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.

Case-based reasoning (CBR) is central to legal practice, relying on precedents to interpret and apply the law. Various formalisms have been proposed to represent cases, including cases represented as situation-outcome pairs (situation-outcome cases) and cases represented as logical formulas (logical cases). Connections between situation-outcome cases and logical cases have been preliminary explored, but interoperability between CBR models of these representations remains underexamined. To address this gap, this paper introduces four formal tools: (1) compatibility, which concerns interpolating a logical case into multiple situation-outcome cases; (2) enumerators, which generalise compatibility by interpolating logical case models into valid situation-outcome cases; (3) prototypers, which relate logical case models to reflexive and consistent situation-outcome CBR models, as illustrated by AA-CBR and the result model of precedential constraint; and (4) translators, which attempting the reverse, namely connecting such situation-outcome CBR models back to logical case models. Our investigation of these tools reveal how implicit cases can be introduced to simulate or align with another CBR model’s reasoning, which contributes to interoperability between CBR models.

Tunnel vision and confirmation bias can lead to miscarriages of justice. A way to avoid tunnel vision is to consider your evidence in light of more than one scenario. Alternative scenarios allow us to consider how probable each scenario is, compared to the other considered scenarios. Bayesian Networks have been proposed as a formal method for reasoning about the probability of scenarios. Specifically, alternative scenarios were modelled using Bayesian networks with a constraint node, which ensures mutual exclusivity. However, the performance of these methods in situations where not all possible alternative scenarios are modeled, the non-exhaustive setting, has not been investigated. Since it is impossible to explicitly cover everything that could possibly have happened in a model, it is important to know how these methods handle non-exhaustiveness. We evaluate four methods using an agent-based model that simulates an environment in which a crime could occur. Taking this as the ground truth, we compare different Bayesian network modeling methods on five aspects related to the quality of the representation of the ground truth as well as computational performance. We find that some methods result in disparities between the ground truth and the predicted posterior probabilities for the scenarios in a non-exhaustive setting. In an exhaustive setting, the proposed methods perform well. The construction approach that models scenarios in terms of conjunctions of events performs well in both settings.

Generative large language models as tools in the legal domain have the potential to improve the justice system. However, the reasoning behavior of current generative models is brittle and poorly understood, hence cannot be responsibly applied in the domains of law and evidence. This paper presents reasoning benchmarks that are dynamically varied, scalable in their complexity, and have formally unambiguous interpretations. In this study, we illustrate the approach on the basis of witness testimony, focusing on the underlying argument attack structure. We dynamically generate both linear and non-linear argument attack graphs of varying complexity and translate these into reasoning puzzles about witness testimony expressed in natural language. We show that state-of-the-art large language models often fail in these reasoning puzzles, already at low complexity. Obvious mistakes are made by the models, and their inconsistent performance indicates that their reasoning capabilities are brittle. Furthermore, at higher complexity, even state-of-the-art models specifically designed for reasoning make mistakes. We show the viability of using a parametrized benchmark with varying complexity to evaluate the reasoning capabilities of generative language models, which contribute to a better understanding of the limitations of the reasoning capabilities of generative models.

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.

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.

Scenario-based Bayesian networks (BNs) have been proposed as a tool for the rational handling of evidence. The proper evaluation of existing methods requires access to a ground truth that can be used to test the quality and usefulness of a BN model of a crime. However, that would require a full probability distribution over all relevant variables used in the model, which is in practice not available. In this paper, we use an agent-based simulation as a proxy for the ground truth for the evaluation of BN models as tools for the rational handling of evidence. We use fictional crime scenarios as a background. First, we design manually constructed BNs using existing design methods in order to model example crime scenarios. Second, we build an agent-based simulation covering the scenarios of criminal and non-criminal behavior. Third, we algorithmically determine BNs using statistics collected experimentally from the agent-based simulation that represents the ground truth. Finally, we compare the manual, scenario-based BNs to the algorithmic BNs by comparing the posterior probability distribution over outcomes of the network to the ground-truth frequency distribution over those outcomes in the simulation, across all evidence valuations. We find that both manual BNs and algorithmic BNs perform similarly well: they are good reflections of the ground truth in most of the evidence valuations. Using ABMs as a ground truth can be a tool to investigate Bayesian Networks and their design methods, especially under circumstances that are implausible in real-life criminal cases, such as full probabilistic information.

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.

Local-HDP (Local Hierarchical Dirichlet Process) is a hierarchical Bayesian method recently used for open-ended 3D object category recognition. It has been proven to be efficient in real-time robotic applications. However, the method is not robust to a high degree of occlusion. We address this limitation in two steps. First, we propose a novel semantic 3D object-parts segmentation method that has the flexibility of Local-HDP. This method is shown to be suitable for open-ended scenarios where the number of 3D objects or object parts are not fixed and can grow over time. We show that the proposed method has a higher percentage of mean intersection over union, using a smaller number of learning instances. Second, we integrate this technique with a recently introduced argumentation-based online incremental learning method, enabling the model to handle a high degree of occlusion. We show that the resulting model produces explicit explanations for the 3D object category recognition task.

One way of reasoning with uncertainties in the context of law is to use probabilities. However, methods for reasoning about the probability of guilt in a court case requires us to specify a prior probability of guilt, which is the probability of guilt before any evidence is known. There is no accepted approach for specifying the prior probability of guilt but multiple solutions have been proposed. In this paper, we consider three approaches: a prior that is based on the population, a prior based on the number of agents that have similar opportunity as the suspect and a prior that represents a legal norm. For comparing and evaluating the approaches, we use an agent-based model as a ground truth in which all probabilities are known. With the data generated in the ground truth model, we investigate how the choice of prior influences the posterior probability of guilt for both guilty and innocent agents. Using a decision threshold, we can determine the effect of the three approaches on the rates of correct and incorrect convictions and acquittals. We find that the opportunity prior results in higher rates of both correct convictions and false convictions and requires more assumptions and access to data and knowledge than the legal prior and population prior.

Data-driven AI systems can make the right decisions for the wrong reasons, which can lead to irresponsible behavior. The rationale of such machine learning models can be evaluated and improved using a previously introduced hybrid method. This method, however, was tested using synthetic data under ideal circumstances, whereas labelled datasets in the legal domain are usually relatively small and often contain missing facts or inconsistencies. In this paper, we therefore investigate rationales under such imperfect conditions. We apply the hybrid method to machine learning models that are trained on court cases, generated from a structured representation of Article 6 of the ECHR, as designed by legal experts. We first evaluate the rationale of our models, and then improve it by creating tailored training datasets. We show that applying the rationale evaluation and improvement method can yield relevant improvements in terms of both performance and soundness of rationale, even under imperfect conditions.

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.

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexity of the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument.

Although argumentation is often studied in AI using abstract frameworks, actual debate often shows a dynamic interaction between argument structure and attack. Often intermediates steps in the reasoning are omitted, but it may be these intermediate steps which are the vulnerable parts of the argument. Inspired by Loui and Norman’s work on the rationale of arguments, we study the relation between argument structure and attack in terms of the unpacking of arguments. The paper provides an analysis of two kinds of rationales discussed by Loui and Norman. Example dialogues inspired by Dutch tort law are used for illustration.

Abstract In social interactions, people often reason about the beliefs, goals and intentions of others. Thistheory of mindallows them to interpret the behavior of others, and predict how they will behave in the future. People can also use this ability recursively: they usehigher-order theory of mindto reason about the theory of mind abilities of others, as in “he thinks that I don’t know that he sent me an anonymous letter”. Previous agent-based modeling research has shown that the usefulness of higher-order theory of mind reasoning can be useful across competitive, cooperative, and mixed-motive settings. In this paper, we cast a new light on these results by investigating how the predictability of the environment influences the effectiveness of higher-order theory of mind. Our results show that the benefit of (higher-order) theory of mind reasoning is strongly dependent on the predictability of the environment. We consider agent-based simulations in repeated one-shot negotiations in a particular negotiation setting known as Colored Trails. When this environment is highly predictable, agents obtain little benefit from theory of mind reasoning. However, if the environment has more observable features that change over time, agents without the ability to use theory of mind experience more difficulties predicting the behavior of others accurately. This in turn allows theory of mind agents to obtain higher scores in these more dynamic environments. These results suggest that the human-specific ability for higher-order theory of mind reasoning may have evolved to allow us to survive in more complex and unpredictable environments.

The environment around general-purpose service robots has a dynamic nature. Accordingly, even the robot’s programmer cannot predict all the possible external failures which the robot may confront. This research proposes an online incremental learning method that can be further used to autonomously handle external failures originating from a change in the environment. Existing research typically offers special-purpose solutions. Furthermore, the current incremental online learning algorithms cannot generalize well with just a few observations. In contrast, our method extracts a set of hypotheses, which can then be used for finding the best recovery behavior at each failure state. The proposed argumentation-based online incremental learning approach uses an abstract and bipolar argumentation framework to extract the most relevant hypotheses and model the defeasibility relation between them. This leads to a novel online incremental learning approach that overcomes the addressed problems and can be used in different domains including robotic applications. We have compared our proposed approach with state-of-the-art online incremental learning approaches, an approximation-based reinforcement learning method, and several online contextual bandit algorithms. The experimental results show that our approach learns more quickly with a lower number of observations and also has higher final precision than the other methods. Note to Practitioners—This work proposes an online incremental learning method that learns faster by using a lower number of failure states than other state-of-the-art approaches. The resulting technique also has higher final learning precision than other methods. Argumentation-based online incremental learning generates an explainable set of rules which can be further used for human-robot interaction. Moreover, testing the proposed method using a publicly available dataset suggests wider applicability of the proposed incremental learning method outside the robotics field wherever an online incremental learner is required. The limitation of the proposed method is that it aims for handling discrete feature values.

In AI and law, systems that are designed for decision support should be explainable when pursuing justice. In order for these systems to be fair and responsible, they should make correct decisions and make them using a sound and transparent rationale. In this paper, we introduce a knowledge-driven method for model-agnostic rationale evaluation using dedicated test cases, similar to unit-testing in professional software development. We apply this new quantitative human-in-the-loop method in a machine learning experiment aimed at extracting known knowledge structures from artificial datasets from a real-life legal setting. We show that our method allows us to analyze the rationale of black box machine learning systems by assessing which rationale elements are learned or not. Furthermore, we show that the rationale can be adjusted using tailor-made training data based on the results of the rationale evaluation.

Stare decisis is a fundamental principle of case-based reasoning. Yet its application varies in complexity and depends, in particular, on whether relevant past decisions agree, or exist at all. The contribution of this paper is a formal treatment of types of the hardness of case-based decisions. The typology of hardness is defined in terms of the arguments for and against the issue to be decided, and their kind of validity (conclusive, presumptive, coherent, incoherent). We apply the typology of hardness to Berman and Hafner's research on the dynamics of case-based reasoning and show formally how the hardness of decisions varies with time.

Human agents can acquire knowledge and learn through argumentation. Inspired by this fact, we propose a novel argumentation-based machine learning technique that can be used for online incremental learning scenarios. Existing methods for online incremental learning problems typically do not generalize well from just a few learning instances. Our previous argumentation-based online incremental learning method outperformed state-of-the-art methods in terms of accuracy and learning speed. However, it was neither memory-efficient nor computationally efficient since the algorithm used the power set of the feature values for updating the model. In this paper, we propose an accelerated version of the algorithm, with polynomial instead of exponential complexity, while achieving higher learning accuracy. The proposed method is at least 200 times faster than the original argumentation-based learning method and is more memory-efficient.

The justification of an algorithm’s outcomes is important in many domains, and in particular in the law. However, previous research has shown that machine learning systems can make the right decisions for the wrong reasons: despite high accuracies, not all of the conditions that define the domain of the training data are learned. In this study, we investigate what the system does learn, using state-of-the-art explainable AI techniques. With the use of SHAP and LIME, we are able to show which features impact the decision making process and how the impact changes with different distributions of the training data. However, our results also show that even high accuracy and good relevant feature detection are no guarantee for a sound rationale. Hence these state-of-the-art explainable AI techniques cannot be used to fully expose unsound rationales, further advocating the need for a separate method for rationale evaluation.

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria that have been used to settle the acceptance of arguments are called semantics. However, the notion of semi-stable semantics as studied for abstract argumentation frameworks has received little attention for ADFs. In the current work, we present the concepts of semi-two-valued models and semi-stable models for ADFs. We show that these two notions satisfy a set of plausible properties required for semi-stable semantics of ADFs. Moreover, we show that semi-two-valued and semi-stable semantics of ADFs form a proper generalization of the semi-stable semantics of AFs, just like two-valued model and stable semantics for ADFs are generalizations of stable semantics for AFs.

Abstract dialectical frameworks (ADFs) have been introduced as formalism for the modeling and evaluating argumentation. However, the role of discussion in evaluating of arguments in ADFs has not been clarified well so far. We focus on the grounded semantics of ADFs and provide the grounded discussion game. We show that an argument is acceptable (deniable) in the grounded interpretation of an ADF without any redundant links if and only if the proponent of a claim has a winning strategy in the grounded discussion game.

Formalizing case-based reasoning is an important topic in AI and Law, which has been discussed using various approaches, such as formal dialogue games, abstract dialectical frameworks.In this paper we model case-based reasoning by using the formal argument semantics of case models.With the precedent models we present, the validity of legal arguments in the case-based reasoning process can be shown formally.We also present a case study of precedent models in a real legal domain and evaluate the validity of arguments in case-based reasoning.

We outline a formalization of precedent comparison in the precedent model formalism.

Reasoning with evidence is error prone, especially when qualitative and quantitative evidence is combined, as shown by infamous miscarriages of justice, such as the Lucia de Berk case in the Netherlands. Methods for the rational analysis of evidential reasoning come in different kinds, often with arguments, scenarios and probabilities as primitives. Recently various combinations of argumentative, narrative and probabilistic methods have been investigated. By the complexity and subtlety of the subject matter, it has proven hard to assess the specific strengths and points of attention of different methods. Comparative case studies have only recently started, and never by one team. In this paper, we provide an analysis of a single case in order to compare the relative merits of two methods recently proposed in AI and Law: a method using Bayesian networks with embedded scenarios, and a method using case models that provide a formal analysis of argument validity. To optimise the transparency of the two analyses, we have selected a case about which the final decision is undisputed. The two analyses allow us to provide a comparative evaluation showing strengths and weaknesses of the two methods. We find a core of evidential reasoning that is shared between the methods.

One puzzle studied in AI & Law is how arguments, rules and cases are formally connected. Recently a formal theory was proposed formalizing how the validity of arguments based on rules can be grounded in cases. Three kinds of argument validity were distinguished: coherence, presumptive validity and conclusiveness. In this paper the theory is implemented in a Prolog program, used to evaluate a previously developed model of Dutch tort law. We also test the theory and its implementation with a new case study modeling Chinese copyright infringement law. In this way we illustrate that by the use of the implementation the process of modeling becomes more efficient and less error-prone.

Legal argument is typically backed by two kinds of sources: cases and rules. In much AI & Law research, the formalization of arguments, rules and cases has been investigated. In this paper, the tight formal connections between the three are developed further, in an attempt to show that cases can provide the logical basis for establishing which rules and arguments hold in a domain. We use the recently proposed formalism of case models, that has been applied previously to evidential reasoning and ethical systems design. In the present paper, we discuss with respect to case-based modeling how the analogy and distinction between cases can be modeled, and how arguments can be grounded in cases. With respect to rule-based modeling, we discuss conditionality, generality and chaining. With respect to argument-based modeling, we discuss rebutting, undercutting and undermining attack. We evaluate the approach by developing a case model of the rule-based arguments and attacks in Dutch tort law. In this way, we illustrate how statutory, rule-based law from the civil law tradition can be formalized in terms of cases.

Theory of mind refers to the ability to reason explicitly about unobservable mental content of others, such as beliefs, goals, and intentions. People often use this ability to understand the behavior of others as well as to predict future behavior. People even take this ability a step further, and use higher-order theory of mind by reasoning about the way others make use of theory of mind and in turn attribute mental states to different agents. One of the possible explanations for the emergence of the cognitively demanding ability of higher-order theory of mind suggests that it is needed to deal with mixed-motive situations. Such mixed-motive situations involve partially overlapping goals, so that both cooperation and competition play a role. In this paper, we consider a particular mixed-motive situation known as Colored Trails, in which computational agents negotiate using alternating offers with incomplete information about the preferences of their trading partner. In this setting, we determine to what extent higher-order theory of mind is beneficial to computational agents. Our results show limited effectiveness of first-order theory of mind, while second-order theory of mind turns out to benefit agents greatly by allowing them to reason about the way they can communicate their interests. Additionally, we let human participants negotiate with computational agents of different orders of theory of mind. These experiments show that people spontaneously make use of second-order theory of mind in negotiations when their trading partner is capable of second-order theory of mind as well.

Today's AI applications are so successful that they inspire renewed concerns about AI systems becoming ever more powerful. Addressing these concerns requires AI systems that are designed as ethical systems, in the sense that their choices are context-dependent, value-guided and rule-following. It is shown how techniques connecting qualitative and quantitative primitives recently developed for evidential argumentation in the law can be used for the design of such ethical systems. In this way, AI and Law techniques are extended to the theoretical understanding of intelligent systems guided by embedded values.

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.

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

Pollock's concepts of reasons and defeaters have been widely adopted, but his anti-probabilistic treatment of argument strength less so. After an explanation of how Pollock's concerns can be addressed probabilistically, the paper continues with a formal treatment of reasons, defeaters, and argument strength, while remaining within standard probability theory and its underlying classical logic. Pollock studied puzzles about self-defeat and collective defeat (associated with the lottery paradox), and it is shown how these can be addressed probabilistically. A normative framework for arguments and their strength, as provided here, is needed for the development of rationality support tools for the prevention of reasoning errors.

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.

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.

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.

In this paper, we continue our research on a hybrid narrative-argumentative approach to evidential reasoning in the law by showing the interaction between factual reasoning and legal reasoning. We therefore emphasize the role of legal story schemes (as opposed to factual story schemes that formed the heart of our previous proposal). Legal story schemes steer what needs to be proven, but are also selected on the basis of what can be proven. They provide a coherent, holistic legal perspective on a criminal case that steers investigation and decision making. We present an extension of our previously proposed hybrid theory of reasoning with evidence, by making the connection with reasoning towards legal consequences. We discuss the phenomenon of legal shifts that shows that the step from evidence to (proven) facts cannot be isolated from the step from proven facts to legal consequences. We show how legal shifts can be modelled in terms of legal story schemes. Our model is illustrated by a discussion of the Dutch Wamel murder case.

When reasoning about the facts of a case, we typically use stories to link the known events into coherent wholes. One way to establish coherence is to appeal to past examples, real or fictitious. These examples can be chosen and critiqued using the case-based reasoning (CBR) techniques from the AI and Law literature. In this paper, we apply these techniques to factual stories, assessing a story about the facts using precedents. We thus show how factual and legal reasoning can be combined in a CBR model.

Models of argumentation often take a given set of rules or conditionals as a starting point. Arguments to support or attack a position are then built from these rules. In this paper, an attempt is made to develop constraints on rules and their exceptions in such a way that they correspond exactly to arguments that successfully support their conclusions. The constraints take the form of properties of nonmonotonic consequence relations, similar to the ones that have been studied for cumulative inference.

Current argumentation support software often employs graphical representations of logical relationships. Little is known about the extent to which logical structuring helps to increase a user's task performance. In this research, various levels of graphical representation of the logical structure of legal subject matter are experimentally compared in terms of performance. It is shown that logical structuring significantly increases task performance, but we have found no evidence that the extensive representation of logical structure as employed by several contemporary software applications is more effective or usable than a simplified graphical representation that was previously implemented in an application called ArguGuide.

The two main types of law are legislation and precedents. Both types have a corresponding reasoning pattern determining legal consequences: legislation can be applied and precedents followed. The separate modelling of these two reasoning patterns using logical techniques has recently seen considerable progress. About the logical links between the two less is known, although progress has already been made. This document focuses on such logical relations. The main question is: to what extent can the application of legislation and precedent adherence be considered as two sides of the same logical coin? Findings from the boundaries of logic and law will serve as a starting point.This text is a translated, adapted and extended version of Verheij 2007.

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.

Assumptions are often not considered to be definitely true, but only as prima facie justified. When an assumption is prima facie justified, there can for instance be a reason against it, by which the assumption is not actually justified. The assumption is then said to be defeated. This requires a revision of the standard conception of logical interpretation of sets of assumptions in terms of their models. Whereas in the models of a set of assumptions, all assumptions are taken to be true, an interpretation of prima facie justified assumptions must distinguish between the assumptions that are actually justified in the interpretation and those that are defeated. In the present paper, the logical interpretation of prima facie justified assumptions is investigated. The central notion is that of a dialectical interpretation of a set of assumptions. The basic idea is that a prima facie justified assumption is not actually justified, but defeated when its so-called dialectical negation is justified. The properties of dialectical interpretation are analysed by considering partial dialectical interpretations, or stages, and by establishing the notion of dialectical justification. The latter leads to a characterization of the existence and multiplicity of the dialectical interpretations of a set of assumptions. Since dialectical interpretations are a variant of stable semantics, the results are relevant for existing work on nonmonotonic logic and defeasible reasoning, on which the present work builds. Instead of focusing on defeasible rules or arguments, the present approach is sentence-based. A particular innovation is the use of a conditional that is prima facie justified (just like other assumptions) instead of an inconclusive conditional.

No abstract available.

In recent years, impressive progress has been made in the development of logical tools for the modeling of legal argument. The focus has been primarily on the technical development of these tools, and only in the second place on their practical adequacy for modeling legal argument. Presently a convergence of opinions on the necessary logical tools takes shape, and a systematic practical assessment of the logical tools becomes essential. It has to be shown that the newly developed logical tools improve the logical modeling of legal argument. In this paper we analyze aspects of informal legal arguments as they actually occur in handbooks and cases on Dutch tort law, and show the connections with the modern logical tools. Proceedings of the sixth International Conference on Artificial Intelligence and Law, ACM, New York, pp. 243-249.