Logic And Complexity
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Logic And Complexity
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Author : Richard Lassaigne
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logic And Complexity written by Richard Lassaigne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems. Divided into three parts, it covers: - Model Theory and Recursive Functions - introducing the basic model theory of propositional, 1st order, inductive definitions and 2nd order logic. Recursive functions, Turing computability and decidability are also examined. - Descriptive Complexity - looking at the relationship between definitions of problems, queries, properties of programs and their computational complexity. - Approximation - explaining how some optimization problems and counting problems can be approximated according to their logical form. Logic is important in Computer Science, particularly for verification problems and database query languages such as SQL. Students and researchers in this field will find this book of great interest.
Logical Foundations Of Mathematics And Computational Complexity
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Author : Pavel Pudlák
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-22
Logical Foundations Of Mathematics And Computational Complexity written by Pavel Pudlák and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
Proof Theory And Logical Complexity
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Author : Jean-Yves Girard
language : en
Publisher:
Release Date : 1987
Proof Theory And Logical Complexity written by Jean-Yves Girard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
"This long awaited book ... fills essential gaps in monographic literature on proof theory and prepares readers for volume 2 (to be published soon) containing an exposition of the author's new approach to proof theory for higher order logic. Even in traditional topics, like Gödel's completeness and incompleteness theorems, and cut elemination, accents are different compared to books by Kleene, Schütte, or Takeuti, which are strongly influenced by Hilbert's aim: to make mathematical theories (number theory, analysis etc.) more reliable by transformations of formalized proofs. The author is much closer to the approach of G. Kreisel (to whom this book is dedicated): Hilbert's program needs drastic rethinking and one of the main tasks is in finding mathematical applications of the results obtained in proof theory. Possibly, it is not a pure chance that the system of second order functionals developed by the author in his normalization proof for second order logic (was rediscovered and) became a tool in computer science. The book under review presents not only this material, but also other results by the author which became a part of modern proof theory including analysis of cut-free provability in terms of 3-valued logic. The material which was not previously covered (at least in such detail) in proof-theoretic monographs includes strong normalizability proofs (after Tait and Gandy), applications of reflection principles, recursive ordinals, operations on local correct (but not necessarily well-founded) omega-derivations, no-counterexample interpretation, using proof theory to extract combinatory estimates with a detailed treatment of van der Waerden's theorem. This is a difficult, but rewarding postgraduate-level textbook. The author does not avoid philosophical questions, and such discussion supported by theorems is certainly fruitful, although the reviewer would not agree with all author's conclusions"-- description of volume 1.
Bounded Arithmetic Propositional Logic And Complexity Theory
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Author : Jan Krajicek
language : en
Publisher:
Release Date : 2014-05-18
Bounded Arithmetic Propositional Logic And Complexity Theory written by Jan Krajicek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-18 with Computational complexity categories.
Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
Logic And Computational Complexity
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Author : Daniel Leivant
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-08-02
Logic And Computational Complexity written by Daniel Leivant and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-02 with Computers categories.
This book contains revised versions of papers invited for presentation at the International Workshop on Logic and Computational Complexity, LCC '94, held in Indianapolis, IN in October 1994. The synergy between logic and computational complexity has gained importance and vigor in recent years, cutting across many areas. The 25 revised full papers in this book contributed by internationally outstanding researchers document the state-of-the-art in this interdisciplinary field of growing interest; they are presented in sections on foundational issues, applicative and proof-theoretic complexity, complexity of proofs, computational complexity of functionals, complexity and model theory, and finite model theory.
Logic And Computational Complexity
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Author : Daniel Leivant
language : en
Publisher:
Release Date : 2014-01-15
Logic And Computational Complexity written by Daniel Leivant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Computability Complexity Logic
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Author : E. Börger
language : en
Publisher: Elsevier
Release Date : 1989-07-01
Computability Complexity Logic written by E. Börger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-07-01 with Computers categories.
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.
Advances And Trends In Artificial Intelligence Theory And Practices In Artificial Intelligence
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Author : Hamido Fujita
language : en
Publisher: Springer Nature
Release Date : 2022-08-29
Advances And Trends In Artificial Intelligence Theory And Practices In Artificial Intelligence written by Hamido Fujita and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-29 with Computers categories.
This book constitutes the thoroughly refereed proceedings of the 35th International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, IEA/AIE 2022, held in Kitakyushu, Japan, in July 2022. The 67 full papers and 11 short papers presented were carefully reviewed and selected from 127 submissions. The IEA/AIE 2022 conference focuses on focuses on applications of applied intelligent systems to solve real-life problems in all areas including business and finance, science, engineering, industry, cyberspace, bioinformatics, automation, robotics, medicine and biomedicine, and human-machine interactions.
A First Course In Logic
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Author : Shawn Hedman
language : en
Publisher: OUP Oxford
Release Date : 2004-07-08
A First Course In Logic written by Shawn Hedman and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-08 with Mathematics categories.
The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course.
Induction Algorithmic Learning Theory And Philosophy
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Author : Michèle Friend
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-21
Induction Algorithmic Learning Theory And Philosophy written by Michèle Friend and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-21 with Philosophy categories.
The idea of the present volume emerged in 2002 from a series of talks by Frank Stephan in 2002, and John Case in 2003, on developments of algorithmic learning theory. These talks took place in the Mathematics Department at the George Washington University. Following the talks, ValentinaHarizanovandMichèleFriendraised thepossibility ofanexchange of ideas concerning algorithmic learning theory. In particular, this was to be a mutually bene?cial exchange between philosophers, mathematicians and computer scientists. Harizanov and Friend sent out invitations for contributions and invited Norma Goethe to join the editing team. The Dilthey Fellowship of the George Washington University provided resources over the summer of 2003 to enable the editors and some of the contributors to meet in Oviedo (Spain) at the 12th International Congress of Logic, Methodology and Philosophy of Science. The editing work proceeded from there. The idea behind the volume is to rekindle interdisciplinary discussion. Algorithmic learning theory has been around for nearly half a century. The immediate beginnings can be traced back to E.M. Gold’s papers: “Limiting recursion” (1965) and “Language identi?cation in the limit” (1967). However, from a logical point of view, the deeper roots of the learni- theoretic analysis go back to Carnap’s work on inductive logic (1950, 1952).