Rules, Reasons, Arguments

222 Pages·2012·1.2 MB·Dutch

Rules, Reasons, Arguments
Formal studies of argumentation and defeat

Rules, Reasons, Arguments
Formal studies of argumentation and defeat
PROEFSCHRIFT
ter verkrijging van de graad van doctor
aan de Universiteit Maastricht,
op gezag van de Rector Magnificus, Prof.mr. M.J. Cohen,
volgens het besluit van het College van Decanen,
in het openbaar te verdedigen
op donderdag 5 december 1996 om 14.00 uur
door
Harry Bart Verheij
Promotor:
Prof.dr. H.J. van den Herik
Copromotor:
Dr. J.C. Hage
Beoordelingscommissie:
Prof.dr.ir. A. Hasman (voorzitter)
Prof.dr.ir. J.L.G. Dietz (Technische Universiteit Delft)
Dr. F.M.P. van Dun
Prof.dr. J.L. Pollock (University of Arizona, Tucson)
Dr. H. Prakken (Vrije Universiteit Amsterdam)
Omslag: Grietje Verheij en Charlot Luiting
ISBN 90-9010071-7
Contents
Preface xi
Acknowledgments..................................................................................................xii
Guidelines for the reader.......................................................................................xiii
Contact information..............................................................................................xiii
Chapter 1 Introduction 1
1 The process of argumentation................................................................................1
2 Arguments as reconstructions................................................................................3
3 Arguments and proofs............................................................................................5
4 The defeasibility of arguments...............................................................................5
4.1 Exceptions to rules........................................................................................5
4.2 Conflicting arguments...................................................................................6
4.3 Conclusive force............................................................................................7
4.4 Other arguments taken into account..............................................................8
5 Related research.....................................................................................................9
6 General aims and biases of research.....................................................................10
7 Research goals and method..................................................................................12
8 Outline of the thesis.............................................................................................13
Chapter 2 Reason-Based Logic: a semantics of rules and reasons 15
1 Rules and reasons by example..............................................................................15
1.1 Rules and reasons........................................................................................16
1.2 Exclusionary reasons...................................................................................17
1.3 Weighing reasons........................................................................................17
1.4 Reasons concerning the application of a rule..............................................19
1.5 Overview.....................................................................................................20
2 Semantics.............................................................................................................20
3 Towards a formalization......................................................................................23
3.1 Rules and reasons........................................................................................23
3.2 Exclusionary reasons...................................................................................25
3.3 Weighing reasons........................................................................................26
3.4 Reasons concerning the application of a rule..............................................27
vi Contents
4 Types of facts.......................................................................................................28
4.1 Alphabets of Reason-Based Logic...............................................................28
4.2 Pre-terms and pre-sentences........................................................................29
4.3 A translation from sentences to terms..........................................................30
4.4 Terms and sentences....................................................................................32
4.5 Overview of the types of facts.....................................................................33
5 Relations between facts........................................................................................35
6 Conclusions following from given premises........................................................38
Chapter 3 Reason-Based Logic and law 43
1 Reasoning with rules vs. reasoning with principles..............................................43
2 An integrated view on rules and principles..........................................................45
2.1 A rule and its underlying principles.............................................................46
2.2 A typical rule...............................................................................................47
2.3 A typical principle.......................................................................................48
2.4 A hybrid rule/principle................................................................................49
3 An isolated rule/principle in Reason-Based Logic...............................................49
4 Weighing reasons in Reason-Based Logic...........................................................54
5 Exceptions in Reason-Based Logic......................................................................57
5.1 Exceptions and exclusionary reasons..........................................................57
5.2 Exceptions and reasons against application.................................................59
6 Conflicts in Reason-Based Logic.........................................................................61
6.1 Conflicts and exclusionary reasons..............................................................61
6.2 Conflicts and weighing reasons...................................................................62
7 Rules and principles in Reason-Based Logic.......................................................63
7.1 A rule and its underlying principles.............................................................63
7.2 The differences between rules and principles..............................................66
8 Analogy in Reason-Based Logic..........................................................................67
8.1 Application of underlying principles...........................................................68
8.2 Application of an analogous rule/principle..................................................70
8.3 Analogous application of the original rule..................................................71
Chapter 4 Formalizing rules: a comparative survey 73
1 Rules in argumentation.........................................................................................73
1.1 Rules and arguments....................................................................................74
1.2 Syllogistic and enthymematic arguments.....................................................75
1.3 Ordinary rule application.............................................................................77
2 Rules as material conditionals..............................................................................78
2.1 Relevance and the paradoxes of the material conditional............................78
2.2 Exceptions to rules......................................................................................81
2.3 Rule conflicts...............................................................................................82
2.4 Reasoning about rules..................................................................................84
vii
3 Relevance.............................................................................................................86
3.1 Fixating a set of rules..................................................................................86
3.2 Rules as special sentences...........................................................................87
3.3 Rules as special objects...............................................................................88
4 Exceptions to rules...............................................................................................89
4.1 Representing exceptions..............................................................................89
Negative rule conditions........................................................................90
Rule identifiers and exception predicates..............................................90
Rules as special objects..........................................................................91
4.2 Exceptions and nonmonotonicity.................................................................92
Maxiconsistent sets................................................................................92
Default rules...........................................................................................94
Counterarguments..................................................................................95
5 Rule conflicts.......................................................................................................97
5.1 Representing conflict resolving information................................................97
Conflicts of pairs of rules and rule priorities.........................................98
Bipolar multiple conflicts and weighing................................................98
General multiple conflicts and general conflict resolution..................100
5.2 Conflicts and consistency maintenance.....................................................100
Normal and semi-normal default rules................................................100
Conclusive force...................................................................................102
Collective defeat...................................................................................103
6 Reasoning about rules........................................................................................103
6.1 Rules as special sentences.........................................................................103
6.2 Rule identifiers..........................................................................................104
6.3 Rules as special objects.............................................................................105
Chapter 5 CumulA: a model of argumentation in stages 107
1 Argumentation in stages.....................................................................................107
1.1 Arguments and defeat................................................................................107
1.2 Overview of CumulA................................................................................109
2 Arguments and their structure............................................................................111
2.1 Elementary argument structures................................................................111
2.2 Composite argument structures.................................................................112
2.3 Definition of arguments.............................................................................114
2.4 Initials and narrowings of arguments.........................................................118
3 Defeat and defeaters...........................................................................................120
3.1 Undercutting defeat...................................................................................120
3.2 Rebutting defeat........................................................................................121
3.3 Defeat by sequential weakening................................................................122
3.4 Defeat by parallel strengthening................................................................123
3.5 Collective and indeterministic defeat........................................................124
viii Contents
3.6 Defeater schemes.......................................................................................126
3.7 Definition of defeaters and argumentation theories...................................127
4 Stages of the argumentation process..................................................................129
4.1 Initials, narrowings and defeat...................................................................129
4.2 Relevant, triggered, respected and inactive defeaters................................131
4.3 Stages and defeat.......................................................................................132
4.4 Definition of stages....................................................................................133
5 Lines of argumentation and argumentation diagrams.........................................136
5.1 Construction of arguments.........................................................................137
5.2 Change of status........................................................................................139
5.3 Definition of lines of argumentation and argumentation diagrams............141
6 Examples............................................................................................................144
6.1 Sequential weakening and parallel strengthening......................................144
6.2 Conflicting arguments: collective or multiple stages.................................146
6.3 Stable marriages........................................................................................149
6.4 The neurotic fatalist...................................................................................151
Chapter 6 Analyzing argumentation models using CumulA 155
1 Types of arguments............................................................................................155
2 Argument structure and defeat...........................................................................158
3 Individual and groupwise defeat........................................................................162
4 Triggers of defeat...............................................................................................164
5 Directions of argumentation...............................................................................165
6 Capturing elements of argumentation models in CumulA..................................166
6.1 Propositional Logic...................................................................................167
6.2 Poole’s Logical Framework for Default Reasoning...................................168
6.3 Lin and Shoham’s Argument Systems.......................................................168
6.4 Reiter’s Default Logic...............................................................................169
6.5 Pollock’s Theory of Defeasible Reasoning...............................................170
6.6 Vreeswijk’s Abstract Argumentation Systems...........................................170
6.7 Bondarenko et al.’s Assumption-Based Framework.................................171
6.8 Dung’s Argumentation Frameworks..........................................................172
6.9 Loui and Chen’s Argument Game.............................................................172
7 A comparison of argumentation models.............................................................173
Chapter 7 Results and conclusions 177
1 Rules and reasons...............................................................................................177
2 Legal reasoning..................................................................................................179
3 Dialectical argumentation..................................................................................180
4 Future research...................................................................................................181
ix
References 183
Index 191
Summary 199
Samenvatting 203
Curriculum Vitae 207