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Summary "Formalism about Legal Reasoning" refers to the use of (often logic-based) formalisms to shed light on legal reasoning.  "Formal Models of Legal Reasoning," in contrast refers to the use of such formalisms to model actual legal reasoning.   Some works fit into both categories.  The former is also apt for discussions of the limits of the latter.  Both categories apply best to modeling or shedding light on judicial reasoning, or on the analysis of legal texts (be they statutes, constitutions [written or not], regulations, or exegeses of these), but are  less applicable to modeling or shedding light on the legislative or regulatory processes which produce these.
Key works As the key works, the debate between Haack 2007 and Bulygin 2008 is most interesting, and a good starting point on the limits if any of formal modeling of law.  See also Deleted forthcoming.
Introductions Hage et al 1993 is an excellent book-length article introducing the subject in great depth; it discusses the difficulties and the subtleties involved, reflected in the large number of classifications given the monograph.
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  1. Carlos E. Alchourron (1996). On Law and Logic. Ratio Juris 9 (4):331-348.
  2. Carlos E. Alchourron & Antonio A. Martino (1990). Logic Without Truth. Ratio Juris 3 (1):46-67.
  3. Lennart Åqvist (2007). An Interpretation of Probability in the Law of Evidence Based on Pro-Et-Contra Argumentation. Artificial Intelligence and Law 15 (4):391-410.
    The purpose of this paper is to improve on the logical and measure-theoretic foundations for the notion of probability in the law of evidence, which were given in my contributions Åqvist [ (1990) Logical analysis of epistemic modality: an explication of the Bolding–Ekelöf degrees of evidential strength. In: Klami HT (ed) Rätt och Sanning (Law and Truth. A symposium on legal proof-theory in Uppsala May 1989). Iustus Förlag, Uppsala, pp 43–54; (1992) Towards a logical theory of legal evidence: semantic analysis (...)
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  4. Trevor Bench-Capon (1997). Argument in Artificial Intelligence and Law. Artificial Intelligence and Law 5 (4):249-261.
    In this paper I shall discuss the notion of argument, and the importanceof argument in AI and Law. I shall distinguish four areas where argument hasbeen applied: in modelling legal reasoning based on cases; in thepresentation and explanation of results from a rule based legal informationsystem; in the resolution of normative conflict and problems ofnon-monotonicity; and as a basis for dialogue games to support the modellingof the process of argument. The study of argument is held to offer prospectsof real progress (...)
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  5. Trevor J. M. Bench-Capon (2003). Try to See It My Way: Modelling Persuasion in Legal Discourse. [REVIEW] Artificial Intelligence and Law 11 (4):271-287.
    In this paper I argue that to explain and resolve some kinds of disagreement we need to go beyond what logic alone can provide. In particular, following Perelman, I argue that we need to consider how arguments are ascribed different strengths by different audiences, according to how accepting these arguments promotes values favoured by the audience to which they are addressed. I show how we can extend the standard framework for modelling argumentation systems to allow different audiences to be represented. (...)
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  6. Gustav Bergmann & Lewis Zerby (1945). The Formalism in Kelsen's Pure Theory of Law. Ethics 55 (2):110-130.
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  7. Donald H. Berman & Carole D. Hafner (1988). Obstacles to the Development of Logic-Based Models of Legal Reasoning. In Charles Walter (ed.), Computer power and legal language: The use of computational models in linguistics, artificial intelligence, and expert systems in the law. Quorum Books.
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  8. Daniéle Bourcier & Gérard Clergue (1999). From a Rule-Based Conception to Dynamic Patterns. Analyzing the Self-Organization of Legal Systems. Artificial Intelligence and Law 7 (2-3):211-225.
    The representation of knowledge in the law has basically followed a rule-based logical-symbolic paradigm. This paper aims to show how the modeling of legal knowledge can be re-examined using connectionist models, from the perspective of the theory of the dynamics of unstable systems and chaos. We begin by showing the nature of the paradigm shift from a rule-based approach to one based on dynamic structures and by discussing how this would translate into the field of theory of law. In order (...)
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  9. Michael Clark (1997). Review of P. Wahlgren, Automation of Legal Reasoning. [REVIEW] Information and Communications Technology Law 6.
  10. Joseph S. Fulda (2012). Implications of a Logical Paradox for Computer-Dispensed Justice Reconsidered: Some Key Differences Between Minds and Machines. [REVIEW] Artificial Intelligence and Law 20 (3):321-333.
    We argued [Since this argument appeared in other journals, I am reprising it here, almost verbatim.] (Fulda in J Law Info Sci 2:230–232, 1991/AI & Soc 8(4):357–359, 1994) that the paradox of the preface suggests a reason why machines cannot, will not, and should not be allowed to judge criminal cases. The argument merely shows that they cannot now and will not soon or easily be so allowed. The author, in fact, now believes that when—and only when—they are ready they (...)
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  11. Joseph S. Fulda (1999). Can One Really Reason About Laws? Computers and Society 29 (2):31.
    This is a review article of Tokuyasu Kakuta, Makoto Haraguchi, and Yoshiaki Okubo, "A Goal-Dependent Abstraction for Legal Reasoning by Analogy," /Artificial Intelligence and Law/ 5(March 1997): 97-118.
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  12. Susan Haack (2007). On Logic in the Law: "Something, but Not All". Ratio Juris 20 (1):1-31.
    In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...)
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  13. Jaap Hage (2000). Dialectical Models in Artificial Intelligence and Law. Artificial Intelligence and Law 8 (2-3):137-172.
    Dialogues and dialectics have come to playan important role in the field of ArtificialIntelligence and Law. This paper describes thelegal-theoretical and logical background of this role,and discusses the different services into whichdialogues are put. These services include:characterising logical operators, modelling thedefeasibility of legal reasoning, providing the basisfor legal justification and identifying legal issues,and establishing the law in concrete cases. Specialattention is given to the requirements oflaw-establishing dialogues.
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  14. Jaap Hage (1996). A Theory of Legal Reasoning and a Logic to Match. Artificial Intelligence and Law 4 (3-4):199-273.
    This paper describes a model of legal reasoning and a logic for reasoning with rules, principles and goals that is especially suited to this model of legal reasoning. The paper consists of three parts. The first part describes a model of legal reasoning based on a two-layered view of the law. The first layer consists of principles and goals that express fundamental ideas of a legal system. The second layer contains legal rules which in a sense summarise the outcome of (...)
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  15. Jaap C. Hage, Ronald Leenes & Arno R. Lodder (1993). Hard Cases: A Procedural Approach. [REVIEW] Artificial Intelligence and Law 2 (2):113-167.
    Much work on legal knowledge systems treats legal reasoning as arguments that lead from a description of the law and the facts of a case, to the legal conclusion for the case. The reasoning steps of the inference engine parallel the logical steps by means of which the legal conclusion is derived from the factual and legal premises. In short, the relation between the input and the output of a legal inference engine is a logical one. The truth of the (...)
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  16. Andreas Hamfelt (1995). Formalizing Multiple Interpretation of Legal Knowledge. Artificial Intelligence and Law 3 (4):221-265.
    A representation methodology for knowledge allowing multiple interpretations is described. It is based on the following conception of legal knowledge and its open texture. Since indeterminate, legal knowledge must be adapted to fit the circumstances of the cases to which it is applied. Whether a certain adaptation is lawful or not is measured by metaknowledge. But as this too is indeterminate, its adaptation to the case must be measured by metametaknowledge, etc. This hierarchical model of law is quite well-established and (...)
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  17. John F. Horty (2001). Argument Construction and Reinstatement in Logics for Defeasible Reasoning. Artificial Intelligence and Law 9 (1):1-28.
    This paper points out some problems with two recent logical systems – one due to Prakken and Sartor, the other due to Kowalski and Toni – designedfor the representation of defeasible arguments in general, but with a specialemphasis on legal reasoning.
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  18. Dan Hunter (1999). Out of Their Minds: Legal Theory in Neural Networks. [REVIEW] Artificial Intelligence and Law 7 (2-3):129-151.
    This paper examines the use of connectionism (neural networks) in modelling legal reasoning. I discuss how the implementations of neural networks have failed to account for legal theoretical perspectives on adjudication. I criticise the use of neural networks in law, not because connectionism is inherently unsuitable in law, but rather because it has been done so poorly to date. The paper reviews a number of legal theories which provide a grounding for the use of neural networks in law. It then (...)
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  19. Andrew J. I. Jones (1990). Deontic Logic and Legal Knowledge Representation. Ratio Juris 3 (2):237-244.
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  20. Andrew J. I. Jones & Xavier Parent (2008). Normative-Informational Positions: A Modal-Logical Approach. [REVIEW] Artificial Intelligence and Law 16 (1):7-23.
    This paper is a preliminary investigation into the application of the formal-logical theory of normative positions to the characterisation of normative-informational positions, pertaining to rules that are meant to regulate the supply of information. First, we present the proposed framework. Next, we identify the kinds of nuances and distinctions that can be articulated in such a logical framework. Finally, we show how such nuances can arise in specific regulations. Reference is made to Data Protection Law and Contract Law, among others. (...)
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  21. Andrew J. I. Jones & Marek Sergot (1992). Deontic Logic in the Representation of Law: Towards a Methodology. [REVIEW] Artificial Intelligence and Law 1 (1):45-64.
    There seems to be no clear consensus in the existing literature about the role of deontic logic in legal knowledge representation — in large part, we argue, because of an apparent misunderstanding of what deontic logic is, and a misplaced preoccupation with the surface formulation of legislative texts. Our aim in this paper is to indicate, first, which aspects of legal reasoning are addressed by deontic logic, and then to sketch out the beginnings of a methodology for its use in (...)
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  22. Harm Kloosterhuis (2000). Analogy Argumentation in Law: A Dialectical Perspective. [REVIEW] Artificial Intelligence and Law 8 (2-3):173-187.
    In this paper I investigate the similarities betweenthe dialectical procedure in the pragma-dialecticaltheory and dialectical procedures in AI and Law. I dothis by focusing on one specific type of reasoning inlaw: analogy argumentation. I will argue that analogyargumentation is not only a heuristic forfinding new premises, but also a part of thejustification of legal decisions. The relevantcriteria for the evaluation of analogy argumentationare not to be found at the logical level of inference,but at the procedural level of the discussion. I (...)
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  23. Robert A. Kowalski & Francesca Toni (1996). Abstract Argumentation. Artificial Intelligence and Law 4 (3-4):275-296.
    In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasibility of rules is expressed by means of non-provability claims as additional conditions of the rules.We outline an abstract approach to defeasible reasoning and argumentation which includes many existing formalisms, including default (...)
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  24. Robert Kowalski & Marek Sergot (1990). The Use of Logical Models in Legal Problem Solving. Ratio Juris 3 (2):201-218.
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  25. Jody S. Kraus, Transparency and Determinacy in Common Law Adjudication: A Philosophical Defense of Explanatory Economic Analysis.
    Explanatory economic analysis of the common law has long been subject to deep philosophical skepticism for two reasons. First, common law decisions appear to be cast in the language of deontic morality, not the consequentialist language of efficiency. For this reason, philosophers have claimed that explanatory economic analysis cannot satisfy the transparency criterion, which holds that a legal theory's explanation must provide a plausible account of the relationship between the reasoning it claims judges actually use to decide cases and the (...)
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  26. Jacky Legrand (1999). Some Guidelines for Fuzzy Sets Application in Legal Reasoning. Artificial Intelligence and Law 7 (2-3):235-257.
    As an introduction to our work, we emphasize the parallel interpretation of abstract tools and the concepts of undetermined and vague information. Imprecision, uncertainty and their relationships are inspected. Suitable interpretations of the fuzzy sets theory are applied to legal phenomena in an attempt to clearly circumscribe the possible applications of the theory. The fundamental notion of reference sets is examined in detail, hence highlighting their importance. A systematic and combinatorial classification of the relevant subsets of the legal field is (...)
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  27. Arno R. Lodder (2004). Law, Logic, Rhetoric: A Procedural Model of Legal Argumentation. In. In S. Rahman (ed.), Logic, Epistemology, and the Unity of Science. Dordrecht, Kluwer. 569--588.
  28. Fabrizio Macagno & Douglas Walton (2012). Presumptions in Legal Argumentation. Ratio Juris 25 (3):271-300.
    In this paper a theoretical definition that helps to explain how the logical structure of legal presumptions is constructed by applying the Carneades model of argumentation developed in artificial intelligence. Using this model, it is shown how presumptions work as devices used in evidentiary reasoning in law in the event of a lack of evidence to assist a chain of reasoning to move forward to prove or disprove a claim. It is shown how presumptions work as practical devices that may (...)
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  29. John Mikhail (2009). Moral Grammar and Intuitive Jurisprudence: A Formal Model of Unconscious Moral and Legal Knowledge. In B. H. Ross, D. M. Bartels, C. W. Bauman, L. J. Skitka & D. L. Medin (eds.), Psychology of Learning and Motivation, Vol. 50: Moral Judgment and Decision Making. Academic Press.
    Could a computer be programmed to make moral judgments about cases of intentional harm and unreasonable risk that match those judgments people already make intuitively? If the human moral sense is an unconscious computational mechanism of some sort, as many cognitive scientists have suggested, then the answer should be yes. So too if the search for reflective equilibrium is a sound enterprise, since achieving this state of affairs requires demarcating a set of considered judgments, stating them as explanandum sentences, and (...)
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  30. María G. Navarro (2011). Critical Notice of 'Fundamentos de la Argumentación Jurídica: Revisión de Las Teorías Sobre la Justificación de Las Decisiones Judiciales' by Evelin Feteris. [REVIEW] Ideas y Valores 60 (145):155-163.
    La misma serie editorial en la que aparecieron obras de Robert Walter, Hasso Höfman, Arthur Kaufmann o Robert Alexy ofrece ahora a los lectores interesados por el mundo de la argumentación jurídica una esmerada traducción de la obra de Eveline T. Feteris, Fundamentals of Legal Argumentation, editada por Kluwer Academic en 1999. En los doce capítulos que componen esta obra, Feteris consigue mostrar de manera a un tiempo sustantiva y concisa los problemas teóricos más importantes de las distintas tradiciones que (...)
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  31. María G. Navarro (2010). Dudas Razonables, Sesgos Cognitivos y Emociones En la Argumentación Jurídica. Bajo Palabra. Revista de Filosofía 5:203-214.
    Concepts as reasonable doubt, cognitive biases and emotions are now a theoretical problem for the practice of law, and the law understood as legal argumentation. From a theoretical point of view, the screenplay written by Reginald Rose, Twelve Angry Men, is an outstanding example to analyze some of these concepts, and its influence on procedural stage. Cognitive biases and informal fallacies are theoretical challenge to legal argumentation.
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  32. Aleksander Peczenik (1996). Jumps and Logic in the Law. Artificial Intelligence and Law 4 (3-4):297-329.
    The main stream of legal theory tends to incorporate unwritten principles into the law. Weighing of principles plays a great role in legal argumentation, inter alia in statutory interpretation. A weighing and balancing of principles and other prima facie reasons is a jump. The inference is not conclusive.To deal with defeasibility and weighing, a jurist needs both the belief-revision logic and the nonmonotonic logic. The systems of nonmonotonic logic included in the present volume provide logical tools enabling one to speak (...)
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  33. H. Prakken & G. Sartor (1996). A Dialectical Model of Assessing Conflicting Arguments in Legal Reasoning. Artificial Intelligence and Law 4 (3-4):331-368.
    Inspired by legal reasoning, this paper presents a formal framework for assessing conflicting arguments. Its use is illustrated with applications to realistic legal examples, and the potential for implementation is discussed. The framework has the form of a logical system for defeasible argumentation. Its language, which is of a logic-programming-like nature, has both weak and explicit negation, and conflicts between arguments are decided with the help of priorities on the rules. An important feature of the system is that these priorities (...)
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  34. Henry Prakken (2012). Reconstructing Popov V. Hayashi in a Framework for Argumentation with Structured Arguments and Dungean Semantics. Artificial Intelligence and Law 20 (1):57-82.
    In this article the argumentation structure of the court’s decision in the Popov v. Hayashi case is formalised in Prakken’s (Argument Comput 1:93–124; 2010) abstract framework for argument-based inference with structured arguments. In this framework, arguments are inference trees formed by applying two kinds of inference rules, strict and defeasible rules. Arguments can be attacked in three ways: attacking a premise, attacking a conclusion and attacking an inference. To resolve such conflicts, preferences may be used, which leads to three corresponding (...)
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  35. Henry Prakken (2010). Using Argument Schemes for Hypothetical Reasoning in Law. Artificial Intelligence and Law 18 (2):153-174.
    This paper studies the use of hypothetical and value-based reasoning in US Supreme-Court cases concerning the United States Fourth Amendment. Drawing upon formal AI & Law models of legal argument a semi-formal reconstruction is given of parts of the Carney case, which has been studied previously in AI & law research on case-based reasoning. As part of the reconstruction, a semi-formal proposal is made for extending the formal AI & Law models with forms of metalevel reasoning in several argument schemes. (...)
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  36. Henry Prakken (2001). Modelling Defeasibility in Law: Logic or Procedure? Fundamenta Informaticae 48 (2-3):253-271.
  37. Ron A. Shapira (1999). Fuzzy Measurement in the Mishnah and the Talmud. Artificial Intelligence and Law 7 (2-3):273-288.
    I discuss the attitude of Jewish law sources from the 2nd–:5th centuries to the imprecision of measurement. I review a problem that the Talmud refers to, somewhat obscurely, as impossible reduction. This problem arises when a legal rule specifies an object by referring to a maximized (or minimized) measurement function, e.g., when a rule applies to the largest part of a divided whole, or to the first incidence that occurs, etc. A problem that is often mentioned is whether there might (...)
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  38. Jan-R. Sieckmann (2003). Why Non-Monotonic Logic is Inadequate to Represent Balancing Arguments. Artificial Intelligence and Law 11 (2-3):211-219.
    This paper analyses the logical structure of the balancing of conflicting normative arguments, and asks whether non-monotonic logic is adequate to represent this type of legal or practical reasoning. Norm conflicts are often regarded as a field of application for non-monotonic logics. This paper argues, however, that the balancing of normative arguments consists of an act of judgement, not a logical inference, and that models of deductive as well as of defeasible reasoning do not give an adequate account of its (...)
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  39. Arend Soeteman (2003). Legal Logic? Or Can We Do Without? Artificial Intelligence and Law 11 (2-3):197-210.
    In this paper the thesis is argued that there is no need for a special legal logic to deal with the defeasibility of legal arguments. An important argument for this thesis is that legal judgements ask for a complete justification and that such a complete justification requires a deductively valid argument.
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  40. Lawrence B. Solum (1987). On the Indeterminacy Crisis: Critiquing Critical Dogma. University of Chicago Law Review 54:462.
    This essay investigates the indeterminacy thesis - roughly the claim that the content of authoritative legal materials (such as the texts of constitutions, statutes, cases, rules, and regulations) does not determine the outcome of particular legal disputes. The indeterminacy thesis can be formulated as either "strong" or weak." The strong version of the indeterminacy thesis is demonstrably false, but several weak versions of the thesis are true but lack the radical implications of strong indeterminacy.The strong indeterminacy thesis is the claim (...)
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  41. Richard Susskind (1993). The Importance of Commercial Case Studies in Artificial Intelligence and Law. Artificial Intelligence and Law 2 (1):65-67.
    The field of artificial intelligence and law is remarkably diverse not just because it encompasses many areas of academic study but also because it attracts the interest of both the research and commercial worlds. While much of the research is no doubt too exploratory and tentative to be of direct relevance to practising lawyers, in other projects there is but a short step from the research laboratory to the marketplace.Given that most readers of this journal tend to be involved with, (...)
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  42. Gerard A. W. Vreeswijk (2000). Representation of Formal Dispute with Astanding Order. Artificial Intelligence and Law 8 (2-3):205-231.
    Computational dialectics is concerned with the formal representation of argument and dispute. The field emerged from developments in philosophy, artificial intelligence and legal theory. Its goal is to suggestalgorithms, procedures and protocols to investigate the tenability of logical claims, on the basis of information in the form of rules and cases. Currently, the field slowlyconverges to the opinion that dispute is the most fair and effective way to investigate claims. The basic assumption of this field is that dispute is the (...)
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  43. Douglas Walton (2008). A Dialogical Theory of Presumption. Artificial Intelligence and Law 16 (2):209-243.
    The notions of burden of proof and presumption are central to law, but as noted in McCormick on Evidence, they are also the slipperiest of any of the family of legal terms employed in legal reasoning. However, recent studies of burden of proof and presumption (Prakken et al. 2005; Prakken and Sartor 2006). Gordon et al. (2007) offer formal models that can render them into precise tools useful for legal reasoning. In this paper, the various theories and formal models are (...)
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  44. Anders Wedberg (1951). Some Problems in the Logical Analysis of Legal Science. Theoria 17 (1-3):246-275.
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