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Logical Structures for Representation of Knowledge and Uncertainty

  • Ellen Hisdal

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 14)

Table of contents

  1. Front Matter
    Pages I-XXIII
  2. Introduction

    1. Ellen Hisdal née Gruenwald
      Pages 1-31
  3. BP Logic

    1. Front Matter
      Pages 32-32
    2. Ellen Hisdal née Gruenwald
      Pages 33-51
    3. Ellen Hisdal née Gruenwald
      Pages 70-102
    4. Ellen Hisdal née Gruenwald
      Pages 103-130
    5. Ellen Hisdal née Gruenwald
      Pages 131-164
    6. Ellen Hisdal née Gruenwald
      Pages 165-181
    7. Ellen Hisdal née Gruenwald
      Pages 182-204
    8. Ellen Hisdal née Gruenwald
      Pages 205-223
  4. M Logic

    1. Front Matter
      Pages 224-224
    2. Ellen Hisdal née Gruenwald
      Pages 225-242
    3. Ellen Hisdal née Gruenwald
      Pages 243-255
    4. Ellen Hisdal née Gruenwald
      Pages 256-280
    5. Ellen Hisdal née Gruenwald
      Pages 281-300
    6. Ellen Hisdal née Gruenwald
      Pages 301-325
    7. Ellen Hisdal née Gruenwald
      Pages 326-345
    8. Ellen Hisdal née Gruenwald
      Pages 346-355
    9. Ellen Hisdal née Gruenwald
      Pages 356-379
  5. Attributes and The Alex System versus Chain Sets

    1. Front Matter
      Pages 380-380
    2. Ellen Hisdal née Gruenwald
      Pages 381-386
    3. Ellen Hisdal née Gruenwald
      Pages 387-398
  6. Back Matter
    Pages 399-419

About this book

Introduction

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.

Keywords

Unsicherheit Wissensrepräsentation artificial intelligence calculus künstliche Intelligenz representation of knowledge uncertainty

Authors and affiliations

  • Ellen Hisdal
    • 1
  1. 1.Department of InformaticsUniversity of OsloOsloNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7908-1887-1
  • Copyright Information Physica-Verlag Heidelberg 1998
  • Publisher Name Physica, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-7908-2458-2
  • Online ISBN 978-3-7908-1887-1
  • Series Print ISSN 1434-9922
  • Series Online ISSN 1860-0808
  • Buy this book on publisher's site