Metamathematics Machines And G Del S Proof

Metamathematics Machines And G Del S Proof

Metamathematics Machines And G Del S Proof

Describes the use of computer programs to check several proofs in the foundations of mathematics.

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Genre : Computers
Author : N. Shankar
Publisher : Cambridge University Press
Release : 1997-01-30
Total Pages : 220 Pages
ISBN : 0521585333


Interactive Theorem Proving

Interactive Theorem Proving

This book constitutes the refereed proceedings of the Second International Conference on Interactive Theorem proving, ITP 2011, held in Berg en Dal, The Netherlands, in August 2011. The 25 revised full papers presented were carefully reviewed and selected from 50 submissions. Among the topics covered are counterexample generation, verification, validation, term rewriting, theorem proving, computability theory, translations from one formalism to another, and cooperation between tools. Several verification case studies were presented, with applications to computational geometry, unification, real analysis, etc.

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Genre : Computers
Author : Marko Van Eekelen
Publisher : Springer
Release : 2011-08-02
Total Pages : 383 Pages
ISBN : 9783642228636


Data Refinement

Data Refinement

The goal of this book is to provide a comprehensive and systematic introduction to the important and highly applicable method of data refinement and the simulation methods used for proving its correctness. The authors concentrate in the first part on the general principles needed to prove data refinement correct. They begin with an explanation of the fundamental notions, showing that data refinement proofs reduce to proving simulation. The book's second part contains a detailed survey of important methods in this field, which are carefully analysed, and shown to be either incomplete, with counterexamples to their application, or to be always applicable whenever data refinement holds. This is shown by proving, for the first time, that all these methods can be described and analysed in terms of two simple notions: forward and backward simulation. The book is self-contained, going from advanced undergraduate level and taking the reader to the state of the art in methods for proving simulation.

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Genre : Computers
Author : Willem-Paul de Roever
Publisher : Cambridge University Press
Release : 1998-12-03
Total Pages : 423 Pages
ISBN : 9780521641708


Advanced Topics In Bisimulation And Coinduction

Advanced Topics In Bisimulation And Coinduction

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.

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Genre : Computers
Author : Davide Sangiorgi
Publisher : Cambridge University Press
Release : 2011-10-13
Total Pages : Pages
ISBN : 9781139502900


Introduction To Coalgebra

Introduction To Coalgebra

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Total Pages : Pages
ISBN : 9781107177895


Basic Proof Theory

Basic Proof Theory

Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.

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Genre : Computers
Author : A. S. Troelstra
Publisher : Cambridge University Press
Release : 2000-07-27
Total Pages : 417 Pages
ISBN : 0521779111


Handbook Of Practical Logic And Automated Reasoning

Handbook Of Practical Logic And Automated Reasoning

One-stop reference, self-contained, with theoretical topics presented in conjunction with implementations for which code is supplied.

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Genre : Computers
Author : John Harrison
Publisher : Cambridge University Press
Release : 2009-03-12
Total Pages : 681 Pages
ISBN : 9780521899574


Recursive Functions And Metamathematics

Recursive Functions And Metamathematics

Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.

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Genre : Philosophy
Author : Roman Murawski
Publisher : Springer Science & Business Media
Release : 2013-03-14
Total Pages : 395 Pages
ISBN : 9789401728669


Concurrency Verification

Concurrency Verification

An advanced 2001 textbook on verification of concurrent programs using a semantic approach which highlights concepts clearly.

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Product Details:

Genre : Computers
Author : W.-P. de Roever
Publisher : Cambridge University Press
Release : 2001-11-26
Total Pages : 776 Pages
ISBN : 0521806089


Term Rewriting Systems

Term Rewriting Systems

Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. This 2003 book starts at an elementary level with the earlier chapters providing a foundation for the rest of the work. Much of the advanced material appeared here for the first time in book form. Subjects treated include orthogonality, termination, completion, lambda calculus, higher-order rewriting, infinitary rewriting and term graph rewriting. Many exercises are included with selected solutions provided on the web. A comprehensive bibliography makes this book ideal both for teaching and research. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations.

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Product Details:

Genre : Computers
Author : Terese
Publisher : Cambridge University Press
Release : 2003-03-20
Total Pages : 884 Pages
ISBN : 0521391156