Logical Foundations Of Computer Science (In 2 Volumes)

by Peter A Fejer
Logical Foundations Of Computer Science (In 2 Volumes)
Author: Peter A Fejer
Publisher: World Scientific
Total Pages: 1336
Release: 2024-07-30
Genre: Computers
ISBN: 9811289352
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Logic is a foundational mathematical discipline for Computer Science. This unique compendium provides the main ideas and techniques originating from logic. It is divided into two volumes — propositional logic and predicate logic. The volume presents some of the most important concepts starting with a variety of logic formalisms — Hilbert/Frege systems, tableaux, sequents, and natural deduction in both propositional and first-order logic, as well as transformations between these formalisms. Topics like circuit design, resolution, cutting planes, Hintikka sets, paramodulation, and program verification, which do not appear frequently in logic books are discussed in detail.The useful reference text has close to 800 exercises and supplements to deepen understanding of the subject. It emphasizes proofs and overcomes technical difficulties by providing detailed arguments. Computer scientists and mathematicians will benefit from this volume.

Logical Foundations of Computer Science

by Sergei Artemov
Logical Foundations of Computer Science
Author: Sergei Artemov
Publisher: Springer
Total Pages: 522
Release: 2007-06-30
Genre: Computers
ISBN: 3540727345
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This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2007, held in New York, NY, USA in June 2007. The volume presents 36 revised refereed papers that address all current aspects of logic in computer science.

Logical Foundations of Proof Complexity

by Stephen Cook
Logical Foundations of Proof Complexity
Author: Stephen Cook
Publisher: Cambridge University Press
Total Pages: 0
Release: 2014-03-06
Genre: Mathematics
ISBN: 9781107694118
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This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.

Computability, Complexity, Logic

by E. Börger
Computability, Complexity, Logic
Author: E. Börger
Publisher: Elsevier
Total Pages: 618
Release: 1989-07-01
Genre: Computers
ISBN: 008088704X
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The theme of this book is formed by a pair of concepts: the concept of formal language as carrier of the precise expression of meaning, facts and problems, and the concept of algorithm or calculus, i.e. a formally operating procedure for the solution of precisely described questions and problems.The book is a unified introduction to the modern theory of these concepts, to the way in which they developed first in mathematical logic and computability theory and later in automata theory, and to the theory of formal languages and complexity theory. Apart from considering the fundamental themes and classical aspects of these areas, the subject matter has been selected to give priority throughout to the new aspects of traditional questions, results and methods which have developed from the needs or knowledge of computer science and particularly of complexity theory.It is both a textbook for introductory courses in the above-mentioned disciplines as well as a monograph in which further results of new research are systematically presented and where an attempt is made to make explicit the connections and analogies between a variety of concepts and constructions.

Logical Foundations of Computer Science

by S. I. Adi︠a︡n
Logical Foundations of Computer Science
Author: S. I. Adi︠a︡n
Publisher: Springer Science & Business Media
Total Pages: 456
Release: 1997-05-28
Genre: Computers
ISBN: 9783540630456
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A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.

Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 5: Logic Programming

by Dov M. Gabbay
Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 5: Logic Programming
Author: Dov M. Gabbay
Publisher: Clarendon Press
Total Pages: 818
Release: 1998-01-08
Genre: Computers
ISBN: 0191546283
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The Handbook of Logic in Artificial Intelligence and Logic Programming is a multi-volume work covering all major areas of the application of logic to artificial intelligence and logic programming. The authors are chosen on an international basis and are leaders in the fields covered. Volume 5 is the last in this well-regarded series. Logic is now widely recognized as one of the foundational disciplines of computing. It has found applications in virtually all aspects of the subject, from software and hardware engineering to programming languages and artificial intelligence. In response to the growing need for an in-depth survey of these applications the Handbook of Logic in Artificial Intelligence and its companion, the Handbook of Logic in Computer Science have been created. The Handbooks are a combination of authoritative exposition, comprehensive survey, and fundamental research exploring the underlying themes in the various areas. Some mathematical background is assumed, and much of the material will be of interest to logicians and mathematicians. Volume 5 focuses particularly on logic programming. The chapters, which in many cases are of monograph length and scope, emphasize possible unifying themes.

Symbolic Model Checking

by Kenneth L. McMillan
Symbolic Model Checking
Author: Kenneth L. McMillan
Publisher: Springer Science & Business Media
Total Pages: 202
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 146153190X
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Formal verification means having a mathematical model of a system, a language for specifying desired properties of the system in a concise, comprehensible and unambiguous way, and a method of proof to verify that the specified properties are satisfied. When the method of proof is carried out substantially by machine, we speak of automatic verification. Symbolic Model Checking deals with methods of automatic verification as applied to computer hardware. The practical motivation for study in this area is the high and increasing cost of correcting design errors in VLSI technologies. There is a growing demand for design methodologies that can yield correct designs on the first fabrication run. Moreover, design errors that are discovered before fabrication can also be quite costly, in terms of engineering effort required to correct the error, and the resulting impact on development schedules. Aside from pure cost considerations, there is also a need on the theoretical side to provide a sound mathematical basis for the design of computer systems, especially in areas that have received little theoretical attention.

Uncertain Reasoning in Justification Logic

by Ioannis Kokkinis
Uncertain Reasoning in Justification Logic
Author: Ioannis Kokkinis
Publisher: Lulu.com
Total Pages: 116
Release: 2016-06
Genre: Computers
ISBN: 1326645102
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This thesis studies the combination of two well known formal systems for knowledge representation: probabilistic logic and justification logic. Our aim is to design a formal framework that allows the analysis of epistemic situations with incomplete information. In order to achieve this we introduce two probabilistic justification logics, which are defined by adding probability operators to the minimal justification logic J. We prove soundness and completeness theorems for our logics and establish decidability procedures. Both our logics rely on an infinitary rule so that strong completeness can be achieved. One of the most interesting mathematical results for our logics is the fact that adding only one iteration of the probability operator to the justification logic J does not increase the computational complexity of the logic.