Mathematical Logic And Computation

Author : Jeremy Avigad
Publisher : Cambridge University Press
ISBN 13 : 1108478751
Total Pages : 527 pages
Book Rating : 4.55/5 ( download)

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Download or read book Mathematical Logic and Computation written by Jeremy Avigad and published by Cambridge University Press. This book was released on 2022-09-30 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough introduction to the fundamental methods and results in mathematical logic, and its foundational role in computer science.

Author : Mordechai Ben-Ari
Publisher : Springer Science & Business Media
ISBN 13 : 1447103351
Total Pages : 311 pages
Book Rating : 4.56/5 ( download)

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Download or read book Mathematical Logic for Computer Science written by Mordechai Ben-Ari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a mathematics textbook with theorems and proofs. The choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. In order to provide a balanced treatment of logic, tableaux are related to deductive proof systems. The book presents various logical systems and contains exercises. Still further, Prolog source code is available on an accompanying Web site. The author is an Associate Professor at the Department of Science Teaching, Weizmann Institute of Science.

Author : Zhe Hou
Publisher : Springer Nature
ISBN 13 : 3030878821
Total Pages : 225 pages
Book Rating : 4.25/5 ( download)

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Download or read book Fundamentals of Logic and Computation written by Zhe Hou and published by Springer Nature. This book was released on 2021-12-03 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David Makinson
Publisher : Springer Science & Business Media
ISBN 13 : 1447125002
Total Pages : 302 pages
Book Rating : 4.06/5 ( download)

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Download or read book Sets, Logic and Maths for Computing written by David Makinson and published by Springer Science & Business Media. This book was released on 2012-02-27 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.

Author : Alexander George
Publisher : Oxford University Press, USA
ISBN 13 : 0195079299
Total Pages : 218 pages
Book Rating : 4.96/5 ( download)

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Download or read book Mathematics and Mind written by Alexander George and published by Oxford University Press, USA. This book was released on 1994 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essays in this volume investigate the conceptual foundations of mathematics illuminating the powers of the mind. Contributors include Alexander George, Michael Dummett, George Boolos, W.W. Tait, Wilfried Sieg, Daniel Isaacson, Charles Parsons, and Michael Hallett.

Author : Robert S. Boyer
Publisher : Academic Press
ISBN 13 : 1483277887
Total Pages : 414 pages
Book Rating : 4.82/5 ( download)

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Download or read book A Computational Logic written by Robert S. Boyer and published by Academic Press. This book was released on 2014-06-25 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: ACM Monograph Series: A Computational Logic focuses on the use of induction in proving theorems, including the use of lemmas and axioms, free variables, equalities, and generalization. The publication first elaborates on a sketch of the theory and two simple examples, a precise definition of the theory, and correctness of a tautology-checker. Topics include mechanical proofs, informal development, formal specification of the problem, well-founded relations, natural numbers, and literal atoms. The book then examines the use of type information to simplify formulas, use of axioms and lemmas as rewrite rules, and the use of definitions. Topics include nonrecursive functions, computing values, free variables in hypothesis, infinite backwards chaining, infinite looping, computing type sets, and type prescriptions. The manuscript takes a look at rewriting terms and simplifying clauses, eliminating destructors and irrelevance, using equalities, and generalization. Concerns include reasons for eliminating isolated hypotheses, precise statement of the generalization heuristic, restricting generalizations, precise use of equalities, and multiple destructors and infinite looping. The publication is a vital source of data for researchers interested in computational logic.

Author : Ulrich Berger
Publisher : Walter de Gruyter
ISBN 13 : 311032492X
Total Pages : 544 pages
Book Rating : 4.21/5 ( download)

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Download or read book Logic, Construction, Computation written by Ulrich Berger and published by Walter de Gruyter. This book was released on 2013-05-02 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few decades the interest of logicians and mathematicians in constructive and computational aspects of their subjects has been steadily growing, and researchers from disparate areas realized that they can benefit enormously from the mutual exchange of techniques concerned with those aspects. A key figure in this exciting development is the logician and mathematician Helmut Schwichtenberg to whom this volume is dedicated on the occasion of his 70th birthday and his turning emeritus. The volume contains 20 articles from leading experts about recent developments in Constructive set theory, Provably recursive functions, Program extraction, Theories of truth, Constructive mathematics, Classical vs. intuitionistic logic, Inductive definitions, and Continuous functionals and domains.

Author : Wolfgang Rautenberg
Publisher : Springer
ISBN 13 : 1441912215
Total Pages : 337 pages
Book Rating : 4.13/5 ( download)

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Download or read book A Concise Introduction to Mathematical Logic written by Wolfgang Rautenberg and published by Springer. This book was released on 2010-07-01 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.

Author : Jean H. Gallier
Publisher : Courier Dover Publications
ISBN 13 : 0486780821
Total Pages : 532 pages
Book Rating : 4.25/5 ( download)

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Download or read book Logic for Computer Science written by Jean H. Gallier and published by Courier Dover Publications. This book was released on 2015-06-18 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Yannai A. Gonczarowski
Publisher : Cambridge University Press
ISBN 13 : 1108957692
Total Pages : 286 pages
Book Rating : 4.94/5 ( download)

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Download or read book Mathematical Logic through Python written by Yannai A. Gonczarowski and published by Cambridge University Press. This book was released on 2022-07-31 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel's completeness theorem. A sneak peek to Gödel's incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed.