# The Essence of Logic

## John Kelly

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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.

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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.

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