Logics for Agents with Bounded Rationality [PhD Thesis]

226 Pages·1994·0.8 MB·English

by  Zhisheng Huang

LOGICS FOR AGENTS
WITH
BOUNDED RATIONALITY
Zhisheng Huang
December 18, 2002
LOGICS FOR AGENTS
WITH
BOUNDED RATIONALITY
Zhisheng Huang
LOGICS FOR AGENTS
WITH
BOUNDED RATIONALITY
ILLC Dissertation Series 1994-10
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Institute for Logic, Language and Computation
Universiteit van Amsterdam
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Logics for Agents
with
Bounded Rationality
Academisch Proefschrift
ter verkrijging van de graad van doctor aan de
Universiteit van Amsterdam,
op gezag van de Rector Magnificus
Prof.dr P.W.M. de Meijer
in het openbaar te verdedigen in de
Aula der Universiteit
(Oude Lutherse Kerk, ingang Singel 411, hoek Spui)
op donderdag 15 december 1994 te 12.00 uur
door
Zhisheng Huang
geboren te Fujian, China.
Promotor: Dr. Peter van Emde Boas
Faculteit Wiskunde en Informatica
Universiteit van Amsterdam
Plantage Muidergracht 24
1018 TV Amsterdam
Co-Promotor: Dr. Michael Masuch
Center for Computer Science in Organization and Management (CCSOM)
Faculteit der Politieke en Sociaal-Culturele Wetenschappen
Universiteit van Amsterdam
Oude Turfmarkt 151
1012 GC Amsterdam
Copyright (cid:13)c 1994 by Zhisheng Huang
Cover design by Zhisheng Huang
ISBN: 90–74795–13–7
Contents
Acknowledgments 1
1 Introduction 3
1.1 Main Work and its Significance . . . . . . . . . . . . . . . . . . . . . 3
1.2 Organizations of This Thesis . . . . . . . . . . . . . . . . . . . . . . . 5
I Logics for Belief Dependence 9
2 Bounded Rationality and Belief Dependence 11
2.1 Bounded Rationality: the wide interpretation . . . . . . . . . . . . . 11
2.2 Belief Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Compartmentalized Information and Incorporated Information 13
2.2.2 The Roles of Source Indexing of Information . . . . . . . . . . 15
2.3 Logics of Knowledge and Belief and Logical Omniscience . . . . . . . 16
2.3.1 General Logic of Knowledge and Beliefs . . . . . . . . . . . . . 16
2.3.2 The Problem of Logical Omniscience . . . . . . . . . . . . . . 18
2.4 Syntactic Considerations for Logics of Belief Dependence . . . . . . . 23
2.5 General Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Formalizing Belief Dependence 27
3.1 Several Plausible Systems . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 Belief Dependence Systems Based on the Epistemic Operator
and the Dependency Operator . . . . . . . . . . . . . . . . . . 27
3.1.2 Belief Dependence System Based on Sub-belief Operator . . . 29
3.2 Formalizing Suspicion and Other Features . . . . . . . . . . . . . . . 31
3.3 Formalizing Indirect Dependence . . . . . . . . . . . . . . . . . . . . 34
v
vi Contents
4 Semantic Models 37
4.1 L-Model of Belief Dependence: an approach based on general epis-
temic logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 D-Model of Belief Dependence: a syntactic approach . . . . . . . . . 39
4.2.1 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.2 Soundness and Completeness . . . . . . . . . . . . . . . . . . 41
4.2.3 Decidability and Complexity . . . . . . . . . . . . . . . . . . . 44
4.3 Lij-Model: An Adapted Possible World Approach . . . . . . . . . . . 46
4.3.1 Semantics and Lij Logics . . . . . . . . . . . . . . . . . . . . 46
4.3.2 Decidability and Complexity . . . . . . . . . . . . . . . . . . . 48
4.4 A Brief Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 Belief Dependence, Revision, and Persistence 55
5.1 Belief Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2 A Bit of Belief Revision Theories . . . . . . . . . . . . . . . . . . . . 56
5.3 BeliefMaintenanceUndertheFrameworkofLogicsofBeliefDependence 58
5.4 Types of Belief Maintenance Operation . . . . . . . . . . . . . . . . . 59
5.5 A Belief Maintenance Strategy Using Logics of Belief Dependence . . 61
5.5.1 Update Strategies . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.5.2 Role Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5.3 Roles and Credibilities . . . . . . . . . . . . . . . . . . . . . . 64
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6 Information Acquisition from a Multi-agent Environment 67
6.1 Schoenmakers Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.2 Combining Information from Multiple Agents; the triviality result . . 69
6.3 Information Acquisition in a Belief Dependence Framework . . . . . . 74
6.4 Almost Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.5 Almost Safety on Belief Maintenance Operation . . . . . . . . . . . . 79
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7 Conclusions and Further Work 85
7.1 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
7.2 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
7.2.1 More General Semantic Models . . . . . . . . . . . . . . . . . 85
7.2.2 Other Complexity Problems . . . . . . . . . . . . . . . . . . . 86
7.2.3 Alternative Almost Safety Belief Maintenance Operations . . . 87
II Action Logics for Agents with Bounded Rationality 89
8 Introduction 91
8.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8.2 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 92
8.3 Conditional and Update . . . . . . . . . . . . . . . . . . . . . . . . . 95
Contents vii
8.3.1 Counterfactuals and Conditional Logic . . . . . . . . . . . . . 95
8.3.2 Reasoning about Actions . . . . . . . . . . . . . . . . . . . . . 97
8.3.3 Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
9 Preference Logics 99
9.1 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
9.2 A Preference Logic Based on the Notion of Minimal Change . . . . . 101
9.2.1 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
9.2.2 Formal Semantics (MCP-Semantics) . . . . . . . . . . . . . . 102
9.2.3 An Axiomatic Characterization of Preference Relations . . . . 104
9.3 From Preference Statements to Preferences on Possible Worlds . . . . 109
9.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.4.1 Other Approaches to Preference Logic . . . . . . . . . . . . . 113
9.4.2 Counterexamples . . . . . . . . . . . . . . . . . . . . . . . . . 114
9.5 Transitivity of Preferences . . . . . . . . . . . . . . . . . . . . . . . . 115
10 ALX1: A Propositional ALX Logic 119
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
10.2 Formal Syntax and Semantics . . . . . . . . . . . . . . . . . . . . . . 119
10.2.1 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
10.2.2 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
10.3 Formal Properties of ALX1 . . . . . . . . . . . . . . . . . . . . . . . 123
10.4 Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
10.5 The Finite Model Property of ALX1 . . . . . . . . . . . . . . . . . . 134
10.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
10.6.1 Goodness, Badness and Indifference . . . . . . . . . . . . . . . 145
10.6.2 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
10.6.3 Minimal Change and Actions . . . . . . . . . . . . . . . . . . 147
11 ALX3: A Multi-agent ALX Logic 155
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
11.2 Formal Syntax and Semantics . . . . . . . . . . . . . . . . . . . . . . 155
11.2.1 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
11.2.2 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
11.3 Formal Properties of ALX3 . . . . . . . . . . . . . . . . . . . . . . . 160
11.3.1 Soundness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
11.3.2 More Properties about Action Operators . . . . . . . . . . . . 161
11.4 Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
11.5 More Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
11.5.1 Necessity and Possibility . . . . . . . . . . . . . . . . . . . . . 174
11.5.2 Beliefs and Knowledge . . . . . . . . . . . . . . . . . . . . . . 178
11.6 Application of ALX3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
11.6.1 Second Order Quantifier on Preference Formulas . . . . . . . . 179
11.6.2 Agents and Accessible States . . . . . . . . . . . . . . . . . . 184
11.6.3 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
viii Contents
11.6.4 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
11.6.5 Cooperation and Coordination . . . . . . . . . . . . . . . . . . 191
11.7 Comparing ALX with Other Action Logics . . . . . . . . . . . . . . . 192
11.7.1 Other Action Logics . . . . . . . . . . . . . . . . . . . . . . . 192
11.7.2 Expressibility in Other Action Logics . . . . . . . . . . . . . . 193
11.7.3 Avoidance of Counterintuitive Properties . . . . . . . . . . . . 194
11.7.4 Comparison by Examples . . . . . . . . . . . . . . . . . . . . 195
11.8 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
11.8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
11.8.2 Bounded Rationality . . . . . . . . . . . . . . . . . . . . . . . 196
Bibliography 199
Index 206
List of symbols 210
Samenvatting 213