Conditionals in nonmonotonic reasoning and belief revision( 非单调推理与信念修正的条件 )

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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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.

1.Introduction
1.1 "Believe It or Not" -The Handling of Uncertain Knowledge
1.2 Overview
1.3 Basic Definitions and Notations
1.3.1 Propositional and Conditional Expressions
1.3.2 Probabilistic Logics
2.Belief Revision and Nonmonotonic Reasoning - State of the Art
2.1 Nonmonotonic Reasoning
2.2 Belief Revision
2.3 Nonmonotonic Reasoning and Belief Revision -Two Sides of the Same Coin?
2.4 Iterated Revision, Epistemic States, and Conditionals
2.5 Probabilistic Reasoning - The ME-Approach
3.Conditionals
3.1 Conditionals and Epistemic States
3.2 Conditional Valuation Functions
3.3 Conditional Valuation Functions and Beliefs
3.4 A Dynamic View on Conditionals
3.5 Conditional Structures
3.6 Conditional Indifference
4.Revising Epistemic States by Conditional Beliefs
4.1 Postulates for Revising by Conditional Beliefs
4.2 Representation Theorems
4.3 Conditional Valuation Functions and Revision
4.4 A Revision Operator for Ordinal Conditional Functions
4.5 The Principle of Conditional Preservation
4.6 C-Revisions and C-Representations
5.Characterizing the Principle of Minimum Cross-Entropy .
5.1 Conditional Preservation
5.2 The Functional Concept
5.3 Logical Coherence
5.4 Representation Invariance
5.5 Uniqueness and the Main Theorem
6.Reasoning at Optimum Entropy
6.1 Probabilistic Consequence and Probabilistic Inference
6.2 Basic Properties of the ME-Inference Operation
6.3 ME-Logic and Conditionals
6.4 ME-Deduction Rules
6.4.1 Chaining Rules
6.4.2 Cautious Monotonicity and Cautious Cut
6.4.3 Conjoining Literals in Antecedent and Consequent
6.4.4 Reasoning by Cases
7.Belief Revision and Nonmonotonic Reasoning - Revisited
7.1 Universal Inference Operations
7.2 Simultaneous and Successive Revision
7.3 Separating Background from Evidential Knowledge
7.4 Revising Epistemic States by Sets of Conditionals
7.5 Revision versus Updating
7.6 Focusing in a Probabilistic Framework
8.Knowledge Discovery by Following Conditional Structures
8.1 Probabilistic Knowledge Discovery
8.2 Discovering Conditional Structures
8.3 Examples - ME-Knowledge Discovery
8.4 Open Problems and Concluding Remarks
9.Algorithms and Implementations
9.1 ME-Reasoning with Probabilistic Conditionals
9.2 Probabilistic Knowledge Discovery
9.3 Possibilistic Belief Revision
10. Conclusion
A.Proofs
Bibliography
Index