The Classical Decision Problem 1st Edition by Egon Börger (PDF)

Description

This is the most comprehensive treatment available in book form of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. A revealing analysis of the natural order of decidable and undecidable cases is given. The complete classification of the solvable and unsolvable standard cases of the classical decision problem will be of particular interest to the reader. The classification comes complete with the complexity analysis of the solvable cases, with the comprehensive treatment of the reduction method, and with the model-theoretical analysis of solvable cases. Many cases are treated here for the first time, and a great number of simple proofs and exercises have been included. The results and methods of the book are extensively used in logic, computer science and artificial intelligence.

User’s Reviews

Editorial Reviews: Review From the reviews of the first edition:”The authors … describe their effort as that of ‘combining the features of a research monograph and a textbook.’ They suggest that the book – or selected chapters of it – might be used for an introductory course on decision problems, undecidability, and the complexity of decision procedures. … So there is usually a lot to think about in making sense of the author’s arguments. This is part of what makes this book so enjoyable.” (R. Gregory Taylor, The Review of Modern Logic, Vol. 9 (3-4), 2004)”This is the most comprehensive treatment available in book form of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. A revealing analysis of the natural order of decidable and undecidable cases is given. … Many cases are treated here for the first time, and a great number of simple proofs and exercises have been included.” (L’Enseignement Mathematique, Vol. 48 (1-2), 2002)”The book is dedicated to a comprehensive presentation of the classical decision problem of first-order logic. … This book is an essential reference for any researcher in logic, complexity, and artificial intelligence. … Historical references that are placed at the end of each chapter are very enjoyable and help the reader follow the literature and gain a perspective of the field. … an excellent reference book for researchers in the field, and for advanced doctoral students in theoretical computer science and logic.” (Dan A. Simovici, SIGACT News, Vol. 35 (1), 2004)

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