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In the original publication, some of the references were published twice by mistake. Now it has been corrected in the original publication.

First Online: 05 March 2019 Disputes over causes play a central role in legal argumentation and liability attribution. Legal approaches to causation often struggle to capture cause-in-fact in complex situations, e.g. overdetermination, preemption, omission. In this paper, we first assess three current theories of causation (but-for, NESS, ‘actual causation’) to illustrate their strengths and weaknesses in capturing cause-in-fact. Secondly, we introduce a semi-formal framework for modelling causal arguments through strict and defeasible rules. Thirdly, the framework is applied to the Althen vaccine injury case. And lastly, we discuss the need for new criteria based on a common causal argumentation framework and propose ideas on how to integrate the current theories of causation to assess the strength of causal arguments, while also acknowledging the tension between evidence-based and policy-based causal analysis in law.

First Online: 22 March 2016 This paper proposes an argumentation-based procedure for legal interpretation, by reinterpreting the traditional canons of textual interpretation in terms of argumentation schemes, which are then classified, formalized, and represented through argument visualization and evaluation tools. The problem of statutory interpretation is framed as one of weighing contested interpretations as pro and con arguments. The paper builds an interpretation procedure by formulating a set of argumentation schemes that can be used to comparatively evaluate the types of arguments used in cases of contested statutory interpretation in law. A simplified version of the Carneades Argumentation System is applied in a case analysis showing how the procedure works. A logical model for statutory interpretation is finally presented, covering pro-tanto and all-things-considered interpretive conclusions.

Are we satisfied with current approaches to the study of norms? Unfortunately not, as a number of questions are still open. First, a major dichotomy can be observed in the scientific treatment of norms. Theories of norms are grounded on two, unrelated notions, regularities and prescriptions. On the one hand, social scientists view norms as regularities of behaviour, supported by social expectations and possibly enforced through sanctions. On the other hand, philosophers of law and logicians focus on norms as prescriptions issued by definite authorities and enforced though institutional sanctions. Hence, a first set of questions pertaining to the connection between social norms and institutionalised laws comes forth. How can we distinguish normative behaviour (both social and legal) from normal conduct on the one hand and acquiescence under menace on the other? What are commonalities and differences between social conventions and institutional prescriptions? Regularities, or behavioural norms, are spontaneously emerging social phenomena, while, institutional prescriptions, are deliberately issued commands. Behavioural norms are often found either in the moral variant, as good or pro-social conduct, or in the statistical variant, as frequent, normal behaviours, while institutional prescriptions tend to collapse into legal norms, issued by specified authorities. Despite these differences it seems to us that the present gap between theories of social and institutional norms is neither desirable nor inevitable: social and institutional norms should be viewed as complementary phenomena, to be integrated in a common theoretical framework.

We provide a logical analysis of private international law, a rather esoteric, but increasingly important, domain of the law. Private international law addresses overlaps and conflicts between legal systems by distributing cases between the authorities of such systems (jurisdiction) and establishing what rules these authorities have to apply to each case (choice of law). A formal model of the resulting interactions between legal systems is proposed based on modular argumentation. It is argued that this model may also be useful for governing the interactions between heterogeneous agents, belonging to different and differently regulated virtual societies, without recourse to a central regulatory agency. The model also provides for multiple interpretations concerning rules of private international law as well as substantive rules of the different legal systems.

I shall argue that software agents can be attributed cognitive states, since their behaviour can be best understood by adopting the intentional stance. These cognitive states are legally relevant when agents are delegated by their users to engage, without users’ review, in choices based on their the agents’ own knowledge. Consequently, both with regard to torts and to contracts, legal rules designed for humans can also be applied to software agents, even though the latter do not have rights and duties of their own. The implications of this approach in different areas of the law are then discussed, in particular with regard to contracts, torts, and personality.

We shall introduce a set of fundamental legal concepts, providing a definition of each of them. This set will include, besides the usual deontic modalities (obligation, prohibition and permission), the following notions: obligative rights (rights related to others' obligations), permissive rights, erga-omnes rights, normative conditionals, liability rights, different kinds of legal powers, potestative rights (rights to produce legal results), resultive declarations (acts intended to produce legal determinations), and sources of the law.

In this paper we provide a formal analysis of the idea of normative co-ordination. We argue that this idea is based on the assumption that agents can achieve flexible co-ordination by conferring normative positions to other agents. These positions include duties, permissions, and powers. In particular, we explain the idea of declarative power, which consists in the capacity of the power-holder of creating normative positions, involving other agents, simply by "proclaiming" such positions. In addition, we account also for the concepts of representation, namely the representative's capacity of acting in the name of his principal, and of mandate, which is the mandatee's duty to act as the mandator has requested. Finally, we show how the framework can be applied to represent the contract-net protocol. Some brief remarks on future research and applications conclude this contribution.

This paper proposes to model legal reasoning asdialectical theory-constructiondirected by teleology. Precedents are viewed asevidence to be explained throughtheories. So, given a background of factors andvalues, the parties in a case canbuild their theories by using a set of operators,which are called theory constructors.The objective of each party is to provide theoriesthat both explain the evidence (theprecedents) and support the decision wished by thatparty. This leads to theory-basedargumentation, i.e., a dialectical exchange ofcompeting theories, which support opposedoutcomes by explaining the same evidence and appealingto the same values. The winneris the party that can reply with a more coherent theoryto all theories of its adversary.

Computational approaches to the law have frequently been characterized as being formalistic implementations of the syllogistic model of legal cognition: using insufficient or contradictory data, making analogies, learning through examples and experiences, applying vague and imprecise standards. We argue that, on the contrary, studies on neural networks and fuzzy reasoning show how AI & law research can go beyond syllogism, and, in doing that, can provide substantial contributions to the law.

This paper proposes an approach to investigate norm-governed learning agents which combines a logic-based formalism with an equation-based counterpart. This dual formalism enables us to describe the reasoning of such agents and their interactions using argumentation, and, at the same time, to capture systemic features using equations. The approach is applied to norm emergence and internalisation in systems of learning agents. The logical formalism is rooted into a probabilistic defeasible logic instantiating Dung’s argumentation framework. Rules of this logic are attached with probabilities to describe the agents’ minds and behaviours as well as uncertain environments. Then, the equation-based model for reinforcement learning, defined over this probability distribution, allows agents to adapt to their environment and self-organise.

This article proposes a formal analysis of a fundamental aspect of legal reasoning: dealing with normative conflicts. Firstly, examples are illustrated concerning the dynamics of legal systems, the application of rules and exceptions, and the semantic indeterminacy of legal sources. Then two approaches to cope with conflicting information are presented: the preferred theories of Brewka, and the belief change functions of Alchourron, Gardenfors, and Makinson. The relations between those approaches are closely examined, and some aspects of a model of reasoning with normative conflicts are outlined. Since this model takes into account an ordering of the involved regulations, criteria to order legal norms are finally specified.