An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems
Cambridge University Press, 4/24/2008
EAN 9780521707572, ISBN10: 0521707579
Paperback, 342 pages, 22.8 x 15.2 x 1.5 cm
Language: English
Originally published in English
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.
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.