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An Introduction to Many-Valued and Fuzzy Logic
Semantics, Algebras, and Derivation Systems

  • Date Published: January 2008
  • availability: Available
  • format: Hardback
  • isbn: 9780521881289


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About the Authors
  • Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.

    • Accessible introduction explains the basic theories to the reader
    • Clear presentation allows the reader to get to grips with technical concepts
    • Includes algebras and axiomatics along with semantics and philosophical issues
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    Product details

    • Date Published: January 2008
    • format: Hardback
    • isbn: 9780521881289
    • length: 342 pages
    • dimensions: 260 x 183 x 20 mm
    • weight: 0.75kg
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Review of classical propositional logic
    3. Review of classical first-order logic
    4. Alternative semantics for truth-values and truth-functions
    5. Three-valued propositional logics: semantics
    6. Derivation systems for three-valued propositional logic
    7. Three-valued first-order logics: semantics
    8. Derivation systems for three-valued first-order logics
    9. Alternative semantics for three-valued systems
    10. The principle of charity reconsidered and a new problem of the fringe
    11. Fuzzy propositional logics: semantics
    12. Fuzzy algebras
    13. Derivational systems for fuzzy propositional logics
    14. Fuzzy first-order logics: semantics
    15. Derivation systems for fuzzy first-order logics
    16. Extensions of fuzziness
    17. Fuzzy membership functions.

  • Instructors have used or reviewed this title for the following courses

    • Intro to Logic
    • Mathematical Logic I
    • Research program
    • Rough Set Theory
    • Topics in Philosophical Logic
  • Author

    Merrie Bergmann, Smith College, Massachusetts
    Merrie Bergmann is associate professor in the department of computer science at Smith College. She is the co-author, with James Moor and Jack Nelson, of The Logic Book.

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