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1 edition of Nonmonotonic Logic found in the catalog.

Nonmonotonic Logic

Context-Dependent Reasoning

by V. Wiktor Marek

  • 6 Want to read
  • 22 Currently reading

Published by Springer Berlin Heidelberg in Berlin, Heidelberg .
Written in English

    Subjects:
  • Symbolic and mathematical Logic,
  • Computer science,
  • Artificial intelligence

  • About the Edition

    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 Many of the results are deep and surprising, some of them previously unpublished.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.

    Edition Notes

    Statementby V. Wiktor Marek, Mirosław Truszczyński
    SeriesArtificial Intelligence, Artificial Intelligence
    ContributionsTruszczyński, Mirosław
    Classifications
    LC ClassificationsQ334-342, TJ210.2-211.495
    The Physical Object
    Format[electronic resource] :
    Pagination1 online resource (xiv, 420 p.)
    Number of Pages420
    ID Numbers
    Open LibraryOL27077689M
    ISBN 103662029081, 3662029065
    ISBN 109783662029084, 9783662029060
    OCLC/WorldCa851389426

    These bridge systems, which are called 'paraclassical' logics, are very simple to define and easy to study. Specialists in nonmonotonic reasoning can also benefit from reading the chapters discussing the author's proposals. This information helps us design a better experience for all users. They alert us when OverDrive services are not working as expected.

    The final prices may differ from the prices shown due to specifics of VAT rules About this book When I first participated in exploring theories of nonmonotonic reasoning in the late s, I had no idea of the wealth of conceptual and mathematical results that would emerge from those halting first steps. The text shows that there are logics that act as natural bridges between classical consequence and the principal kinds of nonmonotonic logic to be found in the literature. Please review the types of cookies we use below. Then it considers ways of getting similar results by excluding certain classical valuations, and a third means to the same end, adding rules alongside the premises. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations.

    To learn more about how we use and protect your data, please see our privacy policy. For example, the most likely explanation for seeing wet grass is that it rained; however, this explanation has to be retracted when learning that the real cause of the grass being wet was a sprinkler. Nonmonotonic reasoning methods provide rigor similar to that of classical reasoning; they form a base for validation and verification and therefore increase confidence in intelligent systems that work with incomplete and changing information. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained. Marek, SIGART Bulletin "One group who would find this book useful is PhD researchers in logic and AI embarking on research programmes in nonmonotonic reasoning: before committing themselves to any particular approach they should read this book thoroughly.


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Nonmonotonic Logic book

However, at this point, Nonmonotonic Reasoning starts throwing in some more unusual topics. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together.

It provides recapitulations at the end of each chapter, exercises and problems, selected solutions to them, suggested projects, and guides to further reading. On the second, or non-monotonic, approach, constraints are placed on inputs and sometimes on outputs of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference.

Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false.

The book examines the three bridges one by one. It is particularly appropriate that Marek and Truszczynski should have authored this book, since so much of the research that went into these results is due to them. Dialetheic logics are a case in point.

A Tour Through Mathematical Logic

Free shipping for individuals worldwide Usually dispatched within 3 to 5 business days. An abductive logic should not be monotonic because the most likely explanations are not necessarily correct. This information helps us design a better experience for all users.

Since the idea was first mooted around ,1 there has been a vast amount of work under the banner of nonmonotonic reasoning, and it is neither surprising nor unreasonable that Antoniou only covers part of the territory.

Nonmonotonic theorem proving; 4. Grigoris Antoniou's Nonmonotonic Reasoning is just such a milestone-well written, informative, and a good source of information on an important and complex subject.

Two final chapters serve to locate nonmonotonic reasoning in a wider landscape. Without these cookies, we won't know if you have any performance-related issues that we may be able to address. Research and analytics cookies These cookies help us understand user behavior within our services.

Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. Unlike some proof-theoretic formalizations that suffered from well-known paradoxes and were often hard to evaluate with respect of their consistency with the intuitions they were supposed to capture, model-theoretic formalizations were paradox-free and left little, if any, room for confusion about what non-monotonic patterns of reasoning they covered.

Handbook of the History of Logic, Volume 8: The Many Valued and Nonmonotonic Turn in Logic

A logic for reasoning about knowledge is the autoepistemic logic. In the assumption that the new belief is correct, some of the old ones have to be retracted in order to maintain consistency.The purpose of this book is to take the mystery out of the subject, giving a clear overall picture of what is going on.

It makes the essential ideas and main approaches to nonmonotonic logic accessible, and meaningful, to anyone with a few basic tools of discrete mathematics and a minimal background in classical propositional logic.

Handbook of the History of Logic, Volume 8 book. Read reviews from world’s largest community for readers. The present volume of the Handbook of the Histo 4/5(1). Aug 13,  · Read "The Many Valued and Nonmonotonic Turn in Logic" by available from Rakuten Kobo.

The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20t. This book constitutes the refereed proceedings of the 5th Internationa l Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR '9 9, held in El Paso, Texas, USA, in December The volume presents 26 contributed papers and four invited talks, three appearing as exten ded Author: Michael Gelfond.

The relationship between nonmonotonic reasoning and logic is part of a larger story of the relations between AI and logic (see View chapter Purchase book. The Many Valued and Nonmonotonic Turn in Logic.

Grigoris Antoniou, Kewen Wang, in Handbook of the History of Logic, Legal Rules, Legal Reasoning, and Nonmonotonic Logic by Adam W. Rigoni A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Philosophy) in the University of Michigan Doctoral Committee: Professor Richmond H.

Thomason, Chair Professor Kevin D. Ashley, University of Pittsburgh.

Miroslaw Truszczynski