A Logical Theory of Nonmonotonic Inference and Belief Change

1. Front Matter

   Pages I-XII

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2. Introduction

   1. Introduction

      • Alexander Bochman

      Pages 1-10

3. The Framework

   1. Front Matter

      Pages 11-11

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   2. Consequence Relations

      • Alexander Bochman

      Pages 13-41

   3. Epistemic States

      • Alexander Bochman

      Pages 43-76

   4. Similarity, Equivalence and Decomposition of Epistemic States

      • Alexander Bochman

      Pages 77-110

   5. Epistemic Entrenchment and Its Relatives

      • Alexander Bochman

      Pages 111-134

4. Nonmonotonic Inference

   1. Front Matter

      Pages 135-135

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   2. The Basic Inference Relation

      • Alexander Bochman

      Pages 137-161

   3. Skeptical Inference Relations

      • Alexander Bochman

      Pages 163-212

   4. Prolegomena to a Theory of Defeasible Entailment

      • Alexander Bochman

      Pages 213-250

   5. Credulous Nonmonotonic Inference

      • Alexander Bochman

      Pages 251-269

   6. Contraction Inference

      • Alexander Bochman

      Pages 271-317

5. Belief Change

   1. Front Matter

      Pages 319-319

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   2. Belief Change and Its Problems

      • Alexander Bochman

      Pages 321-343

   3. Contractions of Epistemic States

      • Alexander Bochman

      Pages 345-378

   4. Merge and Expansion

      • Alexander Bochman

      Pages 379-402

   5. Compound and Derived Changes

      • Alexander Bochman

      Pages 403-424

6. Back Matter

   Pages 425-435

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The main subject and objective of this book are logical foundations of non­ monotonic reasoning. This bears a presumption that there is such a thing as a general theory of non monotonic reasoning, as opposed to a bunch of systems for such a reasoning existing in the literature. It also presumes that this kind of reasoning can be analyzed by logical tools (broadly understood), just as any other kind of reasoning. In order to achieve our goal, we will provide a common logical basis and semantic representation in which different kinds of non monotonic reasoning can be interpreted and studied. The suggested framework will subsume ba­ sic forms of nonmonotonic inference, including not only the usual skeptical one, but also various forms of credulous (brave) and defeasible reasoning, as well as some new kinds such as contraction inference relations that express relative independence of pieces of data. In addition, the same framework will serve as a basis for a general theory of belief change which, among other things, will allow us to unify the main approaches to belief change existing in the literature, as well as to provide a constructive view of the semantic representation used. This book is a monograph rather than a textbook, with all its advantages (mainly for the author) and shortcomings (for the reader).

• Nonmonotonic reasoning
• artificial intelligence
• belief change
• epistemic logic
• formal methods
• fuzzy systems
• intelligence
• knowledge
• knowledge representation
• knowledge-based systems
• logic
• mathematical logics
• multi-agent systems
• nonmonotonic logics
• uncertainty

From the reviews:

"This text provides a broad overview of topics related to non-classical consequence operators, nonmonotonic inference and belief change. The presentation is abstract and precise, and is grounded in a formal setting of logic." (Miroslav Truszezynski, Mathematical Reviews, Issue 2002 b)

"The author does not merely present a digest of work that has already entered the mainstream. He gives the subject an individual shape based on concepts that he has himself developed in a series of recent papers. … In brief, the book is based on a novel and coherent vision, developed according to a definite overall plan to yield non-trivial results ... ." (David Makinson, Zentralblatt MATH, Vol. 977, 2002)

• Computer Science Department, Holon Academic Institute of Technology (HAIT), Holon, Israel

  Alexander Bochman

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