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E-raamat: Rational Reasoning with Finite Conditional Knowledge Bases: Theoretical and Implementational Aspects

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  • Ilmumisaeg: 28-Dec-2018
  • Kirjastus: J.B. Metzler
  • Keel: eng
  • ISBN-13: 9783476048240
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 28-Dec-2018
  • Kirjastus: J.B. Metzler
  • Keel: eng
  • ISBN-13: 9783476048240

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Nonmonotonic reasoning is a discipline of computer science, epistemology, and cognition: It models inferences where classical logic is inadequate in symbolic AI, defines normative models for reasoning with defeasible information in epistemology, and models human reasoning under information change in cognition. Its building blocks are defeasible rules formalised as DeFinetti conditionals. In this thesis, Christian Eichhorn examines qualitative and semi-quantitative inference relations on top said conditionals, using the conditional structure of the knowledge base and Spohn"s Ordinal Conditional Functions, using established properties. Converting network approaches from probabilistics, he shows how to approach the relations with regard to implementation.

Contents Properties of Nonmonotonic Reasoning.- Reasoning with Sets of c-Representations.- Network Approaches to Ordinal Conditional Functions.- Formal Inferences and Commonsense Reasoning: Connections to Psychology and Cognition.

The Author Christian Eichhorn received his doctorate from the Computer Science Department at the Technical University, Dortmund. His research was supported by the interdisciplinary Priority Programme SPP1516 "New Frameworks of Rationality" of the Deutsche Forschungsgemeinschaft.
1 Introduction
1(14)
1.1 Context and Motivation
1(4)
1.2 Research Questions
5(5)
1.3 Own contributions to joint articles
10(1)
1.4 Overview
11(4)
2 Preliminaries
15(22)
2.1 Propositional Logic and Satisfaction
15(4)
2.2 Conditionals and Knowledge Bases
19(10)
2.3 Inference Relations
29(3)
2.4 Graphs and Hypergraphs
32(4)
2.5 Interim Summary
36(1)
3 Basic Techniques
37(40)
3.1 Preferential Models and Preferential Inference
37(3)
3.2 Conditional Structures
40(4)
3.3 Ordinal Conditional Functions (OCF)
44(20)
3.3.1 Definition and Properties
45(8)
3.3.2 Inference with OCF
53(1)
3.3.3 Inductive Approaches to Generating OCF
54(1)
3.3.3.1 System Z
54(1)
3.3.3.2 System Z+
55(4)
3.3.3.3 c-Representations
59(5)
3.4 Probabilistic Reasoning
64(4)
3.5 Bayesian Networks and LEG Networks
68(5)
3.6 Ceteris Paribus Networks
73(3)
3.7 Interim Summary
76(1)
4 Properties of Nonmonotonic Inference Relations
77(56)
4.1 Axiom Systems for Nonmonotonic Reasoning
77(29)
4.1.1 Introduction and Common Properties
77(3)
4.1.2 System O
80(6)
4.1.3 System C
86(9)
4.1.4 System P
95(5)
4.1.5 System R
100(6)
4.2 Selected Formal Properties of Nonmonotonic Inference
106(5)
4.3 Properties of Structural Inference
111(8)
4.4 Properties of Ranking Inference
119(4)
4.5 Properties of Inference with System Z
123(3)
4.6 Properties of Inference with c-Representations
126(3)
4.7 Interim Summary
129(4)
5 Reasoning with Sets of c-Representations
133(26)
5.1 c-Representations as Constraint Satisfaction Problems
133(4)
5.2 Properties of Inference with Sets of c-Representations
137(12)
5.3 Reasoning with Sets of Preferred c-Representations
149(5)
5.4 Interim Summary and Discussion
154(5)
6 Normal Forms of Conditional Knowledge Bases
159(10)
6.1 Equivalences for Conditional Knowledge Bases
159(2)
6.2 Transformation Systems for Knowledge Bases
161(6)
6.3 Interim Summary
167(2)
7 Networks for Compact Representation and Implementation
169(84)
7.1 OCF-Networks
170(31)
7.1.1 Structure and Properties
171(4)
7.1.2 Inductive Generation of OCF-Networks
175(1)
7.1.2.1 ... Network Component
176(3)
7.1.2.2 ... OCF-Component w/Semi-Quantitat. KB
179(8)
7.1.2.3 Complexity Results
187(2)
7.1.2.4 Correctness Results
189(6)
7.1.2.5 ... OCF-component w/Qualitative KB
195(3)
7.1.3 Discussion
198(1)
7.1.4 Interim Summary
199(2)
7.2 Comparing OCF- and CP-networks
201(24)
7.2.1 Plain Generation OCF-Networks ↔ CP-Networks
201(11)
7.2.2 Bottom-Up Induction of OCF-Networks
212(10)
7.2.3 Interim Summary and Discussion
222(3)
7.3 OCF-LEG Networks
225(27)
7.3.1 Basic Definition and Properties
225(5)
7.3.2 Inductive Generation
230(15)
7.3.3 Further Reflections on the Consistency Condition
245(3)
7.3.4 Discussion and Comparison to OCF-Networks
248(2)
7.3.5 Interim Summary
250(2)
7.4 Interim Summary of the
Chapter
252(1)
8 Connections to Psychology and Cognition
253(38)
8.1 Simulating Human Inference in the Suppression Task
254(21)
8.1.1 Modelling the Suppression Task
255(10)
8.1.2 Background Knowledge in the Suppression Task
265(4)
8.1.3 Strengthening / Weakening in the Suppression Task
269(6)
8.2 Inference Patterns
275(13)
8.3 Interim Conclusion and Discussion
288(3)
9 Summary and Final Remarks
291(4)
9.1 Summary
291(1)
9.2 Further and Future Work
291(2)
9.3 Conclusion
293(2)
A Proofs of Technical Findings
295(52)
A.1 Proofs for
Chapter 2
295(3)
A.2 Proofs for
Chapter 3
298(7)
A.3 Proofs for
Chapter 4
305(8)
A.4 Proofs for
Chapter 5
313(11)
A.5 Proofs for
Chapter 6
324(3)
A.6 Proofs for
Chapter 7
327(19)
A.7 Proofs for
Chapter 8
346(1)
Bibliography 347
The AuthorChristian Eichhorn received his doctorate from the Computer Science Department at the Technical University, Dortmund.  His research was supported by the interdisciplinary Priority Programme SPP1516 New Frameworks of Rationality of the Deutsche Forschungsgemeinschaft.