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.

Cauman, Leigh S., and . First Order Logic: An Introduction

1998, Walter de Gruyter & Co.

Publisher’s Note: This teaching book is designed to help its readers to reason systematically, reliably, and to some extent self-consciously, in the course of their ordinary pursuits-primarily in inquiry and in decision making. The principles and techniques recommended are explained and justified – not just stated; the aim is to teach orderly thinking, not the manipulation of symbols. The structure of material follows that of Quine’s Methods of Logic, and may be used as an introduction to that work, with sections on truth-functional logic, predicate logic, relational logic, and identity and description. Exercises are based on problems designed by authors including Quine, John Cooley, Richard Jeffrey, and Lewis Carroll.

Comment: This book is adequate for a first course on formal logic. Moreover, its table of contents follows that of Quine's "Methods of Logic", thus it can serve as an introduction or as a reference text for the study of the latter.

Klenk, Virginia, and . Understanding Symbolic Logic

2008, Pearson Prentice Hall.

Description – This comprehensive introduction presents the fundamentals of symbolic logic clearly, systematically, and in a straightforward style accessible to readers. Each chapter, or unit, is divided into easily comprehended small bites that enable learners to master the material step-by-step, rather than being overwhelmed by masses of information covered too quickly. The book provides extremely detailed explanations of procedures and techniques, and was written in the conviction that anyone can thoroughly master its content. A four-part organization covers sentential logic, monadic predicate logic, relational predicate logic, and extra credit units that glimpse into alternative methods of logic and more advanced topics.

Comment: This book is ideal for a first introduction course to formal logic. It doesn't presuppose any logical knowledge. It covers propositional and first-order logic (monadic and relational).

Merrie Bergmann, and James Moor, Jack Nelson. The Logic Book

2008 (5th ed), Random House, New York.

Description: This book is a leading text for symbolic or formal logic courses. All techniques and concepts are presented with clear, comprehensive explanations and numerous, carefully constructed examples. Its flexible organization (all chapters are complete and self-contained) allows instructors the freedom to cover the topics they want in the order they choose. A free Student Solutions Manual is packaged with every copy of the textbook. Two logic programs, Bertie III and Twootie, are available as a free download from the University of Connecticut Philosophy Department’s Web site. The Web address for downloading the software is http://www.ucc.uconn.edu/~wwwphil/software.html. Bertie 3 is a proof checker for the natural deduction method and Twootie is a proof checker for the truth tree method.

CONTENTS: Chapter 1: Basic Notions of Logic, Chapter 2: Sentential Logic: Symbolization and Syntax, Chapter 3: Sentential Logic: Semantics, Chapter 4: Sentential Logic: Truth-Trees, Chapter 5: Sentential Logic: Derivations, Chapter 6: Sentential Logic: Metatheory, Chapter 7: Predicate Logic: Symbolization and Syntax, Chapter 8: Predicate Logic: Semantics, Chapter 9: Predicate Logic: Truth-Trees, Chapter 10: Predicate Logic: Derivations, Chapter 11: Predicate Logic: Metatheory.

Comment: This book may serve as the main reading or reference book for an introductory course to formal logic. It doesn't presuppose any knowledge of logic and is thus recommended for use in undergrad level logic courses. It comes with solutions to most of its exercises, which is great for students to practice and study on their own, but may be a drawback, since the teacher will need to design exercises of her own in order to assign homework to the students.