A logical approach to computational theory building: with applications to sociology
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
Inst. for Logic, Language and computation, Univ. van Amsterdam
2000
|
| Series: | Instituut voor Taal, Logica en Informatie <Amsterdam>: ILLC dissertation series
2000,2 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009298439&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Zugl.: Amsterdam, Univ., Diss., 2000 |
| Physical Description: | XVIII, 195 S. graph. Darst. |
| ISBN: | 9057760444 |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Table of Contents v
List of Illustrations ix
List of Tables xi
Acknowledgments xiii
Preliminaries xv
1 Introduction Overview 1
1.1 Overview 3
1.1.1 Introduction and Overview 3
1.1.2 Formal Theory Building Using Automated Reasoning Tools 3
1.1.3 A Formal Theory of Organizations in Action 5
1.1.4 Criteria for Formal Theory Building 5
1.1.5 The Process of Axioinatizing Scientific Theories G
1.1.6 Partial Deductive Closure 7
1.1.7 Qualitative Reasoning beyond the Physics Domain .... S
1.1.8 Discussion and Related Work 0
2 Formal Theory Building Using Automated Reasoning Tools 11
2.1 Introduction 11
2.2 Formal Theory Building 12
2.3 A Social Science Case Study 15
2.3.1 Hopkins Theory of Small Groups 15
2.3.2 Fonnalization 17
2.3.3 Soundness of Argumentation 19
2.3.4 Consistency of the Theory 22
v
vj Contents
2.3.5 Satisfiability, Falsifiability, and Contingence 23
2.3.6 Examining the Theorems 25
2.3.7 Examining the Axioms 27
2.3.8 Minimal Sets of Axioms 31
2.3.9 Recapitulating 33
2.4 Discussion and Conclusions 34
3 Reducing Uncertainty: A Formal Theory of Organizations in
Action 37
3.1 Introduction 37
3.2 Research Methodology: Logical Formalization 38
3.2.1 The Product of Logical Formalization 39
3.2.2 The Process of Logical Formalization 41
3.3 Thompson s Organizations in Action 42
3.3.1 Complex Organizations 44
3.3.2 Sealing Off 47
3.3.3 Beyond Thompson: Atomic Organizations 50
3.3.4 Buffering and Anticipating 54
3.3.5 Smoothing or Leveling 58
3.3.6 Beyond Thompson: Negotiating 60
3.4 Discussion and Conclusions 63
3.4.1 Related and further research 66
4 Criteria for Formal Theory Building 71
4.1 Introduction 71
4.2 Logical formalization 72
4.2.1 Criteria for Evaluating Theories 73
4.2.2 Computational tools 76
4.3 Case Study: A Formal Theory of Organizations in Action 77
4.4 Discussion and Conclusions 84
5 The Process of Axiomatizing Scientific Theories 87
5.1 Introduction 87
5.2 Axiomatizing Theories 88
5.2.1 The Product of Formalization 88
5.2.2 The Process of Formalization 89
5.3 Case Study: Zetterberg s Theory 91
5.3.1 Formalization 92
5.3.2 Axioms 93
5.3.3 Theorems 94
5.3.4 Recapitulating 96
5.4 Revision gg
5.4.1 Limit Explanatory/Predictive Power 96
Contents vii
5.4.2 Nonintended Models and Real Counterexamples 97
5.4.3 Weaken Theorems 99
5.4.4 Strengthen Axioms 100
5.4.5 Proposition 10 103
5.4.6 Recapitulating 105
5.5 Discussion and Conclusions 107
6 Partial Deductive Closure 109
6.1 Introduction 109
6.2 Developing Theories with Logical Tools Ill
6.3 Deduction of Theorems 113
6.3.1 Informal Description of the Algorithm 113
6.3.2 Formal Specification 114
6.4 Inertia Fragment of Organizational Ecology 119
6.5 Application of PDC 1 to the Inertia Fragment 124
6.6 Discussion and Conclusions 127
7 Qualitative Reasoning beyond the Physics Domain 131
7.1 Introduction 131
7.2 Representational Context 132
7.3 The Density Dependence Theory 133
7.4 Applying the Theory 134
7.5 Qualitative Density Dependence 136
7.6 Results 139
7.7 Discussion 142
7.7.1 Finding the Right Model for the Job 142
7.7.2 Finding the Right Job for the Model 143
8 Discussion Related Work 145
8.1 Computational Theory Building 145
8.2 Formal Theory 117
8.3 Logical Criteria 150
8.4 The Process of Axiomatization 15!
8.5 Discovery? 100
8.6 Sociology 163
Bibliography 169
Index 187
Abstract (in Dutch) 191
Illustrations
2.1 Hopkins axioms (based on page 52) 17
3.1 Reducing uncertainty (structure of the theory 1) 47
3.2 Sealing off (structure of the theory 2) 49
3.3 Atomic organizations (structure of the theory 3) 54
3.4 Buffering and anticipating (structure of the theory 4) 57
3.5 Smoothing (structure of the theory 5) 60
3.6 Negotiating (structure of the theory 6) 63
4.1 Inferences in the Formal Theory 82
6.1 The logical cycle 112
6.2 The assumptions (An) and theorems (Trc) of the inertia fragment. 128
7.1 Legitimation and competition as functions of density 135
7.2 Growth rate as a function of density 135
7.3 Expected behavior for an empty environment 136
7.4 Dependencies of qualitative density dependence 137
7.5 Case A: An empty environment 138
7.6 Case B: A population in equilibrium 138
7.7 Case C: An overcrowded environment 139
7.8 Monotonically growing population 140
7.9 Forever expanding population 141
7.10 Expected behavior for an overcrowded environment 141
ix
Tables
2.1 Properties of groups and corresponding status properties 16
2.2 The propositions of Hopkins Theory 18
2.3 Functions and relations used in the formalization 18
2.4 A formal version of Hopkins axioms 19
2.5 A formal version of Hopkins theorems 19
2.6 A model of Hopkins axioms 22
2.7 A model in which T.3 is false 23
2.8 A model in which T.5 is false 24
2.9 A model in which T.10 is false 24
2.10 A model in which T.ll is false 24
2.11 A model in which T.13 is false 24
2.12 A model in which T.I5 is false 24
2.13 The missing propositions of Hopkins 25
2.14 Further theorems 26
2.15 A model in which A.I is false, and the other axioms hold 29
2.16 A model in which A.14 is false, and the other axioms hold 30
2.17 A minimal axiom set for Hopkins theory 31
2.18 A model in which A.4 is false, and the axioms A.I. A.7. A.8. and
A.14 hold 32
2.19 A model in which A.7 is false, and the axioms A.I. A.4, A.8. and
A.14 hold 32
2.20 A model in which A.8 is false, and the axioms A.I. A.4. A.7. and
A.14 hold 32
2.21 A second minimal axiom set for Hopkins theory 32
3.1 Propositions of Thompson s Chapter 2 43
3.2 Reduction of Constraints in the Environment . 61
3.3 Notation Used in the Formal Theory 64
xi
xjj Tables
4.1 Criteria and Automated Reasoning Tools 76
4.2 Predicates (Kamps and Polos 1999) 78
4.3 A Formal Theory of Organizations in Action (Kamps and Polos
1999) 79
4.4 Evaluating the Theory 80
4.5 A Model of the Theory (only primitives) 81
4.6 Selected Defined Predicates (extending Table 4.5) 81
5.1 The propositions of Zetterberg s theory 92
5.2 Functions and predicates 93
5.3 A formalization of Propositions 7 10 93
5.4 A model of Axioms 7 10 93
5.5 A formalization of Propositions 1 6 94
5.6 Counterexample to Propositions 2 95
5.7 Counterexample to Propositions 4 95
5.8 The Verbal and Formal Theory 96
5.9 Background assumptions 97
5.10 Counterexamples to Propositions 2 98
5.11 Counterexamples to Propositions 4 98
5.12 Revised formalization of Propositions 7 9 102
5.13 A model of Axioms A.7*, A.8*, A.9*, and A.10 102
5.14 A revised formalization of Theorems 1 3 103
5.15 Revised formalization of Propositions 10 104
5.16 A revised formalization of Theorems 4 6 104
5.17 The Verbal and Formal Theory 105
5.18 Four Formal Version of the Theory 105
5.19 Number of Models on a Simple Domain 106
6.1 Premise sets and theorems 115
6.2 The Inertia Fragment of Organizational Ecology 120
6.3 The meaning of the relation symbols 121
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| indexdate | 2024-12-20T10:50:27Z |
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| publisher | Inst. for Logic, Language and computation, Univ. van Amsterdam |
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| series | Instituut voor Taal, Logica en Informatie <Amsterdam>: ILLC dissertation series |
| series2 | Instituut voor Taal, Logica en Informatie <Amsterdam>: ILLC dissertation series |
| spellingShingle | Kamps, Jaap A logical approach to computational theory building with applications to sociology Instituut voor Taal, Logica en Informatie <Amsterdam>: ILLC dissertation series Mathematische Logik (DE-588)4037951-6 gnd Soziologie (DE-588)4077624-4 gnd Automatentheorie (DE-588)4003953-5 gnd Theoriebildung (DE-588)4185105-5 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4077624-4 (DE-588)4003953-5 (DE-588)4185105-5 (DE-588)4113937-9 |
| title | A logical approach to computational theory building with applications to sociology |
| title_auth | A logical approach to computational theory building with applications to sociology |
| title_exact_search | A logical approach to computational theory building with applications to sociology |
| title_full | A logical approach to computational theory building with applications to sociology Jaap Kamps |
| title_fullStr | A logical approach to computational theory building with applications to sociology Jaap Kamps |
| title_full_unstemmed | A logical approach to computational theory building with applications to sociology Jaap Kamps |
| title_short | A logical approach to computational theory building |
| title_sort | a logical approach to computational theory building with applications to sociology |
| title_sub | with applications to sociology |
| topic | Mathematische Logik (DE-588)4037951-6 gnd Soziologie (DE-588)4077624-4 gnd Automatentheorie (DE-588)4003953-5 gnd Theoriebildung (DE-588)4185105-5 gnd |
| topic_facet | Mathematische Logik Soziologie Automatentheorie Theoriebildung Hochschulschrift |
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