Three Views of Logic (Paperback)

Donald W. Loveland

ISBN 10: 0691160449 / ISBN 13: 9780691160443

Published by Princeton University Press, New Jersey, 2014

About this Item

Paperback. Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section.The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. * Gives an exceptionally broad view of logic * Treats traditional logic in a modern format * Presents relevance logic with applications * Provides an ideal text for a variety of one-semester upper-level undergraduate courses Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this title covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. It presents relevance logic with applications. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780691160443

Bibliographic Details

• Title: Three Views of Logic (Paperback)
• Publisher: Princeton University Press, New Jersey
• Publication Date: 2014
• Language: English
• ISBN 10: 0691160449
• ISBN 13: 9780691160443
• Binding: Paperback
• Condition: new

About this title

Synopsis

The first interdisciplinary textbook to introduce students to three critical areas in applied logic

Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity.

The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time.

Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings.

• Gives an exceptionally broad view of logic
• Treats traditional logic in a modern format
• Presents relevance logic with applications
• Provides an ideal text for a variety of one-semester upper-level undergraduate courses

About the Author

Donald W. Loveland is professor emeritus of computer science at Duke University and the author of Automated Theorem Proving: A Logical Basis. Richard E. Hodel is associate professor emeritus of mathematics at Duke University and the author of An Introduction to Mathematical Logic. S. G. Sterrett is the Curtis D. Gridley Distinguished Professor of History and Philosophy of Science at Wichita State University and the author of Wittgenstein Flies a Kite: A Story of Models of Wings and Models of the World.