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Logical Structures for Representation of Knowledge and Uncertainty

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  • © 1998
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Overview

Authors:
  1. Ellen Hisdal

    1. Department of Informatics, University of Oslo, Oslo, Norway

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  • Describes a new truth table logic with built-in probabilities
  • Includes exercises and solutions to difficult exercises

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

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Table of contents (19 chapters)

  1. Front Matter

    Pages I-XXIII
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  2. Introduction

    1. Introduction

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

    1. Front Matter

      Pages 32-32
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    2. Chain Set and Probability Overview

      • Ellen Hisdal née Gruenwald
      Pages 33-51
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    3. BP Chain Sets I, Affirmation, Negation, Conjunction, Disjunction

      • Ellen Hisdal née Gruenwald
      Pages 52-69
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    4. BP Chain Sets II, Special Cases of Chain Sets

      • Ellen Hisdal née Gruenwald
      Pages 70-102
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    5. BP Chain Sets III, Precise Formulations

      • Ellen Hisdal née Gruenwald
      Pages 103-130
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    6. Inferences or the Answering of Questions

      • Ellen Hisdal née Gruenwald
      Pages 131-164
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    7. Inferences with Higher Level Chain Sets

      • Ellen Hisdal née Gruenwald
      Pages 165-181
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    8. IF THEN Information

      • Ellen Hisdal née Gruenwald
      Pages 182-204
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    9. Various IF THEN Topics

      • Ellen Hisdal née Gruenwald
      Pages 205-223
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  4. M Logic

    1. Front Matter

      Pages 224-224
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    2. The M-Notation and Ignorance vs Uncertainty

      • Ellen Hisdal née Gruenwald
      Pages 225-242
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    3. Two Types of Updating of Probabilities

      • Ellen Hisdal née Gruenwald
      Pages 243-255
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    4. Operations and Ignorance in the M Logic

      • Ellen Hisdal née Gruenwald
      Pages 256-280
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    5. Modus Ponens and Existence Updating

      • Ellen Hisdal née Gruenwald
      Pages 281-300
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    6. IF THEN Information in the M Logic

      • Ellen Hisdal née Gruenwald
      Pages 301-325
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    7. Existence Structures

      • Ellen Hisdal née Gruenwald
      Pages 326-345
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    8. Existence Inferences

      • Ellen Hisdal née Gruenwald
      Pages 346-355
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    9. Conditional and Joint Existence Information and Inferences

      • Ellen Hisdal née Gruenwald
      Pages 356-379
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Keywords

About this book

It is the business of science not to create laws, but to discover them. We do not originate the constitution of our own minds, greatly as it may be in our power to modify their character. And as the laws of the human intellect do not depend upon our will, so the forms of science, of (1. 1) which they constitute the basis, are in all essential regards independent of individual choice. George Boole [10, p. llJ 1. 1 Comparison with Traditional Logic The logic of this book is a probability logic built on top of a yes-no or 2-valued logic. It is divided into two parts, part I: BP Logic, and part II: M Logic. 'BP' stands for 'Bayes Postulate'. This postulate says that in the absence of knowl­ edge concerning a probability distribution over a universe or space one should assume 1 a uniform distribution. 2 The M logic of part II does not make use of Bayes postulate or of any other postulates or axioms. It relies exclusively on purely deductive reasoning following from the definition of probabilities. The M logic goes an important step further than the BP logic in that it can distinguish between certain types of information supply sentences which have the same representation in the BP logic as well as in traditional first order logic, although they clearly have different meanings (see example 6. 1. 2; also comments to the Paris-Rome problem of eqs. (1. 8), (1. 9) below).

Authors and Affiliations

  • Department of Informatics, University of Oslo, Oslo, Norway

    Ellen Hisdal

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