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Bergmann, Merrie, , . An Introduction to Many-Valued and Fuzzy Logic
2009, Cambridge University Press.
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Added by: Berta Grimau, Contributed by:

Publisher’s Note: 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.

Comment: In the words of the author: ‘This textbook can be used as a complete basis for an introductory course on formal many-valued and fuzzy logics, at either the upper-level undergraduate or the graduate level, and it can also be used as a supplementary text in a variety of courses. There is considerable flexibility in either case. The truth-valued semantic chapters are independent of the algebraic and axiomatic ones, so that either of the latter may be skipped. Except for Section 13.3 of Chapter 13, the axiomatic chapters are also independent of the algebraic ones, and an instructor who chooses to skip the algebraic material can simply ignore the latter part of 13.3. Finally, Lukasiewicz fuzzy logic is presented independently of Gödel and product fuzzy logics, thus allowing an instructor to focus solely on the former. There are exercises throughout the text. Some pose straightforward problems for the student to solve, but many exercises also ask students to continue proofs begun in the text, to prove results analogous to those in the text, and to compare the various logical systems that are presented.’ The book does include a review of classical propositional and first-order logic, but the students should’ve taken at least one basic logic course before getting into this material.

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Bergmann, Merrie, , . An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems
2008, Cambridge University Press.
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Added by: Berta Grimau, Contributed by:

Publisher’s note: This volume is an accessible introduction to the subject of many-valued and fuzzy logic suitable for use in relevant advanced undergraduate and graduate courses. The text opens with a discussion of 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, Godel, and product logics – are then presented as generalizations of three-valued systems that successfully address the problems of vagueness. Semantic and axiomatic systems for three-valued and fuzzy logics are examined along with an introduction to the algebras characteristic of those systems. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, ask students to continue proofs begun in the text, and engage them in the comparison of logical systems.

Comment: This book is ideal for an intermediate-level course on many-valued and/or fuzzy logic. Although it includes a presentation of propositional and first-order logic, it is intended for students who are familiar with classical logic. However, no previous knowledge of many-valued or fuzzy logic is required. It can also be used as a secondary reading for a general course on non-classical logics.

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