Introduction to Mathematical Logic Fourth Edition

Author: Elliott Mendelson
Publisher: CRC Press
ISBN: 0412808307
Release Date: 1997-06-01
Genre: Mathematics

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

Computability

Author: Richard L. Epstein
Publisher: Chapman and Hall/CRC
ISBN: 0534103561
Release Date: 1989-11-09
Genre: Mathematics

An introduction to recursion theory and particularly to the theory of computing, including fourteen readings by Hilbert, Godel, Turing, Post, Church, and others along with a discussion of issues such as self-reference and infinite sets. Annotation copyrighted by Book News, Inc., Portland, OR

Proof Complexity and Feasible Arithmetics

Author: Paul W. Beame
Publisher: American Mathematical Soc.
ISBN: 0821870823
Release Date:
Genre: Mathematics

Questions of mathematical proof and logical inference have been a significant thread in modern mathematics and have played a formative role in the development of computer science and artificial intelligence. Research in proof complexity and feasible theories of arithmetic aims at understanding not only whether or not logical inferences can be made but also what resources are required to carry them out. Understanding the resources required for logical inferences has major implications for some of the most important problems in computational complexity, particularly the problem of whether or not NP is equal to co-NP. In addition, these have important implications for the efficiency of automated reasoning systems. The last dozen years have seen several breakthroughs in the study of these resource requirement. Papers in this volume represent the proceedings of the DIMACS workshop on "Feasible Arithmetics and Proof Complexity" held in April 1996 in Rutgers, NJ, as part of the DIMACS Institute's Special Year on Logic and Algorithms. This book brings together some of the most recent work of leading researchers in proof complexity and feasible arithmetic reflecting many of these advances. It covers a number of aspects of the field including lower bounds in proof complexity, witnessing theorems and proof systems for feasible arithmetic, algebraic and combinatorial proof systems, interpolation theorems, and the relationship between proof complexity and Boolean circuit complexity.

Truth in Mathematics

Author: Harold G. Dales
Publisher: Oxford University Press
ISBN: 019851476X
Release Date: 1998
Genre: Mathematics

The nature of truth in mathematics is a problem which has exercised the minds of thinkers from at least the time of the ancient Greeks. This book is an overview of the most recent work undertaken in this subject, and is unique in being the result of interactions between researchers from both philosophy and mathematics. The articles are written by world leaders in their respective fields and are of interest to researchers in both disciplines.

AI IA 99 Advances in Artificial Intelligence

Author: Associazione italiana per l'intelligenza artificiale. Congress
Publisher: Springer Science & Business Media
ISBN: 9783540673507
Release Date: 2000-03-29
Genre: Computers

This book constitutes the thoroughly refereed post-conference proceedings of the 6th Congress of the Italian Association for Artificial Intelligence, AI*IA 99, held in Bologna, Italy, in September 1999. The 33 revised full papers presented were carefully reviewed and selected for inclusion in the book from a total of 64 congress submissions. The papers are organized in topical sections on knowledge representation; automated reasoning; temporal and qualitative reasoning; machine learning, data mining, and theory revision; natural language processing and web interfaces; multi-agent systems; perception and robotics; and planning and scheduling.

Classical Mathematical Logic

Author: Richard L. Epstein
Publisher: Princeton University Press
ISBN: 9781400841554
Release Date: 2011-12-18
Genre: Mathematics

In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference. Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.

Measure Theory and Probability

Author: Malcolm Adams
Publisher: Springer Science & Business Media
ISBN: 9781461207795
Release Date: 2013-04-17
Genre: Mathematics

"...the text is user friendly to the topics it considers and should be very accessible...Instructors and students of statistical measure theoretic courses will appreciate the numerous informative exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association

Harmonic Analysis

Author: Henry Helson
Publisher: Springer
ISBN: 9789386279477
Release Date: 2010-08-15
Genre: Mathematics

This second edition has been enlarged and considerably rewritten. Among the new topics are infinite product spaces with applications to probability, disintegration of measures on product spaces, positive definite functions on the line, and additional information about Weyl's theorems on equidistribution. Topics that have continued from the first edition include Minkowski's theorem, measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szego, and the Wiener Tauberian theorem. Readers of the book should have studied the Lebesgue integral, the elementary theory of analytic and harmonic functions, and the basic theory of Banach spaces. The treatment is classical and as simple as possible. This is an instructional book, not a treatise. Mathematics students interested in analysis will find here what they need to know about Fourier analysis. Physicists and others can use the book as a reference for more advanced topics.

Discrete Mathematics with Applications

Author: Susanna S. Epp
Publisher: Cengage Learning
ISBN: 9780495391326
Release Date: 2010-08-04
Genre: Mathematics

Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Enumerative Combinatorics

Author: Richard P. Stanley
Publisher: Cambridge University Press
ISBN: 9781107015425
Release Date: 2011-12-12
Genre: Mathematics

"Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets"--

AI IA 99 Advances in Artificial Intelligence

Author: Evelina Lamma
Publisher: Springer
ISBN: UOM:39015047800795
Release Date: 2000-05-11
Genre: Artificial intelligence

This book constitutes the thoroughly refereed post-conference proceedings of the 6th Congress of the Italian Association for Artificial Intelligence, AI*IA 99, held in Bologna, Italy, in September 1999. The 33 revised full papers presented were carefully reviewed and selected for inclusion in the book from a total of 64 congress submissions. The papers are organized in topical sections on knowledge representation; automated reasoning; temporal and qualitative reasoning; machine learning, data mining, and theory revision; natural language processing and web interfaces; multi-agent systems; perception and robotics; and planning and scheduling.