Propositional And Predicate Calculus

Bol

Topics include: - the representation of mathematical statements by formulas in a formal language; - the interpretation of formulas as true or false in a mathematical structure; - logical consequence of one formula from others; - the soundness and completeness theorems connecting logical consequence and formal proof; At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include: - the representation of mathematical statements by formulas in a formal language; - the interpretation of formulas as true or false in a mathematical structure; - logical consequence of one formula from others; - formal proof; - the soundness and completeness theorems connecting logical consequence and formal proof; - the axiomatization of some mathematical theories using a formal language; - the compactness theorem and an introduction to model theory. This book is designed for self-study by students, as well as for taught courses, using principles successfully developed by the Open University and used across the world. It includes exercises embedded within the text with full solutions to many of these. In addition there are a number of exercises without answers so that students studying under the guidance of a tutor may be assessed on the basis of what has been taught. Some experience of axiom-based mathematics is required but no previous experience of logic. Propositional and Predicate Calculus gives students the basis for further study of mathematical logic and the use of formal languages in other subjects. Derek Goldrei is Senior Lecturer and Staff Tutor at the Open University and part-time Lecturer in Mathematics at Mansfield College, Oxford, UK. This is the first book to provide a student-friendly introduction to propositional and predicate calculus, which is central to the broad field of mathematical logic. The book is aimed at undergraduates with no prior experience of logic. It does assume some mathematical background, but only that which is standard in the first year of a mathematical degree, and contains pointers for students without this background making it suitable for both mathematics and computer science courses.The book concentrates on the core material and provides a solid foundation for further study. The emphasis is on statements about mathematical structures, formal proofs representing mathematical arguments, and mathematical applications of results. The final chapter is devoted to some of the applications of the compactness theorem within Model Theory. It is specifically designed for self-study and features a wealth of exercises to encourage students to help develop results and consolidate understanding.

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Pages: 323, Edition: 2005, Paperback, Springer Verlag