Metamath A Computer Language For Mathematical Proofs
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Metamath: A Computer Language for Mathematical Proofs by Norman Megill,David A. Wheeler Pdf
Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the "Formalizing 100 Theorems" challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database.
Metamath is a tiny computer language that can express theorems in abstract mathematics, accompanied by proofs that can be verified by a computer program. The first part of the book provides easy-to-read informal discussion of abstract mathematics and computers for general audiences. The later parts provide in-depth coverage of the foundations of mathematics, the Metamath language, and the Metamath program. More information can be found at the metamath.org web site. (Note: the Preview is an on-line copy of the entire book so that you can see exactly what you'll be buying.)
What Is Computer Assisted Proof A mathematical proof is considered to be computer-assisted if it has been generated by the computer in some way, even if just in part. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Computer-assisted proof Chapter 2: Mathematical proof Chapter 3: Theorem Chapter 4: Metamath Chapter 5: Model checking Chapter 6: Computer algebra Chapter 7: Formal verification Chapter 8: Validated numerics Chapter 9: Logic Theorist Chapter 10: Seventeen or Bust (II) Answering the public top questions about computer assisted proof. (III) Real world examples for the usage of computer assisted proof in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of computer assisted proof' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of computer assisted proof.
Intelligent Computer Mathematics by Fairouz Kamareddine,Claudio Sacerdoti Coen Pdf
This book constitutes the refereed proceedings of the 14th International Conference on Intelligent Computer Mathematics, CICM 2021, held in Timisoara, Romania, in July 2021*. The 12 full papers, 7 system descriptions, 1 system entry, and 3 abstracts of invited papers presented were carefully reviewed and selected from a total of 38 submissions. The papers focus on advances in formalization, automatic theorem proving and learning, search and classification, teaching and geometric reasoning, and logic and systems, among other topics. * The conference was held virtually due to the COVID-19 pandemic.
Gregory Chaitin, one of the world’s foremost mathematicians, leads us on a spellbinding journey, illuminating the process by which he arrived at his groundbreaking theory. Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.
Computer Aided Verification by Alexandra Silva,K. Rustan M. Leino Pdf
This open access two-volume set LNCS 12759 and 12760 constitutes the refereed proceedings of the 33rd International Conference on Computer Aided Verification, CAV 2021, held virtually in July 2021. The 63 full papers presented together with 16 tool papers and 5 invited papers were carefully reviewed and selected from 290 submissions. The papers were organized in the following topical sections: Part I: invited papers; AI verification; concurrency and blockchain; hybrid and cyber-physical systems; security; and synthesis. Part II: complexity and termination; decision procedures and solvers; hardware and model checking; logical foundations; and software verification.
Theoretical Aspects of Computing – ICTAC 2023 by Erika Ábrahám,Clemens Dubslaff,Silvia Lizeth Tapia Tarifa Pdf
This book constitutes the proceedings of the 20th International Colloquium on Theoretical Aspects of Computing, ICTAC 2023, which took place in Lima, Peru, during December 4–8, 2023. The 20 full papers presented in this volume together with 3 invited papers and 1 tool paper were carefully reviewed and selected from 40 submissions. They were organised in the topical sections as follows: Bring Together Practitioners; Researchers from Academia; Industry; Government to Present Research Results and Exchange Experience and Ideas.
Intelligent Computer Mathematics by Christoph Benzmüller,Bruce Miller Pdf
This book constitutes the refereed proceedings of the 13th International Conference on Intelligent Computer Mathematics, CICM 2020, held in Bertinoro, Italy, in July 2020*. The 15 full papers, 1 invited paper and 2 abstracts of invited papers presented were carefully reviewed and selected from a total of 35 submissions. The papers focus on advances in automated theorem provers and formalization, computer algebra systems and their libraries, and applications of machine learning, among other topics. * The conference was held virtually due to the COVID-19 pandemic.
Advances in Computer Games by Michael Hartisch,Chu-Hsuan Hsueh,Jonathan Schaeffer Pdf
This book constitutes the refereed post proceedings of the 18th International Conference on Advances in Computer Games, ACG 2023, held online, during November 28–30, 2023. The 14 full papers included in this book were carefully reviewed and selected from 29 submissions. They were organized in topical sections as follows: Chess and its Variants, Solving Games, Board Games, Card Games, Player Investigation, Math, Games, and Puzzles.
Concepts of Proof in Mathematics, Philosophy, and Computer Science by Dieter Probst,Peter Schuster Pdf
A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.
Types for Proofs and Programs by Marino Miculan,Ivan Scagnetto,Furio Honsell Pdf
This book constitutes the thoroughly refereed post-conference proceedings of TYPES 2007, the concluding conference of the Types project, held in Cividale del Friuli, Italy, in May 2007. The 13 revised full papers presented were carefully reviewed and selected from 22 submissions. The topic of this last annual workshop of the Types Working Group was formal reasoning and computer programming based on type theory. Great importance was attached to languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certified software, formalization of mathematics and mathematics education.
What Is Automated Theorem Proving The process of proving mathematical theorems by the use of computer programs is referred to as automated theorem proving. This subfield of automated reasoning and mathematical logic was developed in the 1980s. A significant driving force behind the development of computer science was the application of automated reasoning to mathematical proof. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Automated theorem proving Chapter 2: Curry-Howard correspondence Chapter 3: Logic programming Chapter 4: Proof complexity Chapter 5: Metamath Chapter 6: Model checking Chapter 7: Formal verification Chapter 8: Program analysis Chapter 9: Ramanujan machine Chapter 10: General Problem Solver (II) Answering the public top questions about automated theorem proving. (III) Real world examples for the usage of automated theorem proving in many fields. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of automated theorem proving. What is Artificial Intelligence Series The artificial intelligence book series provides comprehensive coverage in over 200 topics. Each ebook covers a specific Artificial Intelligence topic in depth, written by experts in the field. The series aims to give readers a thorough understanding of the concepts, techniques, history and applications of artificial intelligence. Topics covered include machine learning, deep learning, neural networks, computer vision, natural language processing, robotics, ethics and more. The ebooks are written for professionals, students, and anyone interested in learning about the latest developments in this rapidly advancing field. The artificial intelligence book series provides an in-depth yet accessible exploration, from the fundamental concepts to the state-of-the-art research. With over 200 volumes, readers gain a thorough grounding in all aspects of Artificial Intelligence. The ebooks are designed to build knowledge systematically, with later volumes building on the foundations laid by earlier ones. This comprehensive series is an indispensable resource for anyone seeking to develop expertise in artificial intelligence.
