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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 Gardner 1987 is a general key work, while Gordon 1995 introduces dialogical models and dialogue logic, more generally, and discusses the issue of epistemic logic in formal models of law.  The seminal book Toulmin 2003 indirectly contributed far more to formal modeling using logic than the author intended, because for each objection Toulmin raised to the use of formal logic as a model, subsequent authors came along and found means of answering them within logic(s).
Introductions Hamfelt 1995 is a wonderful introduction to formal modeling of law, using classical logic as a framework.  The issue of epistemic logic in formal models of law is introduced extensively in Hage 2003.
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  1. M. Abraham, D. M. Gabbay & U. Schild (2011). Obligations and Prohibitions in Talmudic Deontic Logic. Artificial Intelligence and Law 19 (2-3):117-148.
    This paper examines the deontic logic of the Talmud. We shall find, by looking at examples, that at first approximation we need deontic logic with several connectives: O T A Talmudic obligation F T A Talmudic prohibition F D A Standard deontic prohibition O D A Standard deontic obligation. In classical logic one would have expected that deontic obligation O D is definable by $O_DA \equiv F_D\neg A$ and that O T and F T are connected by $O_TA \equiv F_T\neg (...)
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  2. Carlos Alarcon-Cabrera (1998). Von Wright's Deontic Logics and "Contrary-to-Duty Imperatives". Ratio Juris 11 (1):67-79.
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  3. Carlos E. Alchourron (1996). On Law and Logic. Ratio Juris 9 (4):331-348.
  4. Robert Alexy (2000). Henry Prakken (1997), Logical Tools for Modelling Legal Argument. A Study of Defeasible Reasoning in Law. Argumentation 14 (1):65-72.
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  5. Kevin D. Ashley (2002). An AI Model of Case-Based Legal Argument From a Jurisprudential Viewpoint. Artificial Intelligence and Law 10 (1-3):163-218.
    This article describes recent jurisprudential accountsof analogical legal reasoning andcompares them in detail to the computational modelof case-based legal argument inCATO. The jurisprudential models provide a theoryof relevance based on low-levellegal principles generated in a process ofcase-comparing reflective adjustment. Thejurisprudential critique focuses on the problemsof assigning weights to competingprinciples and dealing with erroneously decidedprecedents. CATO, a computerizedinstructional environment, employs ArtificialIntelligence techniques to teach lawstudents how to make basic legal argumentswith cases. The computational modelhelps students test legal hypotheses againsta database of (...)
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  6. Kevin D. Ashley (1992). Case-Based Reasoning and its Implications for Legal Expert Systems. Artificial Intelligence and Law 1 (2-3):113-208.
    Reasoners compare problems to prior cases to draw conclusions about a problem and guide decision making. All Case-Based Reasoning (CBR) employs some methods for generalizing from cases to support indexing and relevance assessment and evidences two basic inference methods: constraining search by tracing a solution from a past case or evaluating a case by comparing it to past cases. Across domains and tasks, however, humans reason with cases in subtly different ways evidencing different mixes of and mechanisms for these components.In (...)
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  7. Katie Atkinson (2012). Introduction to Special Issue on Modelling Popov V. Hayashi. Artificial Intelligence and Law 20 (1):1-14.
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  8. Katie Atkinson (2008). Introduction to Special Issue on Modelling Legal Cases. Artificial Intelligence and Law 16 (4):329-331.
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  9. Katie Atkinson & Trevor J. M. Bench-Capon (2007). Practical Reasoning as Presumptive Argumentation Using Action-Based Alternating Transition Systems. Artificial Intelligence 171 (10-15):855-874.
    In this paper we describe an approach to practical reasoning, reasoning about what it is best for a particular agent to do in a given situation, based on presumptive justifications of action through the instantiation of an argument scheme, which is then subject to examination through a series of critical questions. We identify three particular aspects of practical reasoning which distinguish it from theoretical reasoning. We next provide an argument scheme and an associated set of critical questions which is able (...)
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  10. T. J. M. Bench-Capon (2012). Representing Popov V Hayashi with Dimensions and Factors. Artificial Intelligence and Law 20 (1):15-35.
    Modelling reasoning with legal cases has been a central concern of AI and Law since the 1980s. The approach which represents cases as factors and dimensions has been a central part of that work. In this paper I consider how several varieties of the approach can be applied to the interesting case of Popov v Hayashi. After briefly reviewing some of the key landmarks of the approach, the case is represented in terms of factors and dimensions, and further explored using (...)
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  11. T. J. M. Bench-Capon, T. Geldard & P. H. Leng (2000). A Method for the Computational Modelling of Dialectical Argument with Dialogue Games. Artificial Intelligence and Law 8 (2-3):233-254.
    In this paper we describe a method for the specification of computationalmodels of argument using dialogue games. The method, which consists ofsupplying a set of semantic definitions for the performatives making upthe game, together with a state transition diagram, is described in full.Its use is illustrated by some examples of varying complexity, includingtwo complete specifications of particular dialogue games, Mackenzie's DC,and the authors' own TDG. The latter is also illustrated by a fully workedexample illustrating all the features of the game.
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  12. Trevor Bench-Capon (2004). Book Review: Bram Roth, Case-Based Reasoning in the Law: A Formal Theory of Reasoning by Case Comparison. Ph. D. Thesis, the University of Maastricht, 2003. 181 Pp. [REVIEW] Artificial Intelligence and Law 12 (3):227-229.
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  13. 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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  14. Trevor J. M. Bench-Capon & Giovanni Sartor (2003). A Model of Legal Reasoning with Cases Incorporating Theories and Values. Artificial Intelligence 150 (1-2):97-143.
    Reasoning with cases has been a primary focus of those working in AI and law who have attempted to model legal reasoning. In this paper we put forward a formal model of reasoning with cases which captures many of the insights from that previous work. We begin by stating our view of reasoning with cases as a process of constructing, evaluating and applying a theory. Central to our model is a view of the relationship between cases, rules based on cases, (...)
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  15. Trevor Bench-Capon & 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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  16. Ian Carlo Dapalla Benitez (2015). A Critique of Critical Legal Studies' Claim of Legal Indeterminacy. Lambert Academic Publishing.
    This paper challenges the Critical Legal Studies (CLS) claims of legal indeterminacy. It shall use a legal formalist logic and language as its main assertion, further maintaining that the CLS claims is only grounded in ambiguity and confusion. CLS is a legal theory that challenges and overturns accepted norms and standards in legal theory and practice. They maintained that law in the historical and contemporary society has an alleged impartiality, and it is used as a tool of privilege and power (...)
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  17. R. Bergmann, S. Breen, M. Göker, M. Manago & S. Wess (1999). Developing Case-Based Reasoning Applications: The INRECA-Methodology. In P. Brezillon & P. Bouquet (eds.), Lecture Notes in Artificial Intelligence. Springer
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  18. Floris Bex (2011). Arguments, Stories and Criminal Evidence: A Formal Hybrid Theory. Springer.
    In this book a theory of reasoning with evidence in the context of criminal cases is developed. The main subject of this study is not the law of evidence but rather the rational process of proof, which involves constructing, testing and justifying scenarios about what happened using evidence and commonsense knowledge. A central theme in the book is the analysis of ones reasoning, so that complex patterns are made more explicit and clear. This analysis uses stories about what happened and (...)
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  19. Floris Bex, Henry Prakken, Chris Reed & Douglas Walton (2003). Towards a Formal Account of Reasoning About Evidence: Argumentation Schemes and Generalisations. [REVIEW] Artificial Intelligence and Law 11 (2-3):125-165.
    This paper studies the modelling of legal reasoning about evidence within general theories of defeasible reasoning and argumentation. In particular, Wigmore's method for charting evidence and its use by modern legal evidence scholars is studied in order to give a formal underpinning in terms of logics for defeasible argumentation. Two notions turn out to be crucial, viz. argumentation schemes and empirical generalisations.
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  20. Isabelle Bichindaritz (2009). Prototypical Cases for Retrieval, Reuse, and Knowledge Maintenance in Biomedical Case‐Based Reasoning. In L. Magnani (ed.), Computational Intelligence. 25--3.
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  21. Michael Blome-Tillmann (2015). Sensitivity, Causality, and Statistical Evidence in Courts of Law. Thought: A Journal of Philosophy 4 (2):102-112.
    Recent attempts to resolve the Paradox of the Gatecrasher rest on a now familiar distinction between individual and bare statistical evidence. This paper investigates two such approaches, the causal approach to individual evidence and a recently influential (and award-winning) modal account that explicates individual evidence in terms of Nozick's notion of sensitivity. This paper offers counterexamples to both approaches, explicates a problem concerning necessary truths for the sensitivity account, and argues that either view is implausibly committed to the impossibility of (...)
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  22. L. Karl Branting (2003). A Reduction-Graph Model of Precedent in Legal Analysis. Artificial Intelligence 150 (1-2):59-95.
    Legal analysis is a task underlying many forms of legal problem solving. In the Anglo-American legal system, legal analysis is based in part on legal precedents, previously decided cases. This paper describes a reduction-graph model of legal precedents that accounts for a key characteristic of legal precedents: a precedent's relevance to subsequent cases is determined by the theory under which the precedent is decided. This paper identifies the implementation requirements for legal analysis using the reduction-graph model of legal precedents and (...)
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  23. L. Karl Branting (1993). A Computational Model of Ratio Decidendi. Artificial Intelligence and Law 2 (1):1-31.
    This paper proposes a model ofratio decidendi as a justification structure consisting of a series of reasoning steps, some of which relate abstract predicates to other abstract predicates and some of which relate abstract predicates to specific facts. This model satisfies an important set of characteristics ofratio decidendi identified from the jurisprudential literature. In particular, the model shows how the theory under which a case is decided controls its precedential effect. By contrast, a purely exemplar-based model ofratio decidendi fails to (...)
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  24. Eugenio Bulygin (2008). What Can One Expect From Logic in the Law? (Not Everything, but More Than Something: A Reply to Susan Haack). Ratio Juris 21 (1):150-156.
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  25. Eugenio Bulygin (2003). Review of Jaap Hage's Law and Defeasibility. [REVIEW] Artificial Intelligence and Law 11 (2-3):245-250.
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  26. Alison Chorley & Trevor Bench-Capon (2005). An Empirical Investigation of Reasoning with Legal Cases Through Theory Construction and Application. Artificial Intelligence and Law 13 (3-4):323-371.
    In recent years several proposals to view reasoning with legal cases as theory construction have been advanced. The most detailed of these is that of Bench-Capon and Sartor, which uses facts, rules, values and preferences to build a theory designed to explain the decisions in a set of cases. In this paper we describe CATE (CAse Theory Editor), a tool intended to support the construction of theories as described by Bench-Capon and Sartor, and which produces executable code corresponding to a (...)
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  27. Alison Chorley & Trevor Bench-Capon (2005). Agatha: Using Heuristic Search to Automate the Construction of Case Law Theories. [REVIEW] Artificial Intelligence and Law 13 (1):9-51.
    In this paper we describe AGATHA, a program designed to automate the process of theory construction in case based domains. Given a seed case and a number of precedent cases, the program uses a set of argument moves to generate a search space for a dialogue between the parties to the dispute. Each move is associated with a set of theory constructors, and thus each point in the space can be associated with a theory intended to explain the seed case (...)
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  28. Michael Clark (1997). Review of P. Wahlgren, Automation of Legal Reasoning. [REVIEW] Information and Communications Technology Law 6.
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  29. Michael Clark (1992). Review of Kevin Ashley, Modelling Legal Argument. [REVIEW] Law, Computing and Artificial Intelligence 1 (1).
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  30. Stefania Costantini & Gaetano Aurelio Lanzarone (1995). Explanation-Based Interpretation of Open-Textured Concepts in Logical Models of Legislation. Artificial Intelligence and Law 3 (3):191-208.
    In this paper we discuss a view of the Machine Learning technique called Explanation-Based Learning (EBL) or Explanation-Based Generalization (EBG) as a process for the interpretation of vague concepts in logic-based models of law.The open-textured nature of legal terms is a well-known open problem in the building of knowledge-based legal systems. EBG is a technique which creates generalizations of given examples on the basis of background domain knowledge. We relate these two topics by considering EBG''s domain knowledge as corresponding to (...)
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  31. Barbara Cuthill & Robert McCartney (1993). Issue Spotting in CHASER. Artificial Intelligence and Law 2 (2):83-111.
    For any system that uses previous experience to solve problems in new situations, it is necessary to identify the features in the situation that should match features in the previous cases through some process ofsituation analysis. In this paper, we examine this problem in the legal domain, where lawyers know it asissue spotting. In particular, we present an implementation of issue spotting in CHASER, a legal reasoning system that works in the domain of tort law.This approach is a compromise between (...)
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  32. Phan Minh Dung & Phan Minh Thang (2009). Modular Argumentation for Modelling Legal Doctrines in Common Law of Contract. Artificial Intelligence and Law 17 (3):167-182.
    To create a programming environment for contract dispute resolution, we propose an extension of assumption-based argumentation into modular assumption-based argumentation in which different modules of argumentation representing different knowledge bases for reasoning about beliefs and facts and for representation and reasoning with the legal doctrines could be built and assembled together. A distinct novel feature of modular argumentation in compare with other modular logic-based systems like Prolog is that it allows references to different semantics in the same module at the (...)
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  33. Paul E. Dunne (2005). A Value-Based Argument Model of Convention Degradation. Artificial Intelligence and Law 13 (1):153-188.
    The analysis of how social conventions emerge and become established is rightly viewed as a significant study of great relevance to models of legal and social systems. Such conventions, however, do not operate in a monotonic fashion, i.e. the fact that a convention is recognised and complied with at some instant is no guarantee it will continue to be so indefinitely. In total rules and protocols may evolve, with or without the consent of individual members of the society, even to (...)
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  34. William A. Edmundson (1998). Jaap C. Hage, Reasoning with Rules: An Essay on Legal Reasoning and Its Underlying Logic Reviewed By. Philosophy in Review 18 (3):178-179.
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  35. Norman Fenton, Martin Neil & David A. Lagnado (2013). A General Structure for Legal Arguments About Evidence Using Bayesian Networks. Cognitive Science 37 (1):61-102.
    A Bayesian network (BN) is a graphical model of uncertainty that is especially well suited to legal arguments. It enables us to visualize and model dependencies between different hypotheses and pieces of evidence and to calculate the revised probability beliefs about all uncertain factors when any piece of new evidence is presented. Although BNs have been widely discussed and recently used in the context of legal arguments, there is no systematic, repeatable method for modeling legal arguments as BNs. Hence, where (...)
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  36. Susan Fox & David Leake (1994). Using Introspective Reasoning to Guide Index Refinement in Case-Based Reasoning. In Ashwin Ram & Kurt Eiselt (eds.), Proceedings of the Sixteenth Annual Conference of the Cognitive Science Society. Erlbaum 324--329.
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  37. Kathleen Freeman & Arthur M. Farley (1996). A Model of Argumentation and its Application to Legal Reasoning. Artificial Intelligence and Law 4 (3-4):163-197.
    We present a computational model of dialectical argumentation that could serve as a basis for legal reasoning. The legal domain is an instance of a domain in which knowledge is incomplete, uncertain, and inconsistent. Argumentation is well suited for reasoning in such weak theory domains. We model argument both as information structure, i.e., argument units connecting claims with supporting data, and as dialectical process, i.e., an alternating series of moves by opposing sides. Our model includes burden of proof as a (...)
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  38. Joseph S. Fulda (2010). The Logic of “Asked and Answered!”: The Case of the Traffic Light. Ratio Juris 23 (2):282-287.
    Uses erotetic logic to model the courtroom objection "Asked and Answered!".
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  39. Joseph S. Fulda (2000). The Logic of “Improper Cross”. Artificial Intelligence and Law 8 (4):337-341.
    Uses erotetic logic to model the courtroom objection "Improper Cross!". -/- Readers downloading the article should also please download the erratum et corrigendum, which is locally available.
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  40. Joseph S. Fulda (1999). How Does Formal Logic Fare as a Model of Legal Argumentation? Acm Sigcas Computers and Society 29 (3):34.
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  41. Joseph S. Fulda (1989). The Logic of the Whole Truth. Rutgers Computer and Technology Law Journal 15 (2):435-446.
    Note: The author holds the copyright, and there was no agreement, express or implied, not to use a facsimile PDF. -/- Using erotetic logic, the paper defines the "the whole truth" in a manner consistent with U.S. Supreme Court precedent. It cannot mean "the whole story," as witnesses in an adversary system are permitted /only/ to answer the questions put to them, nor are they permitted to speculate, add irrelevant material, etc. Nor can it mean not to add an admixture (...)
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  42. Joseph S. Fulda (1988). The Logic of Expert Judging Systems and the Rights of the Accused. AI and Society 2 (3):266-269.
    Deals with the problem of enthymemes in expert systems designed to model legal reasoning; suggests that interactivity is crucial.
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  43. Aldo Gangemi (2008). Norms and Plans as Unification Criteria for Social Collectives. Journal of Autonomous Agents and Multi-Agent Systems 16 (3).
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  44. Roberto García, Rosa Gil & Jaime Delgado (2007). A Web Ontologies Framework for Digital Rights Management. Artificial Intelligence and Law 15 (2):137-154.
    In order to improve the management of copyright in the Internet, known as Digital Rights Management, there is the need for a shared language for copyright representation. Current approaches are based on purely syntactic solutions, i.e. a grammar that defines a rights expression language. These languages are difficult to put into practise due to the lack of explicit semantics that facilitate its implementation. Moreover, they are simple from the legal point of view because they are intended just to model the (...)
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  45. Anne von der Lieth Gardner (1987). An Artificial Intelligence Approach to Legal Reasoning. MIT Press.
  46. Simone Gittelson, Alex Biedermann, Silvia Bozza & Franco Taroni (2013). Modeling the Forensic Two-Trace Problem with Bayesian Networks. Artificial Intelligence and Law 21 (2):221-252.
    The forensic two-trace problem is a perplexing inference problem introduced by Evett (J Forensic Sci Soc 27:375–381, 1987). Different possible ways of wording the competing pair of propositions (i.e., one proposition advanced by the prosecution and one proposition advanced by the defence) led to different quantifications of the value of the evidence (Meester and Sjerps in Biometrics 59:727–732, 2003). Here, we re-examine this scenario with the aim of clarifying the interrelationships that exist between the different solutions, and in this way, (...)
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  47. Thomas F. Gordon (1995). The Pleadings Games: An Artificial Intelligence Model of Procedural Justice. Springer.
    The Pleadings Game is a major contribution to artificial intelligence and legal theory. The book draws on jurisprudence and moral philosophy to develop a formal model of argumentation called the pleadings game. From a technical perspective, the work can be viewed as an extension of recent argumentation-based approaches to non-monotonic logic: (1) the game is dialogical rather than mono-logical; (2) the validity and priority of defeasible rules is subject to debate; and (3) resource limitations are acknowledged by rules for fairly (...)
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  48. Thomas F. Gordon (1993). The Pleadings Game. Artificial Intelligence and Law 2 (4):239-292.
    The Pleadings Game is a normative formalization and computational model of civil pleading, founded in Roberty Alexy''s discourse theory of legal argumentation. The consequences of arguments and counterarguments are modelled using Geffner and Pearl''s nonmonotonic logic,conditional entailment. Discourse in focussed using the concepts of issue and relevance. Conflicts between arguments can be resolved by arguing about the validity and priority of rules, at any level. The computational model is fully implemented and has been tested using examples from Article Nine of (...)
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  49. Thomas F. Gordon, Henry Prakken & Douglas N. Walton (2007). The Carneades Model of Argument and Burden of Proof. Artificial Intelligence 171 (10-15):875-896.
    We present a formal, mathematical model of argument structure and evaluation, taking seriously the procedural and dialogical aspects of argumentation. The model applies proof standards to determine the acceptability of statements on an issue-by-issue basis. The model uses different types of premises (ordinary premises, assumptions and exceptions) and information about the dialectical status of statements (stated, questioned, accepted or rejected) to allow the burden of proof to be allocated to the proponent or the respondent, as appropriate, for each premise separately. (...)
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  50. Thomas F. Gordon & Douglas Walton (2012). A Carneades Reconstruction of Popov V Hayashi. Artificial Intelligence and Law 20 (1):37-56.
    Carneades is an open source argument mapping application and a programming library for building argumentation support tools. In this paper, Carneades’ support for argument reconstruction, evaluation and visualization is illustrated by modeling most of the factual and legal arguments in Popov v Hayashi.
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