LOGICAL TOOLS FOR MODELLING LEGAL ARGUMENT Law and Philosophy Library VOLUME32 Managing Editors FRANCISCO J. LAPORTA, Department ofLaw, Autonomous University ofM adrid, Spain ALEKSANDER PECZENIK, Department ofL aw, University ofL und, Sweden FREDERICK SCHAUER, John F. Kennedy School ofGovernment, Harvard University, Cambridge, Mass., U.SA. Former Managing Editors AULIS AARNIO, MICHAEL D. BAY LESt, CONRAD D. JOHNSONt, ALAN MABE Editorial Advisory Board AULIS AARNIO, Research Institutefor Social Sciences, University ofTampere, Finland ZENON BANKOWSKY, Centre for Criminology and the Social and Philosophical Study ofLaw, University ofEdinburgh PAOLO COMANDUCCI, University ofGenua, Italy ERNESTO GARZON V ALDES, Institut für Politikwissenschaft, Johannes Gutenberg Universität Mainz JOHN KLEINIG, Department ofLaw, Police Science and Criminal Justice Administration, John Jay College ofCriminal Justice, City University ofNew York NEIL MacCORMICK, Centre for Criminology and the Social and Philosophical Study ofLaw, Faculty ofLaw, University ofEdinburgh WOJCIECH SADURSKI, Faculty ofLaw, University ofSydney ROBERT S. SUMMERS, School ofLaw, Cornell University CARL WELLMAN, DepartmentofPhilosophy, Washington University HENRYPRAKKEN Department o/Computer Seien ce. Free University 0/ Amsterdam. The Netherlands LOGICAL TOOLS FOR MODELLING LEGAL ARGUMENT A Study of Defeasible Reasoning in Law SPRINGER-SCIENCE+BUSINESS MEDIA, s.y. A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-4928-5 ISBN 978-94-015-8975-8 (eBook) DOI 10.1007/978-94-015-8975-8 Printed on acid-free paper All Rights Reserved © 1997 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1997 Softcover reprint of the hardcover 1s t edition 1997 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, inc\uding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner Table of Contents PREFACE xi 1 INTRODUCTION 1 1.1 AI, Logic and Legal Reasoning: Some General Remarks 1 1.1.1 An Overview . . . . . . . . . . . . . . . . 1 1.1. 2 Artificial Intelligence . . . . . . . . . . . . 2 1.1.3 Computable Aspects of Legal Reasoning . 5 1.1.4 The Role of Logic 6 1.2 The Focus of Research . . . . . . . . . . . . . . 7 1.3 Logic and AI . . . . . . . . . . . . . . . . . . . 8 1.3.1 The Declarative vs. Procedural Debate . 8 1.3.2 Logics and Programming Systems 9 1.3.3 Logic and Reasoning . 11 1.4 Points of Departure .... 12 1.5 The Structure of this Book 13 2 THE ROLE OF LOGIC IN LEGAL REASONING 15 2.1 Three Misunderstandings about Logic . . . . . . . . . 16 2.1.1 'To Formalize is to Define Completely' . . . . . 16 2.1.2 'Formalization Leaves No Room for Interpretation' 17 2.1.3 'Logic Excludes Nondeductive Modes of Reasoning' . 18 2.2 The 'Deductivist Fallacy' 18 2.2.1 'Naive Deductivism' . . 19 2.2.2 The Criticism . . . . . . 20 2.2.3 The Misunderstanding . 23 2.2.4 The Merits of the Criticism 25 2.3 Noninferential Reasoning with Logical Tools . 26 2.4 Rule-based and Case-based Reasolling 30 2.5 Summary . . . . . . . . . . . . . . . . . . . . 31 3 THE NEED FOR NEW LOGICAL TOOLS 33 3.1 The Separation of Rules and Exceptions in Legislation 34 3.1.1 Terminology 35 3.1.2 Examples..................... 36 v vi TABLE OF CONTENTS 3.1.3 Formalizations in Standard Logic . 37 3.1.4 Nonstandard Methods 41 3.2 Defeasibility of Legal Rules . . 47 3.3 Open Texture ......... . 49 3.3.1 Classification Problems 50 3.3.2 Defeasibility of Legal Concepts 52 3.3.3 Vagueness............ 54 3.4 Which Nonstandard Techniques are Needed? 55 3.4.1 Reasoning with Inconsistent Information. 55 3.4.2 Nonmonotonie Reasoning ........ . 56 3.5 AI-and-Iaw Programs with Nonstandard Features. 61 3.5.1 The Law as Logic Programs . 61 3.5.2 TAXMAN II . . . . 61 3.5.3 Gardner's Prog ram . 62 3.5.4 CABARET..... 63 4 LOGICS FOR NONMONOTONIC REASONING 67 4.1 Nonmonotonic Logics ......... 68 4.1.1 Consistency-based Approaches 68 4.1.2 Autoepistemic Logic . . 73 4.1.3 Minimization...... 76 4.1.4 Conditional Approaches 87 4.1.5 Inconsistency Handling 89 4.2 General Issues. . . . . . . . . . 93 4.2.1 Prcferential Entailment 93 4.2.2 Properties of Consequence Notions 94 4.2.3 Connections ......... . 96 4.2.4 Truth Maintenance Systems . 97 4.3 Objections to Nonmonotonie Logics 97 4.3.1 'Logic is Monotonie' 97 4.3.2 Intractability......... 99 5 REPRESENTING EXPLICIT EXCEPTIONS 101 5.1 Introduction..................... 102 5.1.1 Methods of Representing Rules and Exceptions 102 5.1.2 Kinds of Exceptions . . . . . . . . . . . . . . . 102 5.1.3 Requirements for Representing Rules and Exceptions 103 5.2 Default Logic . . . . . . . . . . . . 105 5.2.1 Specific Exception Clauses . 106 5.2.2 General Exception Clauses 107 5.2.3 Evaluation 111 5.3 Circumscription........... 112 TABLE OF CONTENTS VII 5.4 Poole's Framework for Default Reasoning 117 5.5 Logic-programming's Negation as Failure 120 5.5.1 Specific Exception Clauses. . . . . 121 5.5.2 General Exception Clauses .... 122 5.5.3 Logic Programs with Classical Negation 125 5.5.4 Summary............ 129 5.6 Evaluation................ 129 5.6.1 A Formalization Methodology . 130 5.6.2 Directionality of Defaults . . . 134 5.6.3 Contrapositive Inferences . . . 135 5.6.4 Assessment of the Exception Clause Approach 136 6 PREFERRING THE MOST SPECIFIC ARGUMENT 141 6.1 Introduction..................... 141 6.2 Poole: Preferring the Most Specific Explanation. 143 6.3 Problems .................. 148 6.3.1 Some Possible Facts are Irrelevant . . . . 148 6.3.2 Multiple Conflicts Ignored . . . . . . . . . 149 6.3.3 Defaults Cannot be Represented in Standard Logic. 150 6.4 A System for Constructing and Comparing Arguments . 151 6.4.1 General Remarks . . . . . . . . . . 151 6.4.2 The Underlying Logical Language 152 6.4.3 Arguments .......... 154 6.4.4 Confiicts Between Arguments 156 6.4.5 Comparing Arguments. 158 6.4.6 Informal Summary. . . 163 6.5 The Assessment of Arguments. 163 6.5.1 The General Idea . . . . 163 6.5.2 The Dialogue Game Defined . 166 6.5.3 Illustrations.......... 170 6.6 Combining Priorities and Exception Clauses . 172 6.6.1 Extending the System 172 6.6.2 Illustrations. 175 6.7 Evaluation........... 177 7 REASONING WITH INCONSISTENT INFORMATION 179 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .. 179 7.2 Existing Formalizations of Inconsistency Tolerant Reasoning 180 7.2.1 Alchourron & Makinson (1981) . . . . . . 181 7.2.2 Belief Revision Approaches . . . . . . . . 183 7.2.3 Brewka's Preferred-subtheories Approach 187 7.3 Diagnosis . . . . . . . . . . . . . . . . . . . . . . 188 viii TABLE OF CONTENTS 7.4 Hierarchical Defeat . . . . . . . . . . . . 191 7.5 General Features of the System . . . . . 193 7.5.1 Properties of the Consequence Notion 193 7.5.2 Sceptical and Crcdulous Reasoning . 195 7.5.3 Floating Conclusions . 196 7.5.4 Accrual of Arguments . . . . . . . . 198 7.6 Conclusion .................. 200 8 REASONING ABOUT PRIORITY RELATIONS 203 8.1 Introduction.......... 203 8.2 Legal Issues . . . . . . . . . . . . . . . . . . 204 8.2.1 Legal Collision Rules . . . . . . . . . 204 8.2.2 Requirements for a Formal Analysis 205 8.3 Extending the Definitions . . . 206 8.4 A Formalization Methodology . 210 8.5 Examples . . . . . . . . 212 8.6 An Alternative Method .... 217 9 SYSTEMS FOR DEFEASIBLE ARGUMENTATION 219 9.1 Argumentation Systems . . . . . . . . . . . . . . . . . . 219 9.2 Some Argumentation Systems. . . . . . . . . . . . . . . 221 9.2.1 The Bondarenko-Dung-Kowalski-Toni Approach 221 9.2.2 Pollock ..................... 226 9.2.3 Lin and Shoham . . . . . . . . . . . . . . . . 229 9.2.4 Vreeswijk's Abstract Argumentation Systems 230 9.2.5 Nute's Defeasible Logic ........... 232 9.2.6 Simari and Loui ............... 235 9.2.7 Geffner and Pearl's Conditional Entailment 235 9.2.8 General Comparison . 237 9.3 Other Relevant Research. . . 238 9.3.1 Brewka's Later Work . 238 9.3.2 Reason-based Logic . 240 10 USING THE ARGUMENTATION SYSTEM 249 10.1 A Comparison of the Methods for Representing Exceptions 249 10.2 Implementational Concerns . . . . . . . . . . . 253 10.3 Applications. . . . . . . . . . . . . . . . . . . . 255 10.3.1 Toulmin on the Structure of Arguments 255 10.3.2 The System as a Tool in Reasoning. . . 256 10.4 A Logical Analysis of Some Implemented Systems 258 10.4.1 Gardner's Program . . . . . . . . . . . . . 258 10.4.2 CABARET . . . . . . . . . . . . . . . . . 261 10.4.3 Applications of Logic Metaprogramming . 262 TABLE OF CONTENTS IX 10.4.4 Freeman and Farley's DART System . 263 10.4.5 The Pleadings Game . . . . . 264 10.5 Four Layers in Legal Argumentation . . . . . 270 11 CONCLUSION 275 11.1 Summary . . . . . . . . . . . 275 11.2 Main Results . . . . . . . . . 276 11.3 Implications for Other Issues 281 11.4 Suggestions for Further Research 284 A NOTATIONS, ORDERINGS AND GLOSSARY 287 Al General Symbols and Notations. . . . . . . . . . . 287 A2 Ordering Relations . . . . . . . . . . . . . . . . . . 288 A3 Notions of the Argumentation System of Chapters 6-8 289 A4 Glossary.......................... 289 REFERENCES 293 INDEX 303 PREFACE This book is a revised and extended version of my PhD Thesis 'Logical Tools for Modelling Legal Argument', which I defended on 14 January 1993 at the Free University Amsterdam. The first five chapters of the thesis have remained almost completely unchanged but the other chapters have undergone considerable revision and expansion. Most importantly, I have replaced the formal argument-based system of the old Chapters 6, 7 and 8 with a revised and extended system, whieh I have developed during the last three years in collaboration with Giovanni Sartor. Apart from some technical improvements, the main additions to the old system are the enriehment of its language with a nonprovability operator, and the ability to formalise reasoning about preference criteria. Moreover, the new system has a very intuitive dialectieal form, as opposed to the rather unintuitive fixed-point appearance of the old system. Another important revision is the split of the old Chapter 9 into two new chapters. The old Section 9.1 on related research has been updated and expanded into a whole chapter, while the rest of the old chapter is now in revised form in Chapter 10. This chapter also contains two new contributions, a detailed discussion of Gordon's Pleadings Game, and a general description of a multi-Iayered overall view on the structure of argu mentation, comprising a logieal, dialectical, procedural and strategie layer. Finally, in the revised conclusion I have paid more attention to the relevance of my investigations for legal philosophy and argumentation theory. Some parts of this book are based on previously published articles. Section 3.1 is based on Prakken & Schriekx (1991), while Seetions 6.1- 6.3 and 7.1-7.3 are extended and revised versions of parts of, respectively, Prakken (1991a) and Prakken (1991b) (combined in Prakken, 1993). Fur thermore, the Sections 6.4, 6.5, 6.6 (partly), 7.4 and parts of the Sec tions 8.3-8.5 and 9.1 are based on Prakken & Sartor (1996b). Finally, some parts of Section 10.5 are based on Prakken (1995b). AS. Acknowledgements Four and a half years have passed since I defended my PhD thesis, the basis of the present book. I here briefly repeat the acknowledgements and xi