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

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Merrie Bergmann (Smith College, Massachusetts)

An Introduction to Many-Valued and Fuzzy Logic

Semantics, Algebras, and Derivation Systems

Merrie Bergmann (Smith College, Massachusetts)

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English

Cambridge University Press
25 March 2008

Philosophy; Mathematical logic

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.

By: Merrie Bergmann (Smith College Massachusetts)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 253mm, Width: 177mm, Spine: 15mm
Weight: 590g
ISBN: 9780521707572
ISBN 10: 0521707579
Pages: 342
Publication Date: 25 March 2008
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

Preface; 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.

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.