Computational Logic And Set Theory

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Computational Logic And Set Theory

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Author : Jacob T. Schwartz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-16

Computational Logic And Set Theory written by Jacob T. Schwartz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-16 with Computers categories.

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 As A Computational Logic

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Author : Lawrence C. Paulson
language : en
Publisher:
Release Date : 1992

Set Theory As A Computational Logic written by Lawrence C. Paulson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Automatic theorem proving categories.

Set Theory For Computing

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Author : Domenico Cantone
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-26

Set Theory For Computing written by Domenico Cantone and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-26 with Computers categories.

Set Theory for Computing offers an up-to-date and comprehensive account of set-oriented symbolic manipulation and automated reasoning methods. Mastering today's variety of systems with crisp, formal tools is a prerequisite for a high degree of control over sets and aggregates. The many algorithmic methods and deductive techniques in this book offer readers a clear view of the use of set-theoretic notions in such critical areas as specification of problems, data types, and solution methods; algorithmic program verification; and automated deduction. The rigorous and largely self-contained style of presentation addresses readers wanting to complement their set intuition with the ability to exploit it in specification and verification and master it by symbolic, logically based techniques and methods. This book will be of interest to graduates and researchers in theoretical computer science and computational logic and automated reasoning.

Applied Set Theory And Logic

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Author : John-Michael Kuczynski
language : en
Publisher: John-Michael Kuczynski
Release Date : 2025-06-12

Applied Set Theory And Logic written by John-Michael Kuczynski and has been published by John-Michael Kuczynski this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-12 with Philosophy categories.

Applied Set Theory and Logic is a comprehensive guide to the core principles of set theory and mathematical logic, with an emphasis on real-world applications in computer science, engineering, and digital systems. Bridging rigorous theoretical foundations with practical examples, the book explores topics ranging from propositional calculus and predicate logic to modal logic, database systems, circuit verification, and algorithm design. Through hundreds of worked examples and exercises, readers learn to apply logical reasoning to concrete problems in programming, software verification, hardware design, and information systems. Advanced topics include modal logic, recursion, transitivity, Von Neumann and Zermelo ordinals, Boolean algebra, and formal proof techniques. Each chapter highlights the relevance of logic and set theory to contemporary computational systems and digital technologies. Suitable for students, engineers, computer scientists, and researchers, Applied Set Theory and Logic serves both as a theoretical reference and a practical guide to the logical structures that underlie modern technology.

Set Theory And Logic

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Author : Robert Roth Stoll
language : en
Publisher: Courier Corporation
Release Date : 1979-10-01

Set Theory And Logic written by Robert Roth Stoll and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-10-01 with Mathematics categories.

"The best introductory text we have seen." — Cosmos. Lucidly and gradually explains sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories. Its clarity makes this book excellent for self-study.

Computational Logic

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Author : Ulrich Berger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Computational Logic written by Ulrich Berger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.

Recent developments in computer science clearly show the need for a better theoretical foundation for some central issues. Methods and results from mathematical logic, in particular proof theory and model theory, are of great help here and will be used much more in future than previously. This book provides an excellent introduction to the interplay of mathematical logic and computer science. It contains extensively reworked versions of the lectures given at the 1997 Marktoberdorf Summer School by leading researchers in the field. Topics covered include: proof theory and specification of computation (J.-Y. Girard, D. Miller), complexity of proofs and programs (S. R. Buss, S. S. Wainer), computational content of proofs (H. Schwichtenberg), constructive type theory (P. Aczel, H. Barendregt, R. L. Constable), computational mathematics, (U. Martin), rewriting logic (J. Meseguer), and game semantics (S. Abramski).

Merging Hol With Set Theory

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Author : Michael J. C. Gordon
language : en
Publisher:
Release Date : 1994

Merging Hol With Set Theory written by Michael J. C. Gordon 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 programs categories.

Abstract: "Set theory is the standard foundation for mathematics, but the majority of general purpose mechanized proof assistants support versions of type theory (higher order logic). Examples include Alf, Automath, Coq, Ehdm, HOL, IMPS, Lambda, LEGO, Nuprl, PVS and Veritas. For many applications type theory works well and provides, for specification, the benefits of type-checking that are well-known in programming. However, there are areas where types get in the way or seem unmotivated. Furthermore, most people with a scientific or engineering background already know set theory, whereas type theory may appear inaccessable [sic] and so be an obstacle to the uptake of proof assistants based on it. This paper describes some experiments (using HOL) in combining set theory and type theory; the aim is to get the best of both worlds in a single system. Three approaches have been tried, all based on an axiomatically specified type V of ZF-like sets: (i) HOL is used without any additions besides V; (ii) an embedding of the HOL logic into V is provided; (iii) HOL axiomatic theories are not automatically translated into set-theoretic definitional theories. These approaches are illustrated with two examples: the construction of lists and a simple lemma in group theory."

Computation Logic Philosophy

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Author : Wang Hao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Computation Logic Philosophy written by Wang Hao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

~Et moi ... si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Computational Logic And Proof Theory

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Author : Georg Gottlob
language : en
Publisher:
Release Date : 1993

Computational Logic And Proof Theory written by Georg Gottlob and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Automatic theorem proving categories.

"The Third Kurt G

Computational Logic And Proof Theory

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Author : Georg Gottlob
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-08-13

Computational Logic And Proof Theory written by Georg Gottlob and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-13 with Computers categories.

This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.