Studies in Fuzziness and Soft Computing

Logical Structures for Representation of Knowledge and Uncertainty

Authors: Hisdal, Ellen

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About this book

To answer questions concerning previously supplied information the book uses a truth table or 'chain set' logic which combines probabilities with truth values (= possibilities of fuzzy set theory). Answers to questions can be 1 (yes); 0 (no); m (a fraction in the case of uncertain information); 0m, m1 or 0m1 (in the case of 'ignorance' or insufficient information). Ignorance (concerning the values of a probability distribution) is differentiated from uncertainty (concerning the occurrence of an outcome). An IF THEN statement is interpreted as specifying a conditional probability value. No predicate calculus is needed in this probability logic which is built on top of a yes-no logic. Quantification sentences are represented as IF THEN sentences with variables. No 'forall' and 'exist' symbols are needed. This simplifies the processing of information. Strange results of first order logic are more reasonable in the chain set logic. E.g., (p->q) AND (p->NOTq), p->NOT p, (p->q)->(p->NOT q), (p->q)- >NOT(p->q), are contradictory or inconsistent statements only in the chain set logic. Depending on the context, two different rules for the updating of probabilities are shown to exist. The first rule applies to the updating of IF THEN information by new IF THEN information. The second rule applies to other cases, including modus ponens updating. It corresponds to the truth table of the AND connective in propositional calculus. Many examples of inferences are given throughout the book.

Table of contents (19 chapters)

  • Introduction

    Hisdal née Gruenwald, Ellen

    Pages 1-31

  • Chain Set and Probability Overview

    Hisdal née Gruenwald, Ellen

    Pages 33-51

  • BP Chain Sets I, Affirmation, Negation, Conjunction, Disjunction

    Hisdal née Gruenwald, Ellen

    Pages 52-69

  • BP Chain Sets II, Special Cases of Chain Sets

    Hisdal née Gruenwald, Ellen

    Pages 70-102

  • BP Chain Sets III, Precise Formulations

    Hisdal née Gruenwald, Ellen

    Pages 103-130

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-7908-1887-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-7908-1056-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-3-7908-2458-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Logical Structures for Representation of Knowledge and Uncertainty
Authors
Series Title
Studies in Fuzziness and Soft Computing
Series Volume
14
Copyright
1998
Publisher
Physica-Verlag Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-7908-1887-1
DOI
10.1007/978-3-7908-1887-1
Hardcover ISBN
978-3-7908-1056-1
Softcover ISBN
978-3-7908-2458-2
Series ISSN
1434-9922
Edition Number
1
Number of Pages
XXIV, 420
Topics