Logic, Construction, Computation

Logic, Construction, Computation
Author: Ulrich Berger
Publisher: Walter de Gruyter
Total Pages: 544
Release: 2013-05-02
Genre: Philosophy
ISBN: 311032492X

Download Logic, Construction, Computation Book in PDF, Epub and Kindle

Over the last few decades the interest of logicians and mathematicians in constructive and computational aspects of their subjects has been steadily growing, and researchers from disparate areas realized that they can benefit enormously from the mutual exchange of techniques concerned with those aspects. A key figure in this exciting development is the logician and mathematician Helmut Schwichtenberg to whom this volume is dedicated on the occasion of his 70th birthday and his turning emeritus. The volume contains 20 articles from leading experts about recent developments in Constructive set theory, Provably recursive functions, Program extraction, Theories of truth, Constructive mathematics, Classical vs. intuitionistic logic, Inductive definitions, and Continuous functionals and domains.

A Computational Logic

A Computational Logic
Author: Robert S. Boyer
Publisher: Academic Press
Total Pages: 414
Release: 2014-06-25
Genre: Mathematics
ISBN: 1483277887

Download A Computational Logic Book in PDF, Epub and Kindle

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, Computation

Sets, Logic, Computation
Author: Richard Zach
Publisher:
Total Pages: 418
Release: 2021-07-13
Genre:
ISBN:

Download Sets, Logic, Computation Book in PDF, Epub and Kindle

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.

Logic, Computation, Hierarchies

Logic, Computation, Hierarchies
Author: Vasco Brattka
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 389
Release: 2014-09-04
Genre: Philosophy
ISBN: 1614519404

Download Logic, Computation, Hierarchies Book in PDF, Epub and Kindle

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.

Mathematical Logic and Computation

Mathematical Logic and Computation
Author: Jeremy Avigad
Publisher: Cambridge University Press
Total Pages: 527
Release: 2022-09-30
Genre: Computers
ISBN: 1108478751

Download Mathematical Logic and Computation Book in PDF, Epub and Kindle

A thorough introduction to the fundamental methods and results in mathematical logic, and its foundational role in computer science.

Well-Quasi Orders in Computation, Logic, Language and Reasoning

Well-Quasi Orders in Computation, Logic, Language and Reasoning
Author: Peter M. Schuster
Publisher: Springer Nature
Total Pages: 391
Release: 2020-01-01
Genre: Philosophy
ISBN: 3030302296

Download Well-Quasi Orders in Computation, Logic, Language and Reasoning Book in PDF, Epub and Kindle

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.

Digital Logic for Computing

Digital Logic for Computing
Author: John Seiffertt
Publisher: Springer
Total Pages: 324
Release: 2017-05-26
Genre: Computers
ISBN: 3319568396

Download Digital Logic for Computing Book in PDF, Epub and Kindle

The book provides a bottom-up approach to understanding how a computer works and how to use computing to solve real-world problems. It covers the basics of digital logic through the lens of computer organization and programming. The reader should be able to design his or her own computer from the ground up at the end of the book. Logic simulation with Verilog is used throughout, assembly languages are introduced and discussed, and the fundamentals of computer architecture and embedded systems are touched upon, all in a cohesive design-driven framework suitable for class or self-study.

Logic and Computation

Logic and Computation
Author: Lawrence C. Paulson
Publisher: Cambridge University Press
Total Pages: 322
Release: 1987
Genre: Computers
ISBN: 9780521395601

Download Logic and Computation Book in PDF, Epub and Kindle

This book is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines the methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of program statements. Cambridge LCF is based on an earlier theorem-proving system, Edinburgh LCF, which introduced a design that gives the user flexibility to use and extend the system. A goal of this book is to explain the design, which has been adopted in several other systems. The book consists of two parts. Part I outlines the mathematical preliminaries, elementary logic and domain theory, and explains them at an intuitive level, giving reference to more advanced reading; Part II provides sufficient detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach.

Computation Theory and Logic

Computation Theory and Logic
Author: Egon Börger
Publisher: Springer Science & Business Media
Total Pages: 456
Release: 1987-07-29
Genre: Computers
ISBN: 9783540181705

Download Computation Theory and Logic Book in PDF, Epub and Kindle

In Memory of Dieter Rötting. 24.8.1937 - 4.6.1984. On the Occasion of the 50th Anniversary of His Birth

Dynamic Logic

Dynamic Logic
Author: David Harel
Publisher: MIT Press
Total Pages: 492
Release: 2000-09-29
Genre: Computers
ISBN: 9780262263023

Download Dynamic Logic Book in PDF, Epub and Kindle

This book provides the first comprehensive introduction to Dynamic Logic. Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical first-order predicate calculus. Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value. It can be used for formalizing correctness specifications and proving rigorously that those specifications are met by a particular program. Other uses include determining the equivalence of programs, comparing the expressive power of various programming constructs, and synthesizing programs from specifications. This book provides the first comprehensive introduction to Dynamic Logic. It is divided into three parts. The first part reviews the appropriate fundamental concepts of logic and computability theory and can stand alone as an introduction to these topics. The second part discusses PDL and its variants, and the third part discusses DL and its variants. Examples are provided throughout, and exercises and a short historical section are included at the end of each chapter.