Nonmonotonic Logic: Context-Dependent Reasoning

Overview

This monograph provides a thorough analysis of two important formalisms for nonmonotonic reasoning: default logic and modal nonmonotonic logics. It is also shown how they are related to each other and how they provide the formal foundations for logic programming. The discussion is rigorous, and all main results are formally proved. Many of the results are deep and surprising, some of them previously unpublished.
The book has three parts, on ...
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Paperback (Softcover reprint of the original 1st ed. 1993)
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Overview

This monograph provides a thorough analysis of two important formalisms for nonmonotonic reasoning: default logic and modal nonmonotonic logics. It is also shown how they are related to each other and how they provide the formal foundations for logic programming. The discussion is rigorous, and all main results are formally proved. Many of the results are deep and surprising, some of them previously unpublished.
The book has three parts, on default logic, modal nonmonotonic logics, and connections and complexity issues,
respectively. The study of general default logic is followed by a discussion of normal default logic and its connections to the closed world assumption, and also a presentation of related aspects of logic programming. The general theory of the family of modal nonmonotonic logics introduced by
McDermott and Doyle is followed by studies of autoepistemic logic, the logic of reflexive knowledge, and the logic of pure necessitation, and also a short discussion of algorithms for computing knowledge and belief sets. The third part explores connections between default logic and modal nonmonotonic logics and contains results on the complexity of nonmonotonic reasoning.
The ideas are presented with an elegance and unity of perspective that set a new standard of scholarship for books in this area, and the work indicates that the field has reached a very high level of maturity and sophistication.
The book is intended as a reference on default logic,
nonmonotonic logics, and related computational issues, and is addressed to researchers, programmers, and graduate students in the Artificial Intelligence community.
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Product Details

  • ISBN-13: 9783662029084
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 12/28/2012
  • Series: Artificial Intelligence Series
  • Edition description: Softcover reprint of the original 1st ed. 1993
  • Pages: 420
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.89 (d)

Table of Contents

1 Introduction.- 2 Rudiments of logic and set theory.- 3 General default theories.- 4 Normal default theories.- 5 Representation theory for default logic.- 6 Logic programming and nonmonotonic reasoning.- 7 Modal logic.- 8 Stable theories.- 9 Modal nonmonotonic logics.- 10 Nonmonotonic logic of pure necessitation and autoepistemic logics.- 11 Topics in modal nonmonotonic logic.- 12 Relations among nonmonotonic formalisms.- 13 Complexity of some forms of nonmonotonic reasoning.- References.
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