Books in Mathematical logic and foundations

111-120 of 141 results in All results

Recursive Model Theory

• 1st Edition
• Volume 1
• November 30, 1998
• Y.L. Ershov + 3 more
• English
• eBook 978-0-08-053369-8

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Recursive Algebra, Analysis and Combinatorics

• 1st Edition
• Volume 2
• November 30, 1998
• Y.L. Ershov + 3 more
• English
• eBook 978-0-08-053370-4

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Handbook of Proof Theory

• 1st Edition
• Volume 137
• July 9, 1998
• S.R. Buss
• English
• Hardback 978-0-444-89840-1

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• eBook 978-0-08-053318-6

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This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

Principles of Logic and Logic Programming

• 1st Edition
• Volume 13
• June 13, 1996
• G. Metakides + 1 more
• English
• eBook 978-0-08-053964-5

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Logic's basic elements are unfolded in this book. The relation of and the transition from Logic to Logic Programming are analysed.With the use and the development of computers in the beginning of the 1950's, it soon became clear that computers could be used, not only for arithmetical computation, but also for symbolic computation. Hence, the first arithmetical computation programs, and the first programs created to answer elementary questions and prove simple theorems, were written simultaneously. The basic steps towards a general method based on Logic, were accomplished in 1965 by Robinson and later by Kowalski and Colmerauer who made use of Logic directly as a Logic Programming language. Each chapter includes solved as well as unsolved exercises provided to help the reader assimilate the corresponding topics. The solved exercises demonstrate how to work methodically, whereas the unsolved exercises aim to stimulate the reader's personal initiative. The contents of the book are self-contained; only an elementary knowledge of analysis is required. Thus, it can be used by students in every academic year, as simply reading material, or in the context of a course. It can also be used by those who utilize Logic Programming without having any particular theoretical background knowledge of Logic, or by those simply interested in Logic and its applications in Logic Programming.

Logic, Methodology and Philosophy of Science IX

• 1st Edition
• Volume 134
• January 10, 1995
• D. Prawitz + 2 more
• English
• eBook 978-0-08-054495-3

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This volume is the product of the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science and contains the text of most of the invited lectures. Divided into 15 sections, the book covers a wide range of different issues. The reader is given the opportunity to learn about the latest thinking in relevant areas other than those in which they themselves may normally specialise.

Selected Papers on Automath

• 1st Edition
• Volume 133
• October 20, 1994
• R.P. Nederpelt + 2 more
• English
• eBook 978-0-08-088718-0

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The present volume contains a considered choice of the existing literature on Automath. Many of the papers included in the book have been published in journals or conference proceedings, but a number have only circulated as research reports or have remained unpublished. The aim of the editors is to present a representative selection of existing articles and reports and of material contained in dissertations, giving a compact and more or less complete overview of the work that has been done in the Automath research field, from the beginning to the present day. Six different areas have been distinguished, which correspond to Parts A to F of the book. These areas range from general ideas and motivation, to detailed syntactical investigations.

The Quantum Brain

• 1st Edition
• March 3, 1994
• A. Stern
• English
• eBook 978-0-08-057159-1

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While for the majority of physicists the problem of the deciphering of the brain code, the intelligence code, is a matter for future generations, the author boldly and forcefully disagrees. Breaking with the dogma of classical logic he develops in the form of the conversion postulate a concrete working hypothesis for the actual thought mechanism.The reader is invited on a fascinating mathematical journey to the very edges of modern scientific knowledge. From lepton and quark to mind, from cognition to a logic analogue of the Schrödinger equation, from Fibonacci numbers to logic quantum numbers, from imaginary logic to a quantum computer, from coding theory to atomic physics - the breadth and scope of this work is overwhelming. Combining quantum physics, fundamental logic and coding theory this unique work sets the stage for future physics and is bound to titillate and challenge the imagination of physicists, biophysicists and computer designers. Growing from the author's matrix operator formalization of logic, this work pursues a synthesis of physics and logic methods, leading to the development of the concept of infophysics.The experimental verification of the proposed quantum hypothesis of the brain is presently in preparation in cooperation with the Cavendish Laboratory, Cambridge, UK, and, if proved positive, would have major theoretical implications. Even more significant should be the practical applications in such fields as molecular electronics and computer science, biophysics and neuroscience, medicine and education. The new possiblities that could be opened up by quantum level computing could be truly revolutionary.The book aims at researchers and engineers in technical sciences as well as in biophysics and biosciences in general. It should have great appeal for physicists, mathematicians, logicians and for philosophers with a mathematical bent.

Higher Order Logic Theorem Proving and its Applications

• 1st Edition
• Volume 20
• February 3, 1993
• L.J.M. Claesen + 1 more
• English
• eBook 978-1-4832-9840-5

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The HOL system is a higher order logic theorem proving system implemented at Edinburgh University, Cambridge University and INRIA. Its many applications, from the verification of hardware designs at all levels to the verification of programs and communication protocols are considered in depth in this volume. Other systems based on higher order logic, namely Nuprl and LAMBDA are also discussed. Features given particular consideration are: novel developments in higher order logic and its implementations in HOL; formal design and verification methodologies for hardware and software; public domain availability of the HOL system. Papers addressing these issues have been divided as follows: Mathematical Logic; Induction; General Modelling and Proofs; Formalizing and Modelling of Automata; Program Verification; Hardware Description Language Semantics; Hardware Verification Methodologies; Simulation in Higher Order Logic; Extended Uses of Higher Order Logic. Academic and industrial researchers involved in formal hardware and software design and verification methods should find the publication especially interesting and it is hoped it will also provide a useful reference tool for those working at software institutes and within the electronics industries.

Recursive Functionals

• 1st Edition
• Volume 131
• May 18, 1992
• L.E. Sanchis
• English
• eBook 978-0-08-088717-3

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This work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results. Although aiming basically at a theory of higher order computability, attention is restricted to second order functionals, where the arguments are numerical functions and the values, when defined, are natural numbers. This theory is somewhat special, for to some extent it can be reduced to first order theory, but when properly extended and relativized it requires the full machinery of higher order computations. In the theory of recursive monotonic functionals the author formulates a reasonable notion of computation which provides the right frame for what appears to be a convincing form of the extended Church's thesis. At the same time, the theory provides sufficient room to formulate the classical results that are usually derived in terms of singular functionals. Presented are complete proofs of Gandy's selector theorem, Kleene's theorem on hyperarithmetical predicates, and Grilliot's theorem on effectively discontinuous functionals.

Matrix Logic and Mind

• 1st Edition
• February 12, 1992
• A. Stern
• English
• eBook 978-0-08-093413-6

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In this revolutionary work, the author sets the stage for the science ofthe 21st Century, pursuing an unprecedented synthesis of fields previouslyconsidered unrelated. Beginning with simple classical concepts, he endswith a complex multidisciplinary theory requiring a high level ofabstraction. The work progresses across the sciences in severalmultidisciplinary directions: Mathematical logic, fundamental physics,computer science and the theory of intelligence. Extraordinarily enough,the author breaks new ground in all these fields. In the field offundamental physics the author reaches the revolutionary conclusion thatphysics can be viewed and studied as logic in a fundamental sense, ascompared with Einstein's view of physics as space-time geometry. This opensnew, exciting prospects for the study of fundamental interactions. Aformulation of logic in terms of matrix operators and logic vector spacesallows the author to tackle for the first time the intractable problem ofcognition in a scientific manner. In the same way as the findings ofHeisenberg and Dirac in the 1930s provided a conceptual and mathematicalfoundation for quantum physics, matrix operator logic supports an importantbreakthrough in the study of the physics of the mind, which is interpretedas a fractal of quantum mechanics. Introducing a concept of logic quantumnumbers, the author concludes that the problem of logic and theintelligence code in general can be effectively formulated as eigenvalueproblems similar to those of theoretical physics. With this important leapforward in the study of the mechanism of mind, the author concludes thatthe latter cannot be fully understood either within classical or quantumnotions. A higher-order covariant theory is required to accommodate thefundamental effect of high-level intelligence. The landmark resultsobtained by the author will have implications and repercussions for thevery foundations of science as a whole. Moreover, Stern's Matrix Logic issuitable for a broad spectrum of practical applications in contemporarytechnologies.