Bergmann, Merrie. The Logic Book
2003, Mcgraw-Hill.
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Summary:Â This book is an introductory textbook on mathematical logic. It covers Propositional Logic and Predicate Logic. For each of these formalisms it presents its syntax and formal semantics as well as a tableaux-style method of consistency-checking and a natural deduction-style deductive calculus. Moreover, it discusses the metatheory of both logics.

Comment: This book would be ideal for an introductory course on symbolic logic. It presupposes no previous training in logic, and because it covers sentential logic through the metatheory of first-order predicate logic, it is suitable for both introductory and intermediate courses in symbolic logic. The instructor who does not want to emphasize metatheory can simply omit Chapters 6 and 11. The chapters on truth-trees and the chapters on derivations are independent, so it is possible to cover truth-trees but not derivations and vice versa. However, the chapters on truth-trees do depend on the chapters presenting semantics; that is, Chapter 4 depends on Chapter 3 and Chapter 9 depends on Chapter 8. In contrast, the derivation chapters can be covered without first covering semantics. The Logic Book includes large exercise sets for all chapters. Answers to unstarred exercises appear in the Student Solutions Manual, available at www.mhhe.com/bergmann6e, while answers to starred exercises appear in the Instructor's Manual, which can be obtained by following the instructions on the same web page.

Bimbo, Katalin. Proof Theory: Sequent Calculi and Related Formalisms
2015, CRC Press, Boca Raton, FL
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Publisher's Note: Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics.

Comment: This book can be used in a variety of advanced undergraduate and postgraduate courses. Chapters 1, 2, 3 and 8 may be useful in an advanced undergraduate or beginning graduate course, where an emphasis is placed on classical logic and on a range of different proof calculi (mainly for classical logic). Chapters 4, 5 and 6 deal almost exclusively with non-classical logics. Chapters 7 and 9 are rich in meta-logical results, including results that have been obtained specifically using sequent calculus formalizations of various logics. These last five chapters might be used in a graduate course that embraces classical and nonclassical logics together with their meta-theory. To facilitate the use of the book as a text in a course, the text is peppered with exercises. In general, the starring indicates an increase in difficulty, however, sometimes an exercise is starred simply because it goes beyond the scope of the book or it is very lengthy. Solutions to selected exercises may be found on the web at the URL www.ualberta.ca/Ëœbimbo/ProofTheoryBook.

Cauman, Leigh S.. First Order Logic: An Introduction
1998, Walter de Gruyter & Co.
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Added by: Berta Grimau, Contributed by: Matt Clemens
Publisher's Note:Â 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. Understanding Symbolic Logic
2008, Pearson Prentice Hall.
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Publisher’s Note: 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).

Kouri Kissel, Teresa, Stewart Shapiro. Classical Logic
2018, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.)
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Summary: This article provides the basics of a typical logic, sometimes called 'classical elementary logic' or 'classical first-order logic', in a rigorous yet accessible manner. Section 2 develops a formal language, with a syntax and grammar. Section 3 sets up a deductive system for the language, in the spirit of natural deduction. Section 4 provides a model-theoretic semantics. Section 5 turns to the relationships between the deductive system and the semantics, and in particular, the relationship between derivability and validity. The authors show that an argument is derivable only if it is valid (soundness). Then they establish a converse: that an argument is valid only if it is derivable (completeness). They also briefly indicate other features of the logic, some of which are corollaries to soundness and completeness. The final section, Section 6, is devoted to a brief examination of the philosophical position that classical logic is 'the one right logic'.

Comment: This article introduces all the necessary tools in order to understand both the proof-theoretic and the model-theoretic aspects of first-order classical logical consequence. As such it can be used as a main reading in an introductory logic course covering classical first-order logic (assuming the students will have already looked at classical propositional logic). Moreover, the article covers some metatheoretic results (soundness, completeness, compactness, upward and downward LÃ¶wenheim-Skolem), which makes it suitable as a reading for a slightly more advanced course in logic. Finally, the article includes a brief incursion into the topic of logical pluralism. This makes it suitable to be used in a course on non-classical logics with an introduction module on classical logic.

Lehan, Vanessa. Reducing Stereotype Threat in First-Year Logic Classes
2015, Feminist Philosophy Quarterly 1 (2):1-13.
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Added by: Clotilde Torregrossa, Contributed by: Matthew Clemens
Abstract: In this paper I examine some research on how to diminish or eliminate stereotype threat in mathematics. Some of the successful strategies include: informing our students about stereotype threat, challenging the idea that logical intelligence is an 'innate' ability, making students In threatened groups feel welcomed, and introducing counter-stereotypical role models. The purpose of this paper is to take these strategies that have proven successful and come up with specific ways to incorporate them into introductory logic classes. For example, the possible benefit of presenting logic to our undergraduate students by concentrating on aspects of logic that do not result in a clash of schemas.

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Merrie Bergmann, James Moor, Jack Nelson. The Logic Book
, Random House, New York.
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Publisher’s Note: Description:Â 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 //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.

RoÅ¡ker, Jana S.. Classical Chinese Logic
2015, Philosophy Compass, 10(5): 301-309.
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