debated issue in argumentation theory, viz. whether deductive validity is the only criterion for evaluating arguments. I will develop my argument as a critical response to a very interesting recent paper by Leo Groarke in defence of so-called ‘deductivism’ (Groarke 1999). The essence of deductivism is that all natural-language arguments can be understood as attempts to formulate deductive arguments, even if on first sight they seem to be inductive. My main point of criticism is that this approach fails to account for the phenomenon of the burden of proof.

Encoding schemes for a discourse support system for legal argument

Henry Prakken and Gerard Vreeswijk

Intuitions and the modelling of defeasible reasoning: some case studies.

Henry Prakken

Reconstructing causal reasoning about evidence: a case study

Henry Prakken and Silja Renooij

Modelling reasoning about evidence in legal procedure

Henry Prakken

On dialogue systems with speech acts, arguments, and counterarguments.

Henry Prakken

Credulous and sceptical argument games for preferred semantics.

Gerard Vreeswijk & Henry Prakken

Dialectical proof theory for defeasible argumentation with defeasible priorities (preliminary report)

Henry Prakken

Rules of order for electronic group decision making - a formalization methodology.

Henry Prakken & Tom Gordon

A Semantic View on Reasoning About Priorities (extended abstract)

Henry Prakken

Proceedings of the second Dutch\German Workshop on Nonmonotonic Reasoning, Utrecht 1995.

This paper gives a logical analysis in semantic terms of reasoning about preference relations. A method is proposed for extending logics for reasoning with prioritised information with means to express information about priorities as premises, and for defining the logical consequences of such premises. The method is first presented in general terms and then applied to two existing systems, prioritised default logic and a model-theoretic formulation of pointwise circumscription; also its application to argument-based systems is discussed. Finally, the analysis is applied to a realistic example from legal reasoning.

From Logic to Dialectics in Legal Argument

Henry Prakken

Proceedings of the Fifth International Conference on Artificial Intelligence and Law, Washington DC, 1995. ACM Press 1995, 165-174.

This paper investigates the relation between declarative and procedural accounts of adversarial legal argument. A three- leveled model is proposed, where a formal argumentation framework is built around a logical system and itself embedded in a dialectical protocol for dispute, in such a way that, each time a party adds or retracts information, the argumentation framework reassesses the resulting state of the dispute. The proposed link between the first, logical level and an argumentation framework obviates the need for nonmonotonic logics at the first level, while the proposed link between declarative and procedural models of argumentation enables us to regard induction and analogy not as forms of inference but as heuristics for introducing premises.

Niet-monotone logica: heuristiek of legitimatie?

Henry Prakken

In O. Tans, W. Veraert, B. Wolthuis & J. Zwart (eds.): De grenzen van het goede leven. Rechtsgeleerde opstellen aangeboden aan prof. mr. A. Soeteman, pp. 171-180. Nijmegen: Ars Aequi Libri 2009. (In Dutch)

This paper responds to Arend Soeteman's claims that nonmotononic logic is not needed for rational reconstructions of the judicial judgements and that nonmonotonic logic is an aspect of the context of discovery rather than of the context of justification. First it is argued that for giving rational reconstructions of judicial decisions nonmonotonic logic is more useful than deductive logic since it forces a dialectical style of thinking: it not only forces to make explicit the implicit grounds that make a judgement logically valid but it also forces to make explicit the sources of doubt in the judgement and how they have been refuted. Then it is argued that the sharp distinction between the contexts of discovery and justification is in judicial contexts untenable, since the quality of a judgement partly depends on how thorough the search for counterarguments has been. These philosophical claims are then made practically relevant by applying them to some recent miscarriages of justice in the Netherlands. It is argued that a better training of crime investigators, prosecutors and judges in `dialectical' thinking might have prevented some of the mistakes in these cases.

Coherence and Flexibility in Dialogue Games for Argumentation

Henry Prakken

Technical Report UU-CS-2005-021, Department of Information and Computing Sciences, Utrecht University, Utrecht, 2005.

This article carries out a formal study of dialogue games for argumentation. A formal framework for such games is proposed which imposes an explicit reply structure on dialogues, where each dialogue move either attacks or surrenders to some earlier move of the other participant. The framework is flexible in several respects. It allows for different underlying logics, alternative sets of locutions and more or less strict rules for when they are allowed. In particular, it allows for varying degrees of coherence and flexibility when it comes to maintaining focus of a dialogue. Its formal nature supports the study of formal properties of specific dialogue protocols, especially on how they respect the underlying logic.

Formalizing Robert's Rules of Order. An Experiment in Automating Mediation of Group Decision Making

Henry Prakken

GMD Report 12, GMD - German National Research Center for Information Technology, Bonn, 1998.

Robert's Rules of Order are the standard procedure for deliberative societies of all kinds in the USA. This paper reports on an ongoing experiment: formalizing these rules for the purpose of implementing them as a procedural component of automated mediation systems for discussion and group decision making. Robert's Rules of Order have been chosen for this experiment because they are well-known, precisely formulated, and well-tested in practice. Although they need to be adapted for electronic applications, their formalization should nevertheless give useful insights into the problems and prospects of adding a procedural component to automated mediation systems.

The research is carried out in the context of the ZENO mediation system, developed at the GMD Bonn. One of ZENO's components is a WWW-accessible discussion forum. The aim of the ongoing experiment is to extend this forum with rules of order, and with a corresponding mudule that assists the human mediator in maintaining order at the forum, and in giving advice to the users of the forum on their options, rights and obligations in the discussion.

This paper reports on the first part of the experiment, formalizing Robert's Rules of Order in first-order predicate logic. This formal specification should be the basis for a more operational specification, and for the eventual implementation as a component of ZENO.

Book review Bankowski et al., Informatics and the Foundations of Legal Reasoning

Henry Prakken

Argumentation, Vol. 11, No 3 (1997) 377-381.

This is a review of

Zenon Bankowski, Ian White and Ulrike Hahn (editors): Informatics and the Foundations of Legal Reasoning. Law and Philosophy Library, Kluwer Academic Publishers, Dordrecht/Boston/London, 1995. 374 pages.