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˜A œframework for priority arguments par Lerman,, M. Publication : New York Cambridge University Press 2010 . xvi, 176 pages , "This book presents a unifying framework for using priority arguments to prove theorems in computability. Priority arguments provide the most powerful theorem-proving technique in the field, but most of the applications of this technique are ad hoc, masking the unifying principles used in the proofs. The proposed framework presented isolates many of these unifying combinatorial principles and uses them to give shorter and easier-to-follow proofs of computability-theoretic theorems. Standard theorems of priority levels 1, 2, and 3 are chosen to demonstrate the framework's use, with all proofs following the same pattern. The last section features a new example requiring priority at all finite levels. The book will serve as a resource and reference for researchers in logic and computability, helping them to prove theorems in a shorter and more transparent manner"--Provided by publisher. 24 cm. Date : 2010 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

˜The œevolution of Principia mathematica : Bertrand Russell's manuscripts and notes for the second edition par Linsky, Bernard. Publication : Cambridge | New York Cambridge University Press 2011 . vii, 407 pages , "Originally published in 1910, Principia Mathematica led to the development of mathematical logic and computers and thus to information sciences. It became a model for modern analytic philosophy and remains an important work. In the late 1960s the Bertrand Russell Archives at McMaster University in Canada obtained Russell's papers, letters and library. These archives contained the manuscripts for the new Introduction and three Appendices that Russell added to the second edition in 1925. Also included was another manuscript, 'The Hierarchy of Propositions and Functions', which was divided up and re-used to create the final changes for the second edition. These documents provide fascinating insight, including Russell's attempts to work out the theorems in the flawed Appendix B, 'On Induction'. An extensive introduction describes the stages of the manuscript material on the way to print and analyzes the proposed changes in the context of the development of symbolic logic after 1910"-- 26 cm. Date : 2011 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

A concise introduction to mathematical logic par Rautenberg,, Wolfgang. Publication : New York, NY Springer 2006 . xvii, 256 pages 24 cm. Date : 2006 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

A transition to abstract mathematics: learning mathematical thinking and writing par Maddox, Randall. Publication : [S.l.] Academic Press 2009 . 356 p. , Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. Mathematical Thinking and Writing teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point. Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure. After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas. * Covers the full range of techniques used in proofs, including contrapositive, induction, and proof by contradiction * Explains identification of techniques and how they are applied in the specific problem * Illustrates how to read written proofs with many step by step examples * Includes 20% more exercises than the first edition that are integrated into the material instead of end of chapter * The Instructors Guide and Solutions Manual points out which exercises simply must be either assigned or at least discussed because they undergird later results. 24 cm. Date : 2009 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Around classification theory of models par Shelah,, Saharon. Publication : [S.l.] Springer 2008 . 279 p. 24 cm. Date : 2008 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Cognitive reasoning : a formal approach / par Anshakov, O. M. Publication : Heidelberg ; | New York : Springer, 2010 . 1 online resource (x, 437 pages) : Date : 2010 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Computational logic and human thinking : how to be artificially intelligent par Kowalski, Robert. Publication : Cambridge | New York : Cambridge University Press 2011 . xxii, 310 pages , "The practical benefits of computational logic need not be limited to mathematics and computing. As this book shows, ordinary people in their everyday lives can profit from the recent advances that have been developed for artificial intelligence. The book draws upon related developments in various fields from philosophy to psychology and law. It pays special attention to the integration of logic with decision theory, and the use of logic to improve the clarity and coherence of communication in natural languages such as English. This book is essential reading for teachers and researchers who may be out of touch with the latest developments in computational logic. It will also be useful in any undergraduate course that teaches practical thinking, problem solving or communication skills. Its informal presentation makes the book accessible to readers from any background, but optional, more formal, chapters are also included for those who are more technically oriented"-- | "The practical benefits of computational logic need not be limited to mathematics and computing. As this book shows, ordinary people in their everyday lives can profit from the recent advances that have been developed for artificial intelligence. The book draws upon related developments in various fields from philosophy to psychology and law. It pays special attention to the integration of logic with decision theory, and the use of logic to improve the clarity and coherence of communication in natural languages such as English"-- 24 cm. Date : 2011 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Essays in constructive mathematics par Edwards, Harold M. Publication : [S.l.] Springer 2004 . 232 p. , Contents and treatment are fresh and very different from the standard treatments Presents a fully constructive version of what it means to do algebra The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader. 24 cm. Date : 2004 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Essays in the philosophy and history of logic and mathematics / par Murawski, Roman. Publication : Amsterdam ; | New York, NY : Rodopi, 2010 . 343 pages ; , A collection of previously published essays; those originally written in Polish have been translated into English for this publication. 23 cm. Date : 2010 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Essays on the foundations of mathematics par Pasch, Moritz, Publication : Dordrecht | New York Springer 2010 . xi, 245 pages 24 cm. Date : 2010 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Gentzen calculi for modal propositional logic par Poggiolesi, Francesca Publication : Dordrecht | New York Springer 2011 . 222 pages 24 cm. Date : 2011 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Grammatical inference : learning automata and grammars par De la Higuera, Colin. Publication : Cambridge | New York Cambridge University Press 2010 . xiv, 417 pages 26 cm Date : 2010 Disponibilité : Exemplaires disponibles: La bibliothèque des sciences de l'ingénieur (1),

Hybrid logic and its proof-theory par Braüner, Torben. Publication : Dordrecht | New York Springer. 2011 . xiii, 231 pages 24 cm. Date : 2011 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Mathematical thinking and writing A transition to higher mathematics par Maddox, Randall B. Publication : [S.l.] Academic Press 2002 . 304 p. , The ability to construct proofs is one of the most challenging aspects of the world of mathematics. It is, essentially, the defining moment for those testing the waters in a mathematical career. Instead of being submerged to the point of drowning, readers of Mathematical Thinking and Writing are given guidance and support while learning the language of proof construction and critical analysis. Randall Maddox guides the reader with a warm, conversational style, through the task of gaining a thorough understanding of the proof process, and encourages inexperienced mathematicians to step up and learn how to think like a mathematician. A student's skills in critical analysis will develop and become more polished than previously conceived. Most significantly, Dr. Maddox has the unique approach of using analogy within his book to clarify abstract ideas and clearly demonstrate methods of mathematical precision. 25 cm. Date : 2002 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

Purity, spectra and localisation par Prest, Mike. Publication : Cambridge | New York Cambridge University Press 2009 . xxviii, 769 pages 25 cm. Date : 2009 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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