Fundamentals Of Logic And Computation
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Fundamentals Of Logic And Computation
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Author : Zhe Hou
language : en
Publisher: Springer Nature
Release Date : 2021-12-03
Fundamentals Of Logic And Computation written by Zhe Hou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-03 with Computers categories.
This textbook aims to help the reader develop an in-depth understanding of logical reasoning and gain knowledge of the theory of computation. The book combines theoretical teaching and practical exercises; the latter is realised in Isabelle/HOL, a modern theorem prover, and PAT, an industry-scale model checker. I also give entry-level tutorials on the two software to help the reader get started. By the end of the book, the reader should be proficient in both software. Content-wise, this book focuses on the syntax, semantics and proof theory of various logics; automata theory, formal languages, computability and complexity. The final chapter closes the gap with a discussion on the insight that links logic with computation. This book is written for a high-level undergraduate course or a Master's course. The hybrid skill set of practical theorem proving and model checking should be helpful for the future of readers should they pursue a research career or engineering in formal methods.
Foundations Of Logic And Theory Of Computation
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Author : A. Sernadas
language : en
Publisher:
Release Date : 2008
Foundations Of Logic And Theory Of Computation written by A. Sernadas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computational complexity categories.
The book provides a self-contained introduction to mathematical logic and computability theory for students of mathematics or computer science. It is organized around the failures and successes of Hilbert's programme for the formalization of Mathematics. It is widely known that the programme failed with Gödel's incompleteness theorems and related negative results about arithmetic. Unfortunately, the positive outcomes of the programme are less well known, even among mathematicians. The book covers key successes, like Gödel's proof of the completeness of first-order logic, Gentzen's proof of its consistency by purely symbolic means, and the decidability of a couple of useful theories. The book also tries to convey the message that Hilbert's programme made a significant contribution to the advent of the computer as it is nowadays understood and, thus, to the latest industrial revolution. Part I of the book addresses Hilbert's programme and computability. Part II presents first-order logic, including Gödel's completeness theorem and Gentzen's consistency theorem. Part III is focused on arithmetic, representability of computable maps, Gödel's incompleteness theorems and decidability of Presburger arithmetic. Part IV provides detailed answers to selected exercises. The book can be used at late undergraduate level or early graduate level. An undergraduate course would concentrate on Parts I and II, leaving out the Gentzen calculus, and sketching the way to the 1st incompleteness theorem. A more advanced course might skip early material already known to the students and concentrate on the positive and negative results of Hilbert's programme, thus covering Gentzen's proof of consistency and Part III in full.
Fundamentals Of Computing I
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Author : Allen B. Tucker
language : en
Publisher: McGraw-Hill Companies
Release Date : 1994
Fundamentals Of Computing I written by Allen B. Tucker and has been published by McGraw-Hill Companies this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computers categories.
This second edition is based on the ACM curricula 1991 and is the first in a four-book series of introductory texts in computer science. It focuses on topics such as logic, problem-solving and theory and programs, providing an integrated overview of the major areas of computing while introducing students to the key processes of theory, abstraction and design. Topics covered include: algorithms and data structures, architecture, artificial intelligence and operating systems. The text integrates laboratory experience uniting principles with programming, and introduces the social and professional context of the discipline.
Computational Logic
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Author : Dov M. Gabbay
language : en
Publisher: Newnes
Release Date : 2014-12-09
Computational Logic written by Dov M. Gabbay and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-09 with Mathematics categories.
Handbook of the History of Logic brings to the development of logic the best in modern techniques of historical and interpretative scholarship. Computational logic was born in the twentieth century and evolved in close symbiosis with the advent of the first electronic computers and the growing importance of computer science, informatics and artificial intelligence. With more than ten thousand people working in research and development of logic and logic-related methods, with several dozen international conferences and several times as many workshops addressing the growing richness and diversity of the field, and with the foundational role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law and many engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that even the pure logicians working in the early decades of the twentieth century could have hardly anticipated. Logical calculi, which capture an important aspect of human thought, are now amenable to investigation with mathematical rigour and computational support and fertilized the early dreams of mechanised reasoning: “Calculemus . The Dartmouth Conference in 1956 – generally considered as the birthplace of artificial intelligence – raised explicitly the hopes for the new possibilities that the advent of electronic computing machinery offered: logical statements could now be executed on a machine with all the far-reaching consequences that ultimately led to logic programming, deduction systems for mathematics and engineering, logical design and verification of computer software and hardware, deductive databases and software synthesis as well as logical techniques for analysis in the field of mechanical engineering. This volume covers some of the main subareas of computational logic and its applications. Chapters by leading authorities in the field Provides a forum where philosophers and scientists interact Comprehensive reference source on the history of logic
Mathematical Logic And Computation
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Author : Jeremy Avigad
language : en
Publisher: Cambridge University Press
Release Date : 2022-09-30
Mathematical Logic And Computation written by Jeremy Avigad and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-30 with Computers categories.
A thorough introduction to the fundamental methods and results in mathematical logic, and its foundational role in computer science.
Logics For Computer Science Second Edition
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Author : SINGH, ARINDAMA
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2018-06-01
Logics For Computer Science Second Edition written by SINGH, ARINDAMA and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-01 with categories.
Designed primarily as an introductory text on logic for computer science, this well-organized book deals with almost all the basic concepts and techniques that are pertinent to the subject. It provides an excellent understanding of the logics used in computer science today. Starting with the logic of propositions, it gives a detailed coverage of first order logic and modal logics. It discusses various approaches to the proof theory of the logics, e.g. axiomatic systems, natural deduction systems, Gentzen systems, analytic tableau, and resolution. It deals with an important application of logic to computer science, namely, verification of programs. The book gives the flavour of logic engineering through computation tree logic, a logic of model checking. The book concludes with a fairly detailed discussion on nonstandard logics including intuitionistic logic, Lukasiewicz logics, default logic, autoepistemic logic, and fuzzy logic. The Second Edition includes applications of compactness theorem to many interesting problems relevant to mathematics and computer science. It also presents the undecidability of first order logic, inexpressibility of truth, and incompleteness of Peano's Arithmetic in a comprehensive and lively manner. Besides students of Computer Science, those offering courses in Mathematics and Philosophy would greatly benefit from this study. KEY FEATURES • Provides numerous worked-out examples which not only illustrate the concepts and theory developed, but also give a lead to the succeeding notions. • Exercises at the end of each section aim at reinforcing and mastering the techniques, raising issues and preparing background for further development of the subject. • Problems of theoretical nature, which are important for learning the subject, are included at the end of each chapter. • The reader is constantly provoked toworkout the details, promoting interactive learning.
Logic In Computer Science
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Author : Michael Huth
language : en
Publisher: Cambridge University Press
Release Date : 2004-08-26
Logic In Computer Science written by Michael Huth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-26 with Computers categories.
Recent years have seen the development of powerful tools for verifying hardware and software systems, as companies worldwide realise the need for improved means of validating their products. There is increasing demand for training in basic methods in formal reasoning so that students can gain proficiency in logic-based verification methods. The second edition of this successful textbook addresses both those requirements, by continuing to provide a clear introduction to formal reasoning which is both relevant to the needs of modern computer science and rigorous enough for practical application. Improvements to the first edition have been made throughout, with extra and expanded sections on SAT solvers, existential/universal second-order logic, micro-models, programming by contract and total correctness. The coverage of model-checking has been substantially updated. Further exercises have been added. Internet support for the book includes worked solutions for all exercises for teachers, and model solutions to some exercises for students.
Fundamentals Of Computing
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Author : Allen B. Tucker
language : en
Publisher:
Release Date : 1994
Fundamentals Of Computing written by Allen B. Tucker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computer categories.
Essential Logic For Computer Science
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Author : Rex Page
language : en
Publisher: MIT Press
Release Date : 2019-01-08
Essential Logic For Computer Science written by Rex Page and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Computers categories.
An introduction to applying predicate logic to testing and verification of software and digital circuits that focuses on applications rather than theory. Computer scientists use logic for testing and verification of software and digital circuits, but many computer science students study logic only in the context of traditional mathematics, encountering the subject in a few lectures and a handful of problem sets in a discrete math course. This book offers a more substantive and rigorous approach to logic that focuses on applications in computer science. Topics covered include predicate logic, equation-based software, automated testing and theorem proving, and large-scale computation. Formalism is emphasized, and the book employs three formal notations: traditional algebraic formulas of propositional and predicate logic; digital circuit diagrams; and the widely used partially automated theorem prover, ACL2, which provides an accessible introduction to mechanized formalism. For readers who want to see formalization in action, the text presents examples using Proof Pad, a lightweight ACL2 environment. Readers will not become ALC2 experts, but will learn how mechanized logic can benefit software and hardware engineers. In addition, 180 exercises, some of them extremely challenging, offer opportunities for problem solving. There are no prerequisites beyond high school algebra. Programming experience is not required to understand the book's equation-based approach. The book can be used in undergraduate courses in logic for computer science and introduction to computer science and in math courses for computer science students.
Logic For Computer Science
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Author : Jean H. Gallier
language : en
Publisher: Courier Dover Publications
Release Date : 2015-06-18
Logic For Computer Science written by Jean H. Gallier and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-18 with Mathematics categories.
This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.