Formal Legal Reasoning

Formalism about Legal Reasoning

According to Philpapers, “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.

Books and Papers

• Carlos E. Alchourron (1996). On Law and Logic. Ratio Juris 9 (4):331-348.
• Lennart Ã…qvist (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 Ã…qvist [ (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 (…)
• Sol Azuelos-Atias (2010). Semantically Cued Contextual Implicatures in Legal Texts. Journal of Pragmatics 42 (3):728-743. In this article I discuss one of the linguistic means which enables speakers to represent content in their utterances without expressing it explicitly. I will argue, in line with Wilson and Sperber, that the logical form of the argument encoded by an utterance (however fragmentarily or incompletely) is sufficient as a cue directing the hearers to the implicit content of the speaker’s meaning. I will suggest that the logical form of the encoded argument enables the speaker to represent in the (…)
• 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 (…)
• 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. (…)
• 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 (…)
• Gustav Bergmann & Lewis Zerby (1945). The Formalism in Kelsen’s Pure Theory of Law. Ethics 55 (2):110-130. 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
• 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 (…)
• Michael Clark (1997). Review of P. Wahlgren, Automation of Legal Reasoning. [REVIEW] Information and Communications Technology Law 6. Joseph S. Fulda (2012). Implications of a Logical Paradox for Computer-Dispensed Justice Reconsidered: Some Key Differences Between Minds and Machines. 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 (…)
• Joseph S. Fulda (1999). Can One Really Reason About Laws? Acm Sigcas 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.
• 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 (…)
• 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 (…)
• 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.
• 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 (…)
• 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 (…)
• 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 (…)
• 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. (…)
• 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 (…)
• 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, (…)
• Hajime Yoshino (1997). On the Logical Foundations of Compound Predicate Formulae for Legal Knowledge Representation. Artificial Intelligence and Law 5 (1-2):77-96. In order to represent legal knowledge adequately, it is vital to create a formal device that can freely construct an individual concept directly from a predicate expression. For this purpose, a Compound Predicate Formula (CPF) is formulated for use in legal expert systems. In this paper, we willattempt to explain the nature of CPFs by rigorous logical foundation, i.e., establishing their syntax and semantics precisely through the use of appropriate examples. We note the advantages of our system over other such (…)

Formal Models of Legal Reasoning

Books and Papers

• Robert Alexy (2000). Henry Prakken (1997), Logical Tools for Modelling Legal Argument. A Study of Defeasible Reasoning in Law. Argumentation 14 (1):65-72.
• 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 (…)
• 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.
• 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.
• 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, (…)
• 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 (…)
• 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 (…)
• 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.
• 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 (…)
• 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 (…)
• 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.
• 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 (…)
• Michael Clark (1997). Review of P. Wahlgren, Automation of Legal Reasoning. [REVIEW] Information and Communications Technology Law 6.
• Michael Clark (1992). Review of Kevin Ashley, Modelling Legal Argument. [REVIEW] Law, Computing and Artificial Intelligence 1 (1).