Computational Logic And Set Theory

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Computational Logic and Set Theory

Author : Jacob T. Schwartz
Publisher : Springer Science & Business Media
ISBN 13 : 9780857298089
Total Pages : 416 pages
Book Rating : 4.2/5 (98 download)

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Book Synopsis Computational Logic and Set Theory by : Jacob T. Schwartz

Download or read book Computational Logic and Set Theory written by Jacob T. Schwartz and published by Springer Science & Business Media. This book was released on 2011-07-16 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.

Set Theory for Computing

Author : Domenico Cantone
Publisher : Springer Science & Business Media
ISBN 13 : 1475734522
Total Pages : 419 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Set Theory for Computing by : Domenico Cantone

Download or read book Set Theory for Computing written by Domenico Cantone and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date and comprehensive account of set-oriented symbolic manipulation and automated reasoning methods. This book is of interest to graduates and researchers in theoretical computer science and computational logic and automated reasoning.

Sets, Logic, Computation

Author : Richard Zach
Publisher :
ISBN 13 :
Total Pages : 418 pages
Book Rating : 4.5/5 (363 download)

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Book Synopsis Sets, Logic, Computation by : Richard Zach

Download or read book Sets, Logic, Computation written by Richard Zach and published by . This book was released on 2021-07-13 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook on the semantics, proof theory, and metatheory of first-order logic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. It is based on the Open Logic project, and available for free download at slc.openlogicproject.org.

Sets, Logic and Maths for Computing

Author : David Makinson
Publisher : Springer Science & Business Media
ISBN 13 : 1447125002
Total Pages : 283 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Sets, Logic and Maths for Computing by : David Makinson

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 283 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.

A Computational Logic

Author : Robert S. Boyer
Publisher : Academic Press
ISBN 13 : 1483277887
Total Pages : 414 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis A Computational Logic by : Robert S. Boyer

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.

Sets, Logic and Categories

Author : Peter J. Cameron
Publisher : Springer Science & Business Media
ISBN 13 : 1447105893
Total Pages : 191 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Sets, Logic and Categories by : Peter J. Cameron

Download or read book Sets, Logic and Categories written by Peter J. Cameron and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.

Set Theory, Logic and Their Limitations

Author : Moshe Machover
Publisher : Cambridge University Press
ISBN 13 : 9780521479981
Total Pages : 304 pages
Book Rating : 4.4/5 (799 download)

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Book Synopsis Set Theory, Logic and Their Limitations by : Moshe Machover

Download or read book Set Theory, Logic and Their Limitations written by Moshe Machover and published by Cambridge University Press. This book was released on 1996-05-23 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.

Logical Foundations of Mathematics and Computational Complexity

Author : Pavel Pudlák
Publisher : Springer Science & Business Media
ISBN 13 : 3319001191
Total Pages : 699 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Logical Foundations of Mathematics and Computational Complexity by : Pavel Pudlák

Download or read book Logical Foundations of Mathematics and Computational Complexity written by Pavel Pudlák and published by Springer Science & Business Media. This book was released on 2013-04-22 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Logic and Proof Theory

Author : Georg Gottlob
Publisher :
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Computational Logic and Proof Theory by : Georg Gottlob

Download or read book Computational Logic and Proof Theory written by Georg Gottlob and published by . This book was released on 1993 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Third Kurt G

A First Course in Mathematical Logic and Set Theory

Author : Michael L. O'Leary
Publisher : John Wiley & Sons
ISBN 13 : 1118548019
Total Pages : 464 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis A First Course in Mathematical Logic and Set Theory by : Michael L. O'Leary

Download or read book A First Course in Mathematical Logic and Set Theory written by Michael L. O'Leary and published by John Wiley & Sons. This book was released on 2015-09-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.

A Concise Introduction to Mathematical Logic

Author : Wolfgang Rautenberg
Publisher : Springer
ISBN 13 : 1441912215
Total Pages : 337 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A Concise Introduction to Mathematical Logic by : Wolfgang Rautenberg

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.

Lectures in Logic and Set Theory: Volume 2, Set Theory

Author : George Tourlakis
Publisher : Cambridge University Press
ISBN 13 : 9780521168489
Total Pages : 0 pages
Book Rating : 4.1/5 (684 download)

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Book Synopsis Lectures in Logic and Set Theory: Volume 2, Set Theory by : George Tourlakis

Download or read book Lectures in Logic and Set Theory: Volume 2, Set Theory written by George Tourlakis and published by Cambridge University Press. This book was released on 2011-07-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's construstive universe, numerous ways of viewing recursion and Cohen forcing).

A Computational Logic Handbook

Author : Robert S. Boyer
Publisher : Elsevier
ISBN 13 : 148327778X
Total Pages : 426 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis A Computational Logic Handbook by : Robert S. Boyer

Download or read book A Computational Logic Handbook written by Robert S. Boyer and published by Elsevier. This book was released on 2014-05-10 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perspectives in Computing: A Computational Logic Handbook contains a precise description of the logic and a detailed reference guide to the associated mechanical theorem proving system, including a primer for the logic as a functional programming language, an introduction to proofs in the logic, and a primer for the mechanical theorem. The publication first offers information on a primer for the logic, formalization within the logic, and a precise description of the logic. Discussions focus on induction and recursion, quantification, explicit value terms, dealing with features and omissions, elementary mathematical relationships, Boolean operators, and conventional data structures. The text then takes a look at proving theorems in the logic, mechanized proofs in the logic, and an introduction to the system. The text examines the processes involved in using the theorem prover, four classes of rules generated from lemmas, and aborting or interrupting commands. Topics include executable counterparts, toggle, elimination of irrelevancy, heuristic use of equalities, representation of formulas, type sets, and the crucial check points in a proof attempt. The publication is a vital reference for researchers interested in computational logic.

Principia Mathematica

Author : Alfred North Whitehead
Publisher :
ISBN 13 :
Total Pages : 696 pages
Book Rating : 4.L/5 ( download)

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Book Synopsis Principia Mathematica by : Alfred North Whitehead

Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Logic, Computation, Hierarchies

Author : Vasco Brattka
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 1614519404
Total Pages : 424 pages
Book Rating : 4.6/5 (145 download)

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Book Synopsis Logic, Computation, Hierarchies by : Vasco Brattka

Download or read book Logic, Computation, Hierarchies written by Vasco Brattka and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-09-04 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in honor of Victor L. Selivanov, the 17 articles collected in this volume inform on the latest developments in computability theory and its applications in computable analysis; descriptive set theory and topology; and the theory of omega-languages; as well as non-classical logics, such as temporal logic and paraconsistent logic. This volume will be of interest to mathematicians and logicians, as well as theoretical computer scientists.

Computational Logic

Author : Dov M. Gabbay
Publisher : Newnes
ISBN 13 : 0080930670
Total Pages : 736 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Computational Logic by : Dov M. Gabbay

Download or read book Computational Logic written by Dov M. Gabbay and published by Newnes. This book was released on 2014-12-09 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Computable Set Theory

Author : Domenico Cantone
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 370 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Computable Set Theory by : Domenico Cantone

Download or read book Computable Set Theory written by Domenico Cantone and published by Oxford University Press, USA. This book was released on 1989 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors describe computational techniques for deciding formulae in set theory. The eventual aim of such a work is to automate simple proofs over a wide range of mathematical areas. This volume reports on a successful series of investigations in one of the most important sub-domains:elementary set theory.