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A Remark On The Induction Scheme
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Book Synopsis Practical Foundations of Mathematics by : Paul Taylor
Download or read book Practical Foundations of Mathematics written by Paul Taylor and published by Cambridge University Press. This book was released on 1999-05-13 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practical Foundations collects the methods of construction of the objects of twentieth-century mathematics. Although it is mainly concerned with a framework essentially equivalent to intuitionistic Zermelo-Fraenkel logic, the book looks forward to more subtle bases in categorical type theory and the machine representation of mathematics. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries between universal algebra, type theory, category theory, set theory, sheaf theory, topology and programming. Students and teachers of computing, mathematics and philosophy will find this book both readable and of lasting value as a reference work.
Book Synopsis Logic from Russell to Church by : Dov M. Gabbay
Download or read book Logic from Russell to Church written by Dov M. Gabbay and published by Elsevier. This book was released on 2009-06-16 with total page 1069 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.• The entire range of modal logic is covered• Serves as a singular contribution to the intellectual history of the 20th century• Contains the latest scholarly discoveries and interpretative insights
Book Synopsis Subsystems of Second Order Arithmetic by : Stephen G. Simpson
Download or read book Subsystems of Second Order Arithmetic written by Stephen G. Simpson and published by Cambridge University Press. This book was released on 2009-05-29 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic.
Book Synopsis Automated Mathematical Induction by : Hantao Zhang
Download or read book Automated Mathematical Induction written by Hantao Zhang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been shown how the common structure that defines a family of proofs can be expressed as a proof plan [5]. This common structure can be exploited in the search for particular proofs. A proof plan has two complementary components: a proof method and a proof tactic. By prescribing the structure of a proof at the level of primitive inferences, a tactic [11] provides the guarantee part of the proof. In contrast, a method provides a more declarative explanation of the proof by means of preconditions. Each method has associated effects. The execution of the effects simulates the application of the corresponding tactic. Theorem proving in the proof planning framework is a two-phase process: 1. Tactic construction is by a process of method composition: Given a goal, an applicable method is selected. The applicability of a method is determined by evaluating the method's preconditions. The method effects are then used to calculate subgoals. This process is applied recursively until no more subgoals remain. Because of the one-to-one correspondence between methods and tactics, the output from this process is a composite tactic tailored to the given goal. 2. Tactic execution generates a proof in the object-level logic. Note that no search is involved in the execution of the tactic. All the search is taken care of during the planning process. The real benefits of having separate planning and execution phases become appar ent when a proof attempt fails.
Book Synopsis Remarks on Letters Concerning Mind by :
Download or read book Remarks on Letters Concerning Mind written by and published by . This book was released on 1750 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Journal of Symbolic Logic by : Alonzo Church
Download or read book The Journal of Symbolic Logic written by Alonzo Church and published by . This book was released on 1972 with total page 922 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes lists of members.
Book Synopsis Algebraic Geometry II: Cohomology of Schemes by : Ulrich Görtz
Download or read book Algebraic Geometry II: Cohomology of Schemes written by Ulrich Görtz and published by Springer Nature. This book was released on 2023-11-22 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and étale morphisms including the étale fundamental group. The main part is dedicated to the cohomology of quasi-coherent sheaves. The treatment is based on the formalism of derived categories which allows an efficient and conceptual treatment of the theory, which is of crucial importance in all areas of algebraic geometry. After the foundations are set up, several more advanced topics are studied, such as numerical intersection theory, an abstract version of the Theorem of Grothendieck-Riemann-Roch, the Theorem on Formal Functions, Grothendieck's algebraization results and a very general version of Grothendieck duality. The book concludes with chapters on curves and on abelian schemes, which serve to develop the basics of the theory of these two important classes of schemes on an advanced level, and at the same time to illustrate the power of the techniques introduced previously. The text contains many exercises that allow the reader to check their comprehension of the text, present further examples or give an outlook on further results.
Book Synopsis Foundations of Software Technology and Theoretical Computer Science by : P.S. Thiagarajan
Download or read book Foundations of Software Technology and Theoretical Computer Science written by P.S. Thiagarajan and published by Springer Science & Business Media. This book was released on 1994-11-23 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the 14th International Conference on the Foundations of Software Technology and Theoretical Computer Science, FST&TCS-14, held in Madras, India in December 1994. Besides the five invited papers by well-known researchers, it includes 31 full refereed research papers selected out of a total of 140 submissions. The papers contribute to the whole area of theoretical computer science with an emphasis on algorithms and complexity. Other topics covered are program semantics, program verification, formal logic, computational geometry, concurrency, unification, and discrete mathematics.
Book Synopsis Topics in Logic, Philosophy and Foundations of Mathematics, and Computer Science by : Stanisław Krajewski
Download or read book Topics in Logic, Philosophy and Foundations of Mathematics, and Computer Science written by Stanisław Krajewski and published by IOS Press. This book was released on 2007 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume honors Professor Andrzej Grzegorczyk, the nestor of Polish logicians, on his 85th anniversary. The editors would like to express the respect and sympathy they have for him. His textbook The Outline of Mathematical Logic has been published in many editions and translated into several languages. It was this textbook that introduced many of us into the world of mathematical logic. Professor Grzegorczyk has made fundamental contributions to logic and to philosophy. His results, mainly on hierarchy of primitive recursive functions, known as the Grzegorczyk hierarchy, are of fundamental importance to theoretical computer science. In particular, they were precursory for the computational complexity theory. The editors would like to stress that this special publication celebrates a scientist who is still actively pursuing genuinely innovative directions of research. Quite recently, Andrzej Grzegorczyk gave a new proof of undecidability of the first order functional calculus. His proof does not use the arithmetization of Kurt Gödel. In recognition of his merits, the University of Clermont-Ferrand conferred to Professor Andrzej Grzegorczyk the Doctorat Honoris Causa. The work and life of Professor Andrzej Grzegorczyk is presented in the article by Professors Stanislaw Krajewski and Jan Wolenski. The papers in this collection have been submitted on invitational basis.
Book Synopsis Reverse Mathematics 2001 by : Stephen G. Ross
Download or read book Reverse Mathematics 2001 written by Stephen G. Ross and published by CRC Press. This book was released on 2005-09-01 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reverse Mathematics is a program of research in the foundations of mathematics, motivated by the foundational questions of what are appropriate axioms for mathematics, and what are the logical strengths of particular axioms and particular theorems. The book contains 24 original papers by leading researchers. These articles exhibit the exciting rece
Book Synopsis Universal Artificial Intelligence by : Marcus Hutter
Download or read book Universal Artificial Intelligence written by Marcus Hutter and published by Springer Science & Business Media. This book was released on 2005-12-29 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Personal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting? A solution would have enormous implications on our society, and there are reasons to believe that the AI problem can be solved in my expected lifetime. So, it's worth sticking to it for a lifetime, even if it takes 30 years or so to reap the benefits. The AI problem. The science of artificial intelligence (AI) may be defined as the construction of intelligent systems and their analysis. A natural definition of a system is anything that has an input and an output stream. Intelligence is more complicated. It can have many faces like creativity, solving prob lems, pattern recognition, classification, learning, induction, deduction, build ing analogies, optimization, surviving in an environment, language processing, and knowledge. A formal definition incorporating every aspect of intelligence, however, seems difficult. Most, if not all known facets of intelligence can be formulated as goal driven or, more precisely, as maximizing some utility func tion. It is, therefore, sufficient to study goal-driven AI; e. g. the (biological) goal of animals and humans is to survive and spread. The goal of AI systems should be to be useful to humans.
Book Synopsis Automated Deduction – CADE-20 by : Robert Nieuwenhuis
Download or read book Automated Deduction – CADE-20 written by Robert Nieuwenhuis and published by Springer Science & Business Media. This book was released on 2005-07-14 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 20th International Conference on Automated Deduction, CADE-20, held in Tallinn, Estonia, in July 2005. The 25 revised full papers and 5 system descriptions presented were carefully reviewed and selected from 78 submissions. All current aspects of automated deduction are addressed, ranging from theoretical and methodological issues to presentation and evaluation of theorem provers and logical reasoning systems.
Book Synopsis Logic Colloquium '86 by : F.R. Drake
Download or read book Logic Colloquium '86 written by F.R. Drake and published by Elsevier. This book was released on 1987-11-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The result of the European Summer Meeting of the Association for Symbolic Logic, this volume gives an overview of the latest developments in most of the major fields of logic being actively pursued today. Important new developments in the applications of logic in computer science are presented. Other areas examined include model theory, set theory, recursion theory, proof theory, and the history of logic.This volume contains the texts of ten of the invited lectures and six of the contributed papers.
Book Synopsis Forhandlinger - Det Kongelige Norske Videnskabers Selskab by : Kongelige Norske videnskabers selskab
Download or read book Forhandlinger - Det Kongelige Norske Videnskabers Selskab written by Kongelige Norske videnskabers selskab and published by . This book was released on 1950 with total page 914 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Legacy of Kurt Schütte by : Reinhard Kahle
Download or read book The Legacy of Kurt Schütte written by Reinhard Kahle and published by Springer Nature. This book was released on 2020-08-10 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. Schütte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schütte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schütte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schütte himself that have never been published before.
Book Synopsis Freedom and Value by : Ishtiyaque Haji
Download or read book Freedom and Value written by Ishtiyaque Haji and published by Springer Science & Business Media. This book was released on 2008-10-24 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Freedom of the sort implicated in acting freely or with free will is important to the truth of different sorts of moral judgment, such as judgments of moral responsibility and those of moral obligation. Little thought, however, has been invested into whether appraisals of good or evil presuppose free will. This important topic has not commanded the attention it deserves owing to what is perhaps a prevalent assumption that freedom leaves judgments concerning good and evil largely unaffected. The central aim of this book is to dispute this assumption by arguing for the relevance of free will to the truth of two sorts of such judgment: welfare-ranking judgments or judgments of personal well-being (when is one's life intrinsically good for the one who lives it?), and world-ranking judgments (when is a possible world intrinsically better than another?). The book also examines free will’s impact on the truth of such judgments for central issues in moral obligation and in the free will debate. This book should be of interest to those working on intrinsic value, personal well-being, moral obligation, and free will.
Book Synopsis Lectures on Hilbert Schemes of Points on Surfaces by : Hiraku Nakajima
Download or read book Lectures on Hilbert Schemes of Points on Surfaces written by Hiraku Nakajima and published by American Mathematical Soc.. This book was released on 1999 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.
