Computational Logic And Set Theory

Author : Jacob T. Schwartz,Domenico Cantone,Eugenio G. Omodeo
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 48,8 Mb
Release : 2011-07-16
Category : Computers
ISBN : 0857298089

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Computational Logic and Set Theory by Jacob T. Schwartz,Domenico Cantone,Eugenio G. Omodeo Pdf

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.

Author : Domenico Cantone,Eugenio Omodeo,Alberto Policriti
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 47,5 Mb
Release : 2013-06-29
Category : Computers
ISBN : 9781475734522

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Set Theory for Computing by Domenico Cantone,Eugenio Omodeo,Alberto Policriti Pdf

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.

Author : Richard Zach
Publisher : Unknown
Page : 418 pages
File Size : 43,9 Mb
Release : 2021-07-13
Category : Electronic
ISBN : 9798536395509

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Sets, Logic, Computation by Richard Zach Pdf

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.

Author : David Makinson
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 53,6 Mb
Release : 2012-02-27
Category : Computers
ISBN : 9781447125006

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Sets, Logic and Maths for Computing by David Makinson Pdf

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 : Robert S. Boyer,J Strother Moore
Publisher : Academic Press
Page : 414 pages
File Size : 41,5 Mb
Release : 2014-06-25
Category : Mathematics
ISBN : 9781483277882

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A Computational Logic by Robert S. Boyer,J Strother Moore Pdf

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 : Peter J. Cameron
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447105893

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Sets, Logic and Categories by Peter J. Cameron Pdf

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.

Author : Vasco Brattka,Hannes Diener,Dieter Spreen
Publisher : Walter de Gruyter GmbH & Co KG
Page : 424 pages
File Size : 47,9 Mb
Release : 2014-09-04
Category : Philosophy
ISBN : 9781614518044

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Logic, Computation, Hierarchies by Vasco Brattka,Hannes Diener,Dieter Spreen Pdf

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.

Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 50,7 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X

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Principia Mathematica by Alfred North Whitehead,Bertrand Russell Pdf

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

Author : George Tourlakis
Publisher : Cambridge University Press
Page : 0 pages
File Size : 51,7 Mb
Release : 2011-07-21
Category : Mathematics
ISBN : 0521168481

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

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).

Author : Robert S. Boyer,J Strother Moore
Publisher : Elsevier
Page : 426 pages
File Size : 52,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483277783

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A Computational Logic Handbook by Robert S. Boyer,J Strother Moore Pdf

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.

Author : Domenico Cantone,Eugenio Omodeo,Alberto Policriti
Publisher : Springer
Page : 409 pages
File Size : 50,6 Mb
Release : 2013-02-14
Category : Computers
ISBN : 1475734530

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Set Theory for Computing by Domenico Cantone,Eugenio Omodeo,Alberto Policriti Pdf

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.

Author : Wolfgang Rautenberg
Publisher : Springer
Page : 337 pages
File Size : 40,9 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781441912213

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A Concise Introduction to Mathematical Logic by Wolfgang Rautenberg Pdf

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 : Georg Gottlob,Alexander Leitsch,Daniele Mundici
Publisher : Unknown
Page : 376 pages
File Size : 43,9 Mb
Release : 1993
Category : Automatic theorem proving
ISBN : UOM:39015033145890

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Computational Logic and Proof Theory by Georg Gottlob,Alexander Leitsch,Daniele Mundici Pdf

"The Third Kurt G

Author : Domenico Cantone
Publisher : Springer Nature
Page : 280 pages
File Size : 50,5 Mb
Release : 2024-06-11
Category : Electronic
ISBN : 9783031552489

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From Computational Logic to Computational Biology by Domenico Cantone Pdf

Author : Dov M. Gabbay,Jörg H. Siekmann,John Woods
Publisher : Newnes
Page : 736 pages
File Size : 54,9 Mb
Release : 2014-12-09
Category : Mathematics
ISBN : 9780080930671

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Computational Logic by Dov M. Gabbay,Jörg H. Siekmann,John Woods Pdf

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