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Conditionals in Nonmonotonic Reasoning and Belief Revision : Considering Conditionals as Agents - Gabriele Kern-Isberner

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Conditionals in Nonmonotonic Reasoning and Belief Revision

Considering Conditionals as Agents

By: Gabriele Kern-Isberner

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Paperback | 25 July 2001

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208 Pages

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22.86 x 15.24 x 1.27

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Conditionals are omnipresent, in everyday life as well as in scientific environments; they represent generic knowledge acquired inductively or learned from books. They tie a flexible and highly interrelated network of connections along which reasoning is possible and which can be applied to different situations. Therefore, conditionals are important, but also quite problematic objects in knowledge representation.
This book presents a new approach to conditionals which captures their dynamic, non-proportional nature particularly well by considering conditionals as agents shifting possible worlds in order to establish relationships and beliefs. This understanding of conditionals yields a rich theory which makes complex interactions between conditionals transparent and operational. Moreover,it provides a unifying and enhanced framework for knowledge representation, nonmonotonic reasoning, belief revision,and even for knowledge discovery.

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Computing & I.T.Computer Science Artificial Intelligence Expert Systems & Knowledge-Based Systems Medicine Medicine in General Mathematical Theory of Computation

Introduction	p. 1
öBelieve It or Notö - The Handling of Uncertain Knowledge	p. 1
Overview	p. 5
Basic Definitions and Notations	p. 8
Propositional and Conditional Expressions	p. 8
Probabilistic Logics	p. 9
Belief Revision and Nonmonotonic Reasoning - State of the Art	p. 11
Nonmonotonic Reasoning	p. 12
Belief Revision	p. 13
Nonmonotonic Reasoning and Belief Revision - Two Sides of the Same Coin?	p. 17
Iterated Revision, Epistemic States, and Conditionals	p. 17
Probabilistic Reasoning - The ME-Approach	p. 23
Conditionals	p. 27
Conditionals and Epistemic States	p. 27
Conditional Valuation Functions	p. 31
Conditional Valuation Functions and Beliefs	p. 34
A Dynamic View on Conditionals	p. 36
Conditional Structures	p. 39
Conditional Indifference	p. 48
Revising Epistemic States by Conditional Beliefs	p. 53
Postulates for Revising by Conditional Beliefs	p. 54
Representation Theorems	p. 56
Conditional Valuation Functions and Revision	p. 57
A Revision Operator for Ordinal Conditional Functions	p. 60
The Principle of Conditional Preservation	p. 62
C-Revisions and C-Representations	p. 66
Characterizing the Principle of Minimum Cross-Entropy	p. 73
Conditional Preservation	p. 75
The Functional Concept	p. 80
Logical Coherence	p. 85
Representation Invariance	p. 87
Uniqueness and the Main Theorem	p. 89
Reasoning at Optimum Entropy	p. 91
Probabilistic Consequence and Probabilistic Inference	p. 92
Basic Properties of the ME-Inference Operation	p. 93
ME-Logic and Conditionals	p. 95
ME-Deduction Rules	p. 97
Chaining Rules	p. 98
Cautious Monotonicity and Cautious Cut	p. 99
Conjoining Literals in Antecedent and Consequent	p. 100
Reasoning by Cases	p. 101
Belief Revision and Nonmonotonic Reasoning - Revisited	p. 103
Universal Inference Operations	p. 104
Simultaneous and Successive Revision	p. 108
Separating Background from Evidential Knowledge	p. 109
Revising Epistemic States by Sets of Conditionals	p. 112
Revision versus Updating	p. 114
Focusing in a Probabilistic Framework	p. 116
Knowledge Discovery by Following Conditional Structures	p. 119
Probabilistic Knowledge Discovery	p. 120
Discovering Conditional Structures	p. 122
Examples - ME-Knowledge Discovery	p. 131
Open Problems and Concluding Remarks	p. 134
Algorithms and Implementations	p. 137
ME-Reasoning with Probabilistic Conditionals	p. 137
Probabilistic Knowledge Discovery	p. 138
Possibilistic Belief Revision	p. 139
Conclusion	p. 141
Proofs	p. 145
Bibliography	p. 175
Index	p. 187
Table of Contents provided by Publisher. All Rights Reserved.

Conditionals in Nonmonotonic Reasoning and Belief Revision

Considering Conditionals as Agents

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Paperback

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