Download or read book Completeness and Incompleteness Theorems for Hoare like Axiom Systems written by Edmund Nelson Clarke and published by . This book was released on 1976 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Topics in Bisimulation and Coinduction written by Davide Sangiorgi and published by Cambridge University Press. This book was released on 2011-10-13 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.
Download or read book G del s Incompleteness Theorems written by Raymond M. Smullyan and published by Oxford University Press, USA. This book was released on 1992 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the work of the mathematical logician Kurt Godel, which guides the reader through his Theorem of Undecidability and his theories on the completeness of logic, the incompleteness of numbers and the consistency of the axiom of choice.
Download or read book There s Something About G del written by Francesco Berto and published by John Wiley & Sons. This book was released on 2009-11-09 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berto's highly readable and lucid guide introduces students and the interested reader to Gödel's celebrated Incompleteness Theorem, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments. Offers a clear understanding of this difficult subject by presenting each of the key steps of the Theorem in separate chapters Discusses interpretations of the Theorem made by celebrated contemporary thinkers Sheds light on the wider extra-mathematical and philosophical implications of Gödel's theories Written in an accessible, non-technical style
Download or read book Automata Languages and Programming written by G. Ausiello and published by Springer Science & Business Media. This book was released on 1978-07 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple EOL forms under uniform interpretation generating CF languages; Codes: unequal probabilities unequal letter costs; Sur l'inversion des morphismes d'arbres; Grammars with dynamic control sets; Ambiguite forte; Relationship between density and deterministic complexity of NP-complete languages; Stable models of typed calculi; Path measures of turing machines computations; Une famille remarquable de codes indecomposables; Comparisons and reset machines; Size-depth tradeoff in boolean formulas.
Download or read book Journal of the Association for Computing Machinery written by Association for Computing Machinery and published by . This book was released on 1988 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book G del s Theorem written by Torkel Franzén and published by CRC Press. This book was released on 2005-06-06 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel
Download or read book First Order Programming Theories written by Tamas Gergely and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a purely classical first-order logical approach to the field of study in theoretical computer science sometimes referred to as the theory of programs, or programming theory. This field essentially attempts to provide a precise mathematical basis for the common activities involved in reasoning about computer programs and programming languages, and it also attempts to find practical applications in the areas of program specification, verification and programming language design. Many different approaches with different mathematical frameworks have been proposed as a basis for programming theory. They differ in the mathe matical machinery they use to define and investigate programs and program properties and they also differ in the concepts they deal with to understand the programming paradigm. Different approaches use different tools and viewpoints to characterize the data environment of programs. Most of the approaches are related to mathe matical logic and they provide their own logic. These logics, however, are very eclectic since they use special entities to reflect a special world of programs, and also, they are usually incomparable with each other. This Babel's mess irritated us and we decided to peel off the eclectic com ponents and try to answer all the questions by using classical first-order logic.
Download or read book Metatheorems written by Source Wikipedia and published by University-Press.org. This book was released on 2013-09 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 23. Chapters: Abstract model theory, Barwise compactness theorem, Courcelle's theorem, Deduction theorem, Entscheidungsproblem, Frege's theorem, Gentzen's consistency proof, Godel's completeness theorem, Godel's incompleteness theorems, Herbrand's theorem, Lindstrom's theorem, Lob's theorem, Lowenheim-Skolem theorem, Metatheorem, Tarski's undefinability theorem. Excerpt: Godel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Godel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency. Because statements of a formal theory are written in symbolic form, it is possible to mechanically verify that a formal proof from a finite set of axioms is valid. This task, known as automatic proof verification, is closely related to automated theorem proving. The difference is that instead of constructing a new proof, the proof verifier simply checks that a provided formal proof...
Download or read book 18th Annual Symposium on Foundations of Computer Science Oct 31 Nov 2 1977 Providence Rhode Island written by and published by . This book was released on 1977 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Extensions of the UNITY Methodology written by Josyula R. Rao and published by Springer Science & Business Media. This book was released on 1995-04-06 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph extends and generalizes the UNITY methodology, introduced in the late 1980s by K. Mani Chandy and Jayadev Misra as a formalism aiding in the specification and verification of parallel programs, in several directions. This treatise further develops the ideas behind UNITY in order to explore and understand the potential and limitations of this approach: first UNITY is applied to formulate and tackle problems in parallelism such as compositionality; second, the logic and notation of UNITY is generalized in order to increase its range of applicability; finally, paradigms and abstractions useful for the design of probabilistic parallel algorithms are developed. Taken together the results presented reaffirm the promise of UNITY as a versatile medium for treating many problems of parallelism.
Download or read book Proceedings of the ACM Symposium on Theory of Computing written by and published by . This book was released on 1977 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Incompleteness Phenomenon written by Martin Goldstern and published by A K Peters/CRC Press. This book was released on 1995-06-15 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book should interest everyone from mathematicians to philosophers and readers who wish to understand the foundations and limitations of rational thinking. It is used as a textbook at major colleges and universities but lends itself to self-study as well.
Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1984 with total page 904 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1977 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains articles of significant interest to mathematicians, including reports on current mathematical research.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1977 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Information Processing written by and published by . This book was released on 1977 with total page 1032 pages. Available in PDF, EPUB and Kindle. Book excerpt:
