Written in a clear, precise and user-friendly style, Logic as a Tool: A Guide to Formal Logical Reasoning is intended for undergraduates in both mathematics and computer science, and will guide them to learn, understand and master the use of classical logic as a tool for doing correct reasoning. It offers a systematic and precise exposition of classical logic with many examples and exercises, and only the necessary minimum of theory. The book explains the grammar, semantics and use of classical logical languages and teaches the reader how grasp the meaning and translate them to and from natural language. It illustrates with extensive examples the use of the most popular deductive systems -- axiomatic systems, semantic tableaux, natural deduction, and resolution -- for formalising and automating logical reasoning both on propositional and on first-order level, and provides the reader with technical skills needed for practical derivations in them. Systematic guidelines are offered on how to perform logically correct and well-structured reasoning using these deductive systems and the reasoning techniques that they employ. •Concise and systematic exposition, with semi-formal but rigorous treatment of the minimum necessary theory, amply illustrated with examples •Emphasis both on conceptual understanding and on developing practical skills •Solid and balanced coverage of syntactic, semantic, and deductive aspects of logic •Includes extensive sets of exercises, many of them provided with solutions or answers •Supplemented by a website including detailed slides, additional exercises and solutions For more information browse the book's website at: https://logicasatool.wordpress.com

The Logic of Our Language teaches the practical and everyday application of formal logic. Rather than overwhelming the reader with abstract theory, Jackson and McLeod show how the skills developed through the practice of logic can help us to better understand our own language and reasoning processes. The authors’ goal is to draw attention to the patterns and logical structures inherent in our spoken and written language by teaching the reader how to translate English sentences into formal symbols. Other logical tools, including truth tables, truth trees, and natural deduction, are then introduced as techniques for examining the properties of symbolized sentences and assessing the validity of arguments. A substantial number of practice questions are offered both within the book itself and as interactive activities on a companion website.

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.

In the twenty-first century there are two ways to study logic. The more recent approach is symbolic logic. The history of teaching logic since World War II, however, casts doubt on the idea that symbolic logic is best for a first logic course. Logic as a Liberal Art is designed as part of a minority approach, teaching logic in the "verbal" way, in the student's "natural" language, the approach invented by Aristotle. On utilitarian grounds alone, this "verbal" approach is superior for a first course in logic, for the whole range of students. For millennia, this "verbal" approach to logic was taught in conjunction with grammar and rhetoric, christened the trivium. The decline in teaching grammar and rhetoric in American secondary schools has led Dr. Rollen Edward Houser to develop this book. The first part treats grammar, rhetoric, and the essential nature of logic. Those teachers who look down upon rhetoric are free, of course, to skip those lessons. The treatment of logic itself follows Aristotle's division of the three acts of the mind (Prior Analytics 1.1). Formal logic is then taken up in Aristotle's order, with Parts on the logic of Terms, Propositions, and Arguments. The emphasis in Logic as a Liberal Art is on learning logic through doing problems. Consequently, there are more problems in each lesson than would be found, for example, in many textbooks. In addition, a special effort has been made to have easy, medium, and difficult problems in each Problem Set. In this way the problem sets are designed to offer a challenge to all students, from those most in need of a logic course to the very best students.

th This volume is dedicated to Dov Gabbay who celebrated his 50 birthday in October 1995. Dov is one of the most outstanding and most productive researchers we have ever met. He has exerted a profound influence in major fields of logic, linguistics and computer science. His contributions in the areas of logic, language and reasoning are so numerous that a comprehensive survey would already fill half of this book. Instead of summarizing his work we decided to let him speak for himself. Sitting in a car on the way to Amsterdam airport he gave an interview to Jelle Gerbrandy and Anne-Marie Mineur. This recorded conversation with him, which is included gives a deep insight into his motivations and into his view of the world, the Almighty and, of course, the role of logic. In addition, this volume contains a partially annotated bibliography of his main papers and books. The length of the bibliography and the broadness of the topics covered there speaks for itself.