The Essence of Logic [Paperback]

John Kelly (Author)

Book Description

Series: Essence of Computing | Publication Date: October 24, 1996

The Prentice Hall Essence of Computing Series provides a concise, practical and uniform introduction to the core components of an undergraduate computer science degree. Acknowledging recent changes within Higher Education, this approach uses a variety of pedagogical tools, case studies, worked examples and self-test questions to underpin the students's learning. This book is a concise introduction to formal logic. Written for undergraduates, it makes no excessive demands on previous mathematical knowledge, requiring little maturity in mathematical thinking. The main objective of the book is in preparing the reader for the analysis and application of techniques of logic in computing. A wide range of topics in mathematical logic are covered with each new idea introduced in a gentle, yet brisk fashion which quickly leads to the development of important skills. Beginning with the Truth Tables, the reader is introduced to the concepts of Boolean Algebra and thus logical propositions and truth values. Propositional Logic is explored through the use of the methods of Semantic Tableaux, Natural Deduction and the Sequent Calculus. More formal Axiomatic systems are examined and illustrated with some important theorems about such systems. Properties of soundness. completeness and consistency are explained in terms of Propositional systems. Resolution is presented for Propositional Logic in preparation for an understanding of its use in computer science. The book then turns to the First Order Predicate Logic, revising the now familiar topics of deduction and semantic tableaux, as well as soundness completeness and consistency. Resolution is re-examined and the application of First Order Predicate Logic in computing is investigated.

Editorial Reviews

From the Back Cover

A gentle introduction to logic for undergraduate computing students.Beginning with Truth Tables, the reader is introduced to the concepts of Boolean Algebra, logical propositions and truth values. Propositional Logic is explored through using Semantic Tableaux, Natural Deduction and the Sequent Calculus. More formal axiomatic systems are examined and illustrated, and important theorems about these systems are presented. Properties of soundness, completeness and consistency are explained in terms of Propositional Systems; then concepts of resolution are introduced, with an eye towards their use in programming. The book then turns to First Order Predicate Logic, its theoretical underpinnings and uses.Undergraduate computer science and logic courses.

Product Details

• Paperback: 258 pages
• Publisher: Prentice Hall; 1st edition (October 24, 1996)
• Language: English
• ISBN-10: 0133963756
• ISBN-13: 978-0133963755
• Product Dimensions: 9 x 6.1 x 0.6 inches
• Shipping Weight: 14.9 ounces
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,092,220 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

6 of 6 people found the following review helpful:

5.0 out of 5 stars excellent logic intro for computer science, October 22, 2001

By 

M. Rumore (Oswego, il USA) - See all my reviews
(REAL NAME)   

This review is from: The Essence of Logic (Paperback)

I found this book to be an excellent introduction to logic as applied to artificial intelligence. The book first introduces the basics of propositional calculus and truth tables. This allows a reader to become familiar with the material before the axiomatic approach to logic is introduced in a later chapter. The axiomatic system chosen for propositional calculus is different than the one used by Burris in his book (Logic for Mathematics and Computer Science). Burris has the axiom schema of (A and not A). Kelly uses a different set. Kelly's description is very good and he gives many examples. Also, he covers semantic tableaux in good detail (Schaum's outline on logic also covers semantic tableaus, but a different name is given). Finally, he introduces resolution which serves as the basis for many automated reasoning programs and Prolog !!!

The second half of the book repeats the same approach for predicate calculus (introduction, axiomatic approach, semantic tableaux, and resolution). Again, the description is clear and has many examples.

Overall, an excellent book for learning logic from an AI point-of-view.