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

2008, Cambridge University Press.

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.

Haack, Susan, and . Philosophy of Logics

1978, Cambridge: Cambridge University Press.

Publisher’s Note: The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack’s book has established an international reputation (translated into five languages) for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of nonclassical systems of logic, including many-valued logics, fuzzy logic, modal and tense logics, and relevance logics.

Comment: This textbook is intended particularly for philosophy students who have completed a first course in elementary logic. But, though the book is clearly written, such students still may find the content difficult, as it addresses difficult topics in the foundations of logic the primary literature for which is very technical. That said, it has been a widely used textbook for courses on philosophy of logic. Chapters of it can be used individually in accordance with the arrangements of the course.