The widespread application of uninterpretable machine learning systems for sensitive purposes has spurred research into elucidating the decision-making process of these systems. These efforts have their background in many different disciplines, one of which is the field of AI & law. In particular, recent works have observed that machine learning training data can be interpreted as legal cases. Under this interpretation, the formalism developed to study case law, called the theory of precedential constraint, can be used to analyze the way in which machine learning systems draw on training data—or should draw on them—to make decisions. In the present work, we advance the theory underlying these explanation methods, by relating it to order theory and logic. This allows us to write a software implementation of the theory that can be used to compute with the definitions and give automatic proofs of the properties of the model. We use this implementation to evaluate the model on a series of datasets. Through this analysis, we characterize the types of datasets that are more, or less, suitable to be described by the theory.

AF-CBA uses case-based argumentation to justify classifier predictions by arguing about differences between cases. We extend the mechanism by modelling which differences can compensate for each other by constructing arguments using domain knowledge. This involves a secondary argumentation framework. To assist experts in defining the appropriate domain knowledge, we use a rule-based classifier for semi-automated knowledge induction. We use the resulting rule set to derive arguments and demonstrate this with an evaluation procedure.

We propose to model cause-in-fact in legal cases through fresh argumentation-theoretic notions of explanation and support, meant to capture the set of arguments that contribute to making a conclusion justified. This novel argumentation-based approach to causality in law goes beyond the traditional idea of a cause as a necessary antecedent condition (the conditio-sine-qua-non idea), to handle concurrent causal processes leading to overdetermination and preemption. It also provides sound analyses of cases involving omission and ennoblement. Finally, by relying on defeasible argumentation it can capture causal inferences based on defeasible generalisations, which are very often used in judicial reasoning. Through the analysis of causal puzzles in legal cases, we illustrate the framework’s effectiveness in handling complex causal reasoning, and demonstrate its potential to support legal reasoners with structured and intuitive analysis.

In recent years, hierarchical case-based-reasoning models of precedential constraint have been proposed. Trevor Bench-Capon criticised these models, among other things, on the grounds that they would not account for the possibility that intermediate factors are established with different strengths by different base-level factors. In this paper we respond to these criticisms for van Woerkom’s result-based hierarchical models. We argue that in some examples Bench-Capon seems to interpret intermediate factors as dimensions, and that applying van Woerkom’s dimension-based version of the hierarchical result model to these examples avoids Bench-Capon’s criticisms.

This paper reports on an experiment on using case-based reasoning in Dutch administrative law. The use case is decision-support for human medical experts at the Dutch Central Office of Driving Certification who have to decide whether a citizen who applies for a driving licence is fit to drive. Case-based reasoning is investigated for this purposes because of its potential advantages over machine-learning approaches as regards transparency and explainability. Both traditional case-based reasoning, AI & Law models of precedential constraint and their combination are investigated on predictive accuracy relative to a large case base with more than 30.000 cases. A combined model is found to have the highest accuracy. The results indicate that human-in-the-loop support with a tool based on the combined model may be feasible, but whether this is indeed so requires further investigation.

In this paper we build on a formal model of reasoning with dimensions to analyze data from the COMPAS program—a widely used and studied tool for predicting recidivism. We extend the underlying theory of the model by introducing a notion of consistency and apply it to assess whether COMPAS follows this principle in its risk assessments and supervision level recommendations. Our analysis yields three key findings. First, the program’s risk score assignments appear highly inconsistent, but we argue this is due to important input features missing from the dataset. Second, the program’s recommended supervision levels do exhibit a high degree of consistency. Third, we uncover errors in the dataset related to the conversion of raw scores to decile scores. These findings cast doubts on previous studies conducted on the COMPAS dataset, and demonstrate the need for evaluation studies like ours.

This paper presents a formal model of dialectical argument strength in terms of the number of ways in which an argument can be successfully attacked in expansions of an abstract argumentation framework. First a model is proposed that is abstract but designed to avoid overly limiting assumptions on instantiations or dialogue contexts. It is then shown that most principles for argument strength proposed in the literature fail to hold for the proposed notions of dialectical strength, which clarifies the rational foundations of these principles and highlights the importance of distinguishing between kinds of argument strength, in particular logical, dialectical and rhetorical argument strength. The abstract model is then instantiated with ASPIC+ to test the claim that it does not make overly limiting assumptions on the structure of arguments and the nature of their relations.

The widespread application of uninterpretable machine learning systems for sensitive purposes has spurred research into elucidating the decision-making process of these systems. These efforts have their background in many different disciplines, one of which is the field of AI & law. In particular, recent works have observed that machine learning training data can be interpreted as legal cases. Under this interpretation, the formalism developed to study case law, called the theory of precedential constraint, can be used to analyze the way in which machine learning systems draw on training data—or should draw on them—to make decisions. In the present work, we advance the theory underlying these explanation methods, by relating it to order theory and logic. This allows us to write a software implementation of the theory that can be used to compute with the definitions and give automatic proofs of the properties of the model. We use this implementation to evaluate the model on a series of datasets. Through this analysis, we characterize the types of datasets that are more, or less, suitable to be described by the theory.

We define and study the notions of stability and relevance for precedent-based reasoning, focusing on Horty's result model of precedential constraint. According to this model, precedents constrain the possible outcomes for a focus case, which is a yet undecided case, where precedents and the focus case are compared on their characteristics (called dimensions). In this paper, we refer to the enforced outcome for the focus case as its justification status. In contrast to earlier work, we do not assume that all dimension values of the focus case have been established with certainty: rather, each dimension is assigned a set of possible values. We define a focus case as stable if its justification status is the same for every choice of the possible values. For focus cases that are not stable, we study the task of identifying relevance: which possible values should be excluded to make the focus case stable? We show how the tasks of identifying justification, stability and relevance can be exploited for human-in-the-loop decision support. Finally, we discuss the computational complexity of these tasks and provide efficient algorithms.

AF-CBA is an example-based approach to XAI that draws on the case-based argumentation tradition in AI & Law. It means to explain binary classifications made by an opaque machine-learning model by presenting an argument graph to the user, which represents an argument game about the classification of a case on the basis of precedents derived from labelled data used in the training phase of the classifier. We improve the robustness of this method by modifying it to better handle inconsistent labelling and evaluate an alternative setup that does not require access to the labelled data by using earlier predictions instead.

This paper proposes a novel argumentation-based approach to combine legal-reasoning methods that each solve a subproblem of an overall legal problem. The methods can be of any nature (for instance, logical, case-based or probabilistic), as long as their input-output behaviour can be described at the metalevel with deductive or defeasible rules. The model is formulated in the ASPIC+ framework, to profit from its metatheory and explanation methods, and to allow for disagreement about how to solve a subproblem. The model is not meant to be directly implementable but to serve as a semantics for architectures and implementations.

In recent work, theories of case-based legal reasoning have been applied to the development of explainable artificial intelligence methods, through the analogy of training examples as previously decided cases. One such theory is that of precedential constraint. A downside of this theory with respect to this application is that it performs single-step reasoning, moving directly from the case base to an outcome. For this reason we propose a generalization of the theory of precedential constraint which allows multi-step reasoning, moving from the case base through a series of intermediate legal concepts before arriving at an outcome. Our generalization revolves around the notion of factor hierarchy, so we call this hierarchical precedential constraint. We present the theory, demonstrate its applicability to case-based legal reasoning, and perform a preliminary analysis of its theoretical properties.

We extend the result model for precedent-based reasoning with incomplete case bases. In contrast to regular case bases, these consist of incomplete cases for which not all dimension values need to be specified, but rather each dimension is assigned a set of possible values. The outcome of cases then applies for each (combination of) the possible dimension values. Building on earlier proposed notions of justification and stability for incomplete focus cases, we introduce the notion of possible justification statuses, which are required to maintain consistency of the incomplete case base. We demonstrate how these theoretic notions can be applied in practice for human-in-the-loop decision support, discuss their computational complexity and provide efficient algorithms.

In recent years, a model of a fortiori argumentation, developed to describe legal reasoning based on precedent, has been successfully applied in the field of artificial intelligence to improve interpretability of data-driven decision systems. In order to make this model more broadly applicable for this purpose, work has been done to expand the knowledge representation on the basis of which it functions, as the original model accommodates only binary propositional information. In particular, two separate expansions of the original model emerged; one which accounts for non-binary input information, and a second which accommodates hierarchically structured reasoning. In the present work we unify these expansions to a single model, incorporating both dimensional and hierarchical information.

This paper proposes a structured variant in ASPIC+ of the notion of expansions of abstract argumentation frameworks. The purpose of this is threefold: studying what it takes to instantiate the abstract notion of expansions with a structured account of argumentation, studying to which extent assumptions implicitly made at the abstract level hold for structured instantiations and studying which potentially interesting distinctions can be made at the structured level that cannot be expressed at the abstract level.

In this paper we formalise a meta-argumentation framework as an ASPIC+ extension which enables reasoning about conflicts between formulae of the argumentation language. The result is a standard abstract argumentation framework that can be evaluated via grounded semantics.

This paper formally studies a notion of dialectical argument strength in terms of the number of ways in which an argument can be successfully attacked in expansions of an abstract argumentation framework. The proposed model is abstract but its design is motivated by the wish to avoid overly limiting assumptions that may not hold in particular dialogue contexts or in particular structured accounts of argumentation. It is shown that most principles for gradual argument acceptability proposed in the literature fail to hold for the proposed notion of dialectical strength, which clarifies their rational foundations and highlights the importance of distinguishing between logical, dialectical and rhetorical argument strength.

For legislation to be effective, it should not be too complex; otherwise, it cannot be sufficiently understood by those who have to apply the law or comply with it. This paper adds to the research in AI & law on developing precise mathematical complexity measures for legislation and applying these measures by computational means. The framework of Katz & Bommarito (2014) is applied to measure the complexity of Dutch legislation. The aim is twofold: first, to investigate whether this framework is meaningfully more widely applicable by applying it to a different jurisdiction and a corpus of larger size; and second, to identify possible improvements to the framework.

In this article, we discuss case decision predictors, algorithms which, given some features of a legal case predict the outcome of the case (i.e. the decision of the judge). We discuss whether, and if so how, such prediction algorithms can be used to support judges in their decision making process. We conclude that case decision predictors can only be useful in individual cases if they can give legal justifications for their predictions, and that only these legal justifications are what should matter for a judge.

There has recently been talk of algorithms that predict decisions in legal cases being used by the judiciary to improve the predictability and consistency of judicial decision making. We argue that their use may minimise the error rate of decisions in the long run, but that this would require not only major technical advances but also major changes in legal thinking about what is the most important objective of judicial decision-making: optimising individual justice in a particular case or reducing errors in the long run. We further argue that if algorithmic decision predictors give any useful information in individual cases to judges at all, this is not in its predictions but in its explanations.

In this paper, we present the information graph (IG) formalism, which provides a precise account of the interplay between deductive and abductive inference and causal and evidential information, where ‘deduction’ is used for defeasible ‘forward’ inference. IGs formalise analyses performed by domain experts in the informal reasoning tools they are familiar with, such as mind maps used in crime analysis. Based on principles for reasoning with causal and evidential information given the evidence, we impose constraints on the inferences that may be performed with IGs. Our IG-formalism is intended to facilitate the construction of formal representations within AI systems by serving as an intermediary formalism between analyses performed using informal reasoning tools and formalisms that allow for formal evaluation. In this paper, we investigate the use of the IG-formalism as an intermediary formalism in facilitating Bayesian network (BN) graph construction. We propose a structured approach for automatically constructing from an IG a directed BN graph, together with qualitative constraints on the probability distribution represented by the BN. Moreover, we prove a number of formal properties of our approach and identify assumptions under which the construction of an initial BN graph can be fully automated.

In this paper, we propose the information graph (IG) formalism, which provides a precise account of the interplay between deductive and abductive inference and causal and evidential information. IGs formalise analyses performed by domain experts in the informal reasoning tools they are familiar with, such as mind maps used in crime analysis. Based on principles for reasoning with causal and evidential information given the evidence, we impose constraints on the inferences that may be performed with IGs. Moreover, we propose an argumentation formalism based on IGs that allows arguments to be formally evaluated.

Abstract This paper formally compares some central notions from two well-known formalisms for rule-based argumentation, DeLP and ASPIC+. The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure properties. As for differences in the definitions of arguments and attack, it turns out that DeLP’s definitions are intuitively appealing but that they may not fully comply with Caminada and Amgoud’s rationality postulates of strict closure and indirect consistency. For some special cases, the DeLP definitions are shown to fare better than ASPIC+. Next, it is argued that there are reasons to consider a variant of DeLP with grounded semantics, since in some examples its current notion of warrant arguably has counterintuitive consequences and may lead to sets of warranted arguments that are not admissible. Finally, under some minimality and consistency assumptions on ASPIC+ arguments, a one-to-many correspondence between ASPIC+ arguments and DeLP arguments is identified in such a way that if the DeLP warranting procedure is changed to grounded semantics, then ’s DeLP notion of warrant and ASPIC+ ’s notion of justification are equivalent. This result is proven for three alternative definitions of attack.

In this paper a new formal model of argument accrual is proposed as an adaptation of the ASPIC+ framework for structured argumentation. The new model aims to overcome several weaknesses of existing proposals. It is shown to have desirable formal properties that are in line with standard work on formal argumentation, and to be applicable to a range of situations in legal reasoning.

Bayesian networks (BNs) are powerful tools that are increasingly being used by forensic and legal experts to reason about the uncertain conclusions that can be inferred from the evidence in a case. Although in BN construction it is good practice to document the model itself, the importance of documenting design decisions has received little attention. Such decisions, including the (possibly conflicting) reasons behind them, are important for legal experts to understand and accept probabilistic models of cases. Moreover, when disagreements arise between domain experts involved in the construction of BNs, there are no systematic means to resolve such disagreements. Therefore, we propose an approach that allows domain experts to explicitly express and capture their reasons pro and con modelling decisions using argumentation, and that resolves their disagreements as much as possible. Our approach is based on a case study, in which the argumentation structure of an actual disagreement between two forensic BN experts is analysed.

In this paper several existing dimension-based models of precedential constraint are compared and an alternative is proposed, which unlike existing models does not require that for each value assignment to a dimension it is specified whether it is for or against the case’s outcome. This arguably makes the model easier to apply in practice. In addition, it is shown how several factor- and dimension-based models of precedential constraint can be embedded in a Dung-style argumentation-based form, so that general tools from the formal study of argumentation become applicable.

While work on abstract argumentation frameworks has greatly advanced the study of argumentation in AI, its use is not without danger. One danger is that the direct modelling of examples in abstract frameworks instead of through a theory of the structure of arguments and the nature of attacks leads to ad-hoc modellings. Another danger is that it may be overlooked that abstract accounts of argumentation can implicitly make assumptions that are not shared by many of their instantiations. A variant of this is where assumptions valid for specific argumentation contexts are incorrectly generalised by abstracting away from the context. This paper gives examples of both dangers. A lesson drawn from this is that abstraction in AI research, although necessary for understanding the essentials of the object of study, can oversimplify in ways that are not easily noticed without an explicit account of the structure of arguments and the nature of attack.

In this paper, we propose a structured approach for transforming legal arguments to a Bayesian network (BN) graph. Our approach automatically constructs a fully specified BN graph by exploiting causality information present in legal arguments. Moreover, we demonstrate that causality information in addition provides for constraining some of the probabilities involved. We show that for undercutting attacks it is necessary to distinguish between causal and evidential attacked inferences, which extends on a previously proposed solution to modelling undercutting attacks in BNs. We illustrate our approach by applying it to part of an actual legal case, namely the Sacco and Vanzetti legal case.

Among the problems that still need to be solved before autonomous vehicles can fully autonomously participate in traffic is the one of making them respect the traffic laws. This paper discusses this problem by way of a case study of Dutch traffic law. First it is discussed to what extent Dutch traffic law exhibits features that are traditionally said to pose challenges for AI & Law models, such as exceptions, open texture and vagueness and the need for commonsense knowledge. Then three approaches to the design of law-respecting AV are evaluated in light of the challenges posed by Dutch traffic law.

In this paper two discussions between experts about Bayesian modellings of complex criminal cases are analysed on their argumentation structure. The usefulness of several recognised argument schemes is confirmed, two new schemes for interpretation arguments and for arguments from statistics are proposed, and an analysis is given of debates about the validity of arguments. From a practical point of view the case study yields insights into the design of support software for discussions about Bayesian modellings of complex criminal cases.

Much research on structured argumentation aims to satisfy the rationality postulates of direct and indirect consistency and strict (deductive) closure. However, examples like the lottery paradox indicate that it is sometimes rational to accept sets of propositions that are indirectly inconsistent or not deductively closed. This paper proposes a variant of the ASPIC+ framework that violates indirect consistency and full strict closure but satisfies direct consistency and restricted forms of strict closure and indirect consistency.

This paper studies two issues concerning relevance in structured argumentation in the context of the ASPIC+ framework, arising from the combined use of strict and defeasible inference rules. One issue arises if the strict inference rules correspond to classical logic. A longstanding problem is how the trivialising effect of the classical Ex Falso principle can be avoided while satisfying consistency and closure postulates. In this paper, this problem is solved by disallowing chaining of strict rules, resulting in a variant of the ASPIC+ framework called ASPIC*, and then disallowing the application of strict rules to inconsistent sets of formulas. Thus in effect Rescher & Manor's paraconsistent notion of weak consequence is embedded in ASPIC*. Another issue is minimality of arguments. If arguments can apply defeasible inference rules, then they cannot be required to have subset-minimal premises, since defeasible rules based on more information may well make an argument stronger. In this paper instead minimality is required of applications of strict rules throughout an argument. It is shown that under some plausible assumptions this does not affect the set of conclusions. In addition, circular arguments are in the new ASPIC* framework excluded in a way that satisfies closure and consistency postulates and that generates finitary argumentation frameworks if the knowledge base and set of defeasible rules are finite. For the latter result the exclusion of chaining of strict rules is essential. Finally, the combined results of this paper are shown to be a proper extension of classical-logic argumentation with preferences and defeasible rules.

Over the last decades the rise of forensic sciences has led to an increase in the availability of statistical evidence. Reasoning about statistics and probabilities in a forensic science setting can be a precarious exercise, especially so when independencies between variables are involved. To facilitate the correct explanation of such evidence we investigate how argumentation models can help in the interpretation of statistical information. In this paper we focus on the connection between argumentation models and Bayesian belief networks, the latter being a common model to represent and reason with complex probabilistic information. We introduce the notion of a support graph as an intermediate structure between Bayesian networks and argumentation models. A support graph disentangles the complicating graphical properties of a Bayesian network and enhances its intuitive interpretation. Moreover, we show that this model can provide a suitable template for argumentative analysis. Especially in the context of legal reasoning, the correct treatment of statistical evidence is important.

Reasoning about statistics and probabilities can, when not treated with cautiousness, lead to reasoning errors. Over the last decades the rise of forensic sciences has led to an increase in the availability of statistical evidence. To facilitate the correct explanation of such evidence we investigate how argumentation models can help in the interpretation of statistical information. Uncertainties are by forensic experts often expressed numerically, but lawyers, judges and other legal experts have notorious difficulty interpreting these results [3, 1, 2, 5]. In this demonstration of our main paper [6] we focus on the connection between formal models of argumentation and Bayesian belief networks (BNs). We use BNs because they are a well-known model to represent and reason with complex probabilistic information. We introduce the notion of a support graph as an intermediate structure between Bayesian networks and argumentation models. A support graph captures the inferences modelled in a Bayesian network but disentangles the complicating graphical properties of such models and instead emphasises its intuitive understanding. Moreover, we show that this intermediate model can function as a template to generate different arguments based on the data.

In a criminal trial, a judge or jury needs to reach a conclusion about 'what happened' based on the available evidence. Often this includes probabilistic evidence. Whereas Bayesian networks form a good tool for analysing evidence probabilistically, simply presenting the outcome of the network to a judge or jury does not allow them to make an informed decision. In this paper, we propose to combine Bayesian networks with a narrative approach to reasoning with legal evidence, the result of which allows a juror to reason with alternative scenarios while also incorporating probabilistic information. The proposed method aids both the construction and the understanding of Bayesian networks, using scenario schemes. We make three distinct contributions: (1) we propose to use scenario schemes to aid the construction of Bayesian networks, (2) we propose a method for producing scenarios in text form from the resulting networks and (3) we propose a format for reporting the alternative scenarios and their relations to the evidence (including strength).

Legal reasoning about evidence can be a precarious exercise, in particular when statistics are involved. A number of recent miscarriages of justice have provoked a scientific interest in formal models of legal evidence. Two such models are presented by Bayesian networks (BNs) and argumentation. A limitation of argumentation is that it is difficult to embed probabilities. BNs, on the other hand, are probabilistic by nature. A disadvantage of BNs is that it can be hard to explain what is modelled and how the results came about. Assuming that a forensic expert presents evidence in a way that is either already a BN or expressed in terms that easily map to a simple BN, we may wish to express the same information in argumentative terms. We address this issue by translating Bayesian networks to arguments. We do this by means of an intermediate structure, called a support graph, which represents the variables from the Bayesian network, maintaining independence information in the network, but connected in a way that more closely resembles argumentation. In the current paper we test the support graph method on a Bayesian network from the literature. We argue that the resulting support graph adequately captures the possible arguments about the represented case. In addition, we highlight strengths and limitations of the method that are revealed by this case study.

Legal reasoning with evidence can be a challenging task. We study the relation between two formal approaches that can aid the construction of legal proof: argumentation and Bayesian networks (BNs). Argument schemes are used to describe recurring patterns in argumentation. Critical questions for many argument schemes have been identified. Due to the increased use of statistical forensic evidence in court it may be advantageous to consider probabilistic models of legal evidence. In this paper we show how argument schemes and critical questions can be modelled in the graphical structure of a Bayesian network. We propose a method that integrates advantages from other methods in the literature.

Bayesian networks have gained popularity as a probabilistic tool for reasoning with legal evidence. However, two common difficulties are (1) the construction and (2) the understanding of a network. In previous work, we proposed to use narrative tools and in particular scenario schemes to assist the construction and the understanding of Bayesian networks for legal cases. We proposed a construction method and a reporting format for explaining or understanding the network. The quality of a scenario, which plays an important role in the narrative approach to evidential reasoning, was not yet included in this method. In this paper, we provide a discussion of what constitutes the quality of a scenario, in terms of the narrative concepts of completeness, consistency and plausibility. We propose a probabilistic interpretation of these concepts, and show how they can be incorporated in our previously proposed method. We also illustrate with an example how these concepts concerning scenario quality can be used to explain or understand a Bayesian network.

In this article we offer a formal account of reasoning with legal cases in terms of argumentation schemes. These schemes, and undercutting attacks associated with them, are formalized as defeasible rules of inference within the ASPIC+ framework. We begin by modelling the style of reasoning with cases developed by Aleven and Ashley in the CATO project, which describes cases using factors, and then extend the account to accommodate the dimensions used in Rissland and Ashley's earlier HYPO project. Some additional scope for argumentation is then identified and formalized.

One tradition in the logical study of argumentation is to allow for arguments that combine strict and defeasible inference rules, and to derive the strict inference rules from a logic at least as strong as classical logic. An unsolved problem in this tradition is how the trivialising effect of the classical Ex Falso principle can be avoided when two arguments that use defeasible rules have contradictory conclusions. The problem is especially hard since any solution should arguably preserve current results on satisfaction of consistency and logical closure properties. One approach to solve the problem is to replace classical logic as the source for strict rules with a weaker, monotonic paraconsistent logic. This paper explores this approach in the context of the ASPIC+ framework for structured argumentation, by instantiating it with a paraconsistent consequence notion of Rescher & Manor (1970). The results are positive: satisfaction of the closure and consistency postulate is proven.

This demonstration shows how arguments, formalised in a well defined framework, can be automatically constructed from a given Bayesian network.

Arguably the significance of an abstract model of argumentation depends on the range of realistic instantiations it allows. This paper therefore investigates for three frameworks for abstract argumentation with support relations whether they can be instantiated with the ASPIC+framework for structured argumentation. Both evidential argumentation systems and a simple extension of Dung's abstract frameworks with support relations proposed by Dung & Thang (2014) are shown to allow such an instantiation. However, for bipolar argumentation frameworks a positive result is only obtained for variants with only direct and secondary attacks; counterexamples are provided for variants with supported attacks, even for the special case of deductive support.

Recent developments in the forensic sciences have confronted the field of legal reasoning with the new challenge of reasoning under uncertainty. Forensic results come with uncertainty and are described in terms of likelihood ratios and random match probabilities. The legal field is unfamiliar with numerical valuations of evidence, which has led to confusion and in some cases to serious miscarriages of justice. The cases of Lucia de B. in the Netherlands and Sally Clark in the UK are infamous examples where probabilistic reasoning has gone wrong with dramatic consequences. One way of structuring probabilistic information is in Bayesian networks (BNs). In this paper we explore a new method to identify legal arguments in forensic BNs. This establishes a formal connection between probabilistic and argumentative reasoning. Developing such a method is ultimately aimed at supporting legal experts in their decision making process.

In order to make an informed decision in a criminal trial, conclusions about what may have happened need to be derived from the available evidence. Recently, Bayesian networks have gained popularity as a probabilistic tool for reasoning with evidence. However, in order to make sense of a conclusion drawn from a Bayesian network, a juror needs to understand the context. In this paper, we propose to extract scenarios from a Bayesian network to form the context for the results of computations in that network. We interpret the narrative concepts of scenario schemes, local coherence and global coherence in terms of probabilities. These allow us to present an algorithm that takes the most probable configuration of variables of interest, computed from the Bayesian network, and forms a coherent scenario as a context for these variables. This way, we take advantage of the calculations in a Bayesian network, as well as the global perspective of narratives.

Argument schemes can provide a means of explicitly describing reasoning methods in a form that lends itself to computation. The reasoning required to distinguish cases in the manner of CATO has been previously captured as a set of argument schemes. Here we present argument schemes that encapsulate another way of reasoning with cases: using preferences between social values revealed in past decisions to decide cases which have no exact matching precedents when the cases are described in terms of factors. We provide a set of schemes, with variations to capture different ways of comparing sets and varying degrees of promotion of values; we formalise these schemes; and we illustrate them with some examples.

Legal cases involve reasoning with evidence and with the development of a software support tool in mind, a formal foundation for evidential reasoning is required. Three approaches to evidential reasoning have been prominent in the literature: argumentation, narrative and probabilistic reasoning. In this paper a combination of the latter two is proposed.

In previous work we presented argumentation schemes to capture the CATO and value based theory construction approaches to reasoning with legal cases with factors. We formalised the schemes with ASPIC+, a formal representation of instantiated argumentation. In ASPIC+ the premises of a scheme may either be a factor provided in a knowledge base or established using a further argumentation scheme. Thus far we have taken the factors associated with cases to be given in the knowledge base. While this is adequate for expressing factor based reasoning, we can further investigate the justifications for the relationship between factors and facts or evidence. In this paper we examine how dimensions as used in the HYPO system can provide grounds on which to argue about which factors should apply to a case. By making this element of the reasoning explicit and subject to argument, we advance our overall account of reasoning with legal cases and make it more robust.

In most attempts to model legal systems as formal argumentation systems, legal norms are viewed as an argumentation's system inference rules. Since in formal argumentation systems inference rules are generally assumed to be fixed and independent from the inferences they enable, this approach fails to capture the dialectical connection between norms and arguments, where on the one hand legal arguments are based on norms, and on the other hand the validity of norms depends on arguments. The validity of a new norm can be supported by referring to authoritative sources, such as legislation or precedent, but also through interpretations of such sources, or through analogies or a contrario arguments based on existing authoritative norms. In this contribution arguments about norms are modelled as the application of argument schemes to knowledge bases of facts and norms.

Legal reasoning can be approached from various perspectives, traditionally argumentation, probability and narrative. The communication between forensic experts and a judge or jury would benefit from an integration of these approaches. In previous papers we worked on the connection between the narrative and the probabilistic approach. We developed techniques for representing crime scenarios in a Bayesian network. But for complex cases, the construction of a Bayesian network structure using these techniques remained a cumbersome task.

The Argument Interchange Format (AIF) has been devised in order to support the interchange of ideas and data between different projects and applications in the area of computational argumentation. In order to support such interchange, an abstract ontology for argumentation is presented, which serves as an interlingua between various more concrete argumentation languages. In this article, we aim to give what is essentially a logical specification of the AIF ontology by mapping the ontology onto the logical ASPIC+ framework for argumentation. We thus lay foundations for interrelating formal logic-based approaches to argumentation captured by the ASPIC+ framework and the wider class of argumentation languages, including those that are more informal and user-orientated.

Recently resolution of attacks has been studied in the context of abstract argumentation frameworks. In this paper it is claimed that resolutions should be studied under the assumption that they are generated through the acquisition of preference information, and that this implies that the existing study of resolutions has limited applicability. A formalisation of preference-based resolutions is defined in the context of the ASPIC+framework for structured argumentation, and several properties of resolutions are proven or disproven. It is also argued that when resolutions are modelled without specifying the structure of arguments, then it is easy to overlook that assumptions made at the abstract level do not hold for all reasonable instantiations of the abstract framework, thus reducing its significance.

The ASPIC+framework is a general framework for argumentation-based inference which aims to unifies two research strands: those in which arguments can only be attacked on their defeasible inferences and those in which arguments can only be attacked on their premises. The framework is meant to define a wide class of instantiations of abstract argumentation frameworks and to support the investigation of rationality postulates for argumentation-based inference. Recently, it has been argued that the ASPIC+framework suffers from several weaknesses. In this paper these criticisms are argued to be based on a number of misconceptions on the nature of the ASPIC+framework.

This paper presents a case study in which an opinion of a legal scholar on a legislative proposal is formally reconstructed in the ASPIC+framework for argumentation-based inference. The reconstruction uses a version of the argument scheme for good and bad consequences that does not refer to single but to sets of consequences, in order to model aggregation of reasons for and against proposals. The case study is intended to contribute to a comparison between various formal frameworks for argumentation by providing a new benchmark example. It also aims to illustrate the usefulness of two features of ASPIC+: its distinction between deductive and defeasible inference rules and its ability to express arbitrary preference orderings on arguments.

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 `acceptable' criteria) and in the second phase proposals are made and evaluated in light of the acceptable criteria resulting from the first phase. Such a separation gives the discussion a clear structure and prevents time and resources from being wasted on evaluating arguments for proposals based on unacceptable criteria. 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. The acceptability status of criteria and proposals within the resulting argumentation framework is then evaluated using preferred semantics. For cases where preferences are required to choose between proposals, inference rules for deriving preferences between sets from an ordering of their elements are given.

A formal model is proposed of argumentation with burdens and standards of proof, overcoming shortcomings of earlier work. The model is based on a distinction between default and inverted burdens of proof. This distinction is formalised by adapting the definition of defeat of the ASPIC+ framework for structured argumentation. Since ASPIC+ generates abstract argumentation frameworks, the model is thus given a Dungean semantics. It is shown to adequately capture shifting proof burdens as well as Carneades' definitions of proof standards.

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.

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.

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.

In this paper coherence-based models are proposed as an alternative to logic-based BDI and argumentation models for the reasoning of normative agents. A model is provided for how two coherence-based agents can deliberate on how to regulate a domain of interest. First a deductive coher-ence model presented, in which the coherence values are de-rived from the deduction relation of an underlying logic; this makes it possible to identify the reasons for why a proposi-tion is accepted or rejected. Then it is shown how coherence-driven agents can generate candidate norms for deliberation, after which a dialogue protocol for such deliberations is pro-posed. The resulting model is compared to current logic-based argumentation systems for deliberation over action.

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.

Trevor Bench-Capon, Henry Prakken; Editorial: Logic and Law Corner, Journal of Logic and Computation, Volume 19, Issue 6, 1 December 2009, Pages 899, https://do

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.

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.

In this article 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.

In the present paper, we provide a formalised version of a merged argumentative and story-based approach towards the analysis of evidence. As an application, we are able to show how our approach sheds new light on inference to the best explanation with case evidence. More specifically, it will be clarified how the events in a case story that are considered to be proven abductively explain the otherwise unproven events of the case story. We compare our approach with existing AI work on modelling legal reasoning with evidence.

This paper proposes an architecture for a sense-making system for crime investigation named AVERs (Argument Visualization for Evidential Reasoning based on stories). It is targeted at crime investigators who may use it to explain initially observed facts by drawing links between these facts and hypothesized events, and to connect the thus created stories to evidence through argumentation. AVERs draws on a combination of ideas from visualizing argumentation and anchored narratives theory.

In this paper, we develop our previous outline of a multi-agent architecture for regulated information exchange in crime investigations. Interactions about information exchange between agents (representing police officers) are further analysed as negotiation dialogues with embedded persuasion dialogues. An architecture is proposed consisting of two agents, a requesting agent and a responding agent, using a communication language and protocol with which they can interact in order to promote optimal information exchange while respecting the law. Furthermore, the agents' negotiation policies are defined and implemented and an implementation of the agent execution cycle is proposed, which will ultimately enable us to field test our model in order to supply a proof of concept.

This paper presents an argument-based logic for reasoning about allocations of the burden of persuasion. The logic extends the system of Prakken (2001), which in turn modified the system of Prakken & Sartor (1996) with the possibility to distribute the burden of proof over both sides in an argument game. First the (2001) system is put in the context of a distinction of three types of proof burdens and it is argued that the proof burdens of that system are in fact burdens of persuasion. Then the (2001) system is modified to allow for defeasible reasoning about allocations of such burdens within the logic. The usefulness of the resulting system is illustrated with applications to real legal cases.

This paper argues that the best chance of utilising AI & Law models of legal argument in practice in the near future may be in desiging legal argumentation management systems. Such systems do not have a knowledge base and inference engine but allow the user to structure a legal case dossier in terms of the argumentation structure of a case, so that better overview over the dossier is obtained and documents can be better retrieved, compared and drafted. To obtain insight in how such systems should be designed, a case study is presented in which a dossier of a solicitor representing a client in a Dutch civil dispute is analysed according to its argumentation structure. The resulting structures are visualised using the Araucaria software tool. Special attention is paid to the creation of the argumentation structure over time in the course of the dispute, and to the argumentative tactics and strategies employed by the solicitor.

This paper presents a logical formalisation of accrual of arguments as a form of inference. The formalisation is given within the logical framework of Dung as instantiated by Pollock, and is shown to satisfy three principles that any treatment of accrual should satisfy. The formalisation of accrual as inference is contrasted to knowledge-representation treatments of accrual. Also, the formalisation is applied to some concepts from the theory of evidential legal reasoning.

This paper analyses the phenomenon of a shift of the burden of proof in legal persuasion dialogues. Some sample dialogues are analysed of types of situations where such a shift may occur, viz. reasoning with defeasible rules, reasoning with argumentation schemes and reasoning with mere presumptions. It is argued that whether a shift in the burden of proof occurs can itself become the subject of dispute and it is shown how a dialogue game protocol for persuasion can be extended to let it regulate persuasion dialogues about the burden of proof. It is also shown that dialogues about the burden of proof are often implicitly about the precise form of the rules used in an argument.

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.

This paper studies the modelling of legal reasoning about evidence within general theories of defeasible reasoning and argumentation. In particular, it is studied how Wigmore's method for charting evidence and its use by modern legal evidence scholars can be exploited by modern visualisation software for argumentation, and how a formal account of the method can be given in terms of logics for defeasible argumentation. Two notions turn out to be crucial, viz. argumentation schemes and empirical generalisations.

1Computer Science Institute, University of Leipzig 2Institute of Information and Computing Sciences, Utrecht University 3Institute of Information and Computing Sciences, Utrecht University

This article investigates the modelling of reasoning about evidence in legal procedure. To this end, a dialogue game model of the relevant parts of Dutch civil procedure is developed with three players: two adversaries and a judge. The model aims to be both legally realistic and technically well-founded. Legally, the main achievement is a more realistic account of the judge's role in legal procedures than that provided by current models. Technically, the model aims to preserve the features of an earlier-developed framework for two-player argumentative dialogue systems.

Case-based reasoning in HYPO'For simplicity we will in this paper assume, unlike HYPO, that all factors are twovalued, i.e. either true or false.

Tlis 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 nonrnonotonic 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.

This paper investigates how of legal language determine tack and defend argu rnents argumentation framework in the logical aspects possibilities to atin a dispute.An logic-programming style is presented which can cope with the hterplay between assumptions, applicability statements and reasoning about, preference relations between norms.The theory is given a solid semantic foundation, and can be used to formalise a wide range of realistic legal examples.

This paper investigates the relevance of the logical study of argumentation systems for AI-and-law research, in particular for modelling the adversarial aspect of legal reasoning. It does so in applying the argumentation framework of Prakken (1993a/b) to the legal domain. Three elements of the framework are particularly illustrated: firstly, its generality, in that it leaves room for any standard for comparing pairs of arguments; secondly, its ability to model the combined use of these standards; and finally, its relevance for modelling metalevel reasoning. These three features make the framework suitable as a logical framework for any theory of legal argument.

This paper presents a formal theory aibout prefem"ng the most specific argument.l%e theo~y is applied to legal reasoning and used to formulate requirements for legal knowledge-based systems choosing between alternative arguments.It is based on a proposal of Poole, but improves it in two respects: firstly, default Iog"c is shown to be a better underlying Io@"c for defensible reasoning than standard first-order lo~-c; and secondly, specificity is defined iteratively, in order to handle muhiple conflicts and to characterize the set of prefk?red knowledge.lle theory is an example of the fact that Io@"c can be a tool in legal reasoning even if deduction is not regarded as the right way to model it,