Computation As Logic

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A Computational Logic

Robert S. Boyer,J Strother Moore
A Computational Logic Book PDF

Author : Robert S. Boyer,J Strother Moore
Publisher : Academic Press
Page : 414 pages
File Size : 43,6 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.

Fundamentals of Logic and Computation

Zhe Hou
Fundamentals of Logic and Computation Book PDF

Author : Zhe Hou
Publisher : Springer
Page : 0 pages
File Size : 43,9 Mb
Release : 2022-12-05
Category : Computers
ISBN : 3030878848

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Fundamentals of Logic and Computation by Zhe Hou Pdf

This textbook aims to help the reader develop an in-depth understanding of logical reasoning and gain knowledge of the theory of computation. The book combines theoretical teaching and practical exercises; the latter is realised in Isabelle/HOL, a modern theorem prover, and PAT, an industry-scale model checker. I also give entry-level tutorials on the two software to help the reader get started. By the end of the book, the reader should be proficient in both software. Content-wise, this book focuses on the syntax, semantics and proof theory of various logics; automata theory, formal languages, computability and complexity. The final chapter closes the gap with a discussion on the insight that links logic with computation. This book is written for a high-level undergraduate course or a Master's course. The hybrid skill set of practical theorem proving and model checking should be helpful for the future of readers should they pursue a research career or engineering in formal methods.

A Computational Logic Handbook

Robert S. Boyer,J Strother Moore
A Computational Logic Handbook Book PDF

Author : Robert S. Boyer,J Strother Moore
Publisher : Elsevier
Page : 426 pages
File Size : 48,8 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.

Computational Logic

Dov M. Gabbay,Jörg H. Siekmann,John Woods
Computational Logic Book PDF

Author : Dov M. Gabbay,Jörg H. Siekmann,John Woods
Publisher : Newnes
Page : 736 pages
File Size : 43,5 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

Puzzles in Logic, Languages and Computation

Dragomir Radev
Puzzles in Logic Languages and Computation Book PDF

Author : Dragomir Radev
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 44,8 Mb
Release : 2013-02-11
Category : Language Arts & Disciplines
ISBN : 9783642343780

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Puzzles in Logic, Languages and Computation by Dragomir Radev Pdf

This is the first volume of a unique collection that brings together the best English-language problems created for students competing in the Computational Linguistics Olympiad. These problems are representative of the diverse areas presented in the competition and designed with three principles in mind: · To challenge the student analytically, without requiring any explicit knowledge or experience in linguistics or computer science; · To expose the student to the different kinds of reasoning required when encountering a new phenomenon in a language, both as a theoretical topic and as an applied problem; · To foster the natural curiosity students have about the workings of their own language, as well as to introduce them to the beauty and structure of other languages; · To learn about the models and techniques used by computers to understand human language. Aside from being a fun intellectual challenge, the Olympiad mimics the skills used by researchers and scholars in the field of computational linguistics. In an increasingly global economy where businesses operate across borders and languages, having a strong pool of computational linguists is a competitive advantage, and an important component to both security and growth in the 21st century. This collection of problems is a wonderful general introduction to the field of linguistics through the analytic problem solving technique. "A fantastic collection of problems for anyone who is curious about how human language works! These books take serious scientific questions and present them in a fun, accessible way. Readers exercise their logical thinking capabilities while learning about a wide range of human languages, linguistic phenomena, and computational models. " - Kevin Knight, USC Information Sciences Institute

A Concise Introduction to Mathematical Logic

Wolfgang Rautenberg
A Concise Introduction to Mathematical Logic Book PDF

Author : Wolfgang Rautenberg
Publisher : Springer
Page : 337 pages
File Size : 49,8 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.

The Cultural Logic of Computation

David Golumbia
The Cultural Logic of Computation Book PDF

Author : David Golumbia
Publisher : Harvard University Press
Page : 276 pages
File Size : 46,5 Mb
Release : 2009-04-30
Category : Computers
ISBN : 0674032926

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The Cultural Logic of Computation by David Golumbia Pdf

Advocates of computers make sweeping claims for their inherently transformative power: new and different from previous technologies, they are sure to resolve many of our existing social problems, and perhaps even to cause a positive political revolution. In The Cultural Logic of Computation, David Golumbia, who worked as a software designer for more than ten years, confronts this orthodoxy, arguing instead that computers are cultural “all the way down”—that there is no part of the apparent technological transformation that is not shaped by historical and cultural processes, or that escapes existing cultural politics. From the perspective of transnational corporations and governments, computers benefit existing power much more fully than they provide means to distribute or contest it. Despite this, our thinking about computers has developed into a nearly invisible ideology Golumbia dubs “computationalism”—an ideology that informs our thinking not just about computers, but about economic and social trends as sweeping as globalization. Driven by a programmer’s knowledge of computers as well as by a deep engagement with contemporary literary and cultural studies and poststructuralist theory, The Cultural Logic of Computation provides a needed corrective to the uncritical enthusiasm for computers common today in many parts of our culture.

Computational Logic and Set Theory

Jacob T. Schwartz,Domenico Cantone,Eugenio G. Omodeo
Computational Logic and Set Theory Book PDF

Author : Jacob T. Schwartz,Domenico Cantone,Eugenio G. Omodeo
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 52,6 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.

Quantum Computation and Logic

Maria Luisa Dalla Chiara,Roberto Giuntini,Roberto Leporini,Giuseppe Sergioli
Quantum Computation and Logic Book PDF

Author : Maria Luisa Dalla Chiara,Roberto Giuntini,Roberto Leporini,Giuseppe Sergioli
Publisher : Springer
Page : 178 pages
File Size : 47,9 Mb
Release : 2018-12-10
Category : Philosophy
ISBN : 9783030044718

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Quantum Computation and Logic by Maria Luisa Dalla Chiara,Roberto Giuntini,Roberto Leporini,Giuseppe Sergioli Pdf

This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.

Introduction to Computation

Donald Sannella,Michael Fourman,Haoran Peng,Philip Wadler
Introduction to Computation Book PDF

Author : Donald Sannella,Michael Fourman,Haoran Peng,Philip Wadler
Publisher : Springer Nature
Page : 371 pages
File Size : 54,5 Mb
Release : 2022-01-19
Category : Computers
ISBN : 9783030769086

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Introduction to Computation by Donald Sannella,Michael Fourman,Haoran Peng,Philip Wadler Pdf

Computation, itself a form of calculation, incorporates steps that include arithmetical and non-arithmetical (logical) steps following a specific set of rules (an algorithm). This uniquely accessible textbook introduces students using a very distinctive approach, quite rapidly leading them into essential topics with sufficient depth, yet in a highly intuitive manner. From core elements like sets, types, Venn diagrams and logic, to patterns of reasoning, calculus, recursion and expression trees, the book spans the breadth of key concepts and methods that will enable students to readily progress with their studies in Computer Science.

Sets, Logic, Computation

Richard Zach
Sets Logic Computation Book PDF

Author : Richard Zach
Publisher : Unknown
Page : 418 pages
File Size : 43,7 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.

Time & Logic

Leonard Bolc,Andrzej Szałas
Time Logic Book PDF

Author : Leonard Bolc,Andrzej Szałas
Publisher : Routledge
Page : 207 pages
File Size : 47,9 Mb
Release : 2019-10-24
Category : Philosophy
ISBN : 9781000507317

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Time & Logic by Leonard Bolc,Andrzej Szałas Pdf

Originally published in 1995 Time and Logic examines understanding and application of temporal logic, presented in computational terms. The emphasis in the book is on presenting a broad range of approaches to computational applications. The techniques used will also be applicable in many cases to formalisms beyond temporal logic alone, and it is hoped that adaptation to many different logics of program will be facilitated. Throughout, the authors have kept implementation-orientated solutions in mind. The book begins with an introduction to the basic ideas of temporal logic. Successive chapters examine particular aspects of the temporal theoretical computing domain, relating their applications to familiar areas of research, such as stochastic process theory, automata theory, established proof systems, model checking, relational logic and classical predicate logic. This is an essential addition to the library of all theoretical computer scientists. It is an authoritative work which will meet the needs both of those familiar with the field and newcomers to it.

Computational Logic

Jean-Louis Lassez,Gordon Plotkin
Computational Logic Book PDF

Author : Jean-Louis Lassez,Gordon Plotkin
Publisher : MIT Press (MA)
Page : 727 pages
File Size : 54,8 Mb
Release : 1991
Category : Computers
ISBN : 0262121565

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Computational Logic by Jean-Louis Lassez,Gordon Plotkin Pdf

Reflecting Alan Robinson's fundamental contribution to computational logic, this book brings together seminal papers in inference, equality theories, and logic programming. It is an exceptional collection that ranges from surveys of major areas to new results in more specialized topics. Alan Robinson is currently the University Professor at Syracuse University. Jean-Louis Lassez is a Research Scientist at the IBM Thomas J. Watson Research Center. Gordon Plotkin is Professor of Computer Science at the University of Edinburgh. Contents: Inference. Subsumption, A Sometimes Undervalued Procedure, Larry Wos, Ross Overbeek, and Ewing Lusk. The Markgraf Karl Refutation Procedure, Hans Jurgen Ohlbach and Jorg H. Siekmann. Modal Logic Should Say More than it Does, Melvin Fitting. Interactive Proof Presentation, W. W. Bledsoe. Intelligent Backtracking Revisited, Maurice Bruynooghe. A Science of Reasoning, Alan Bundy. Inductive Inference of Theories from Facts, Ehud Y. Shapiro. Equality. Solving Equations in Abstract Algebras: A Rule-based Survey of Unification, Jean-Pierre Jouannaud and Claude Kirchner. Disunification: A Survey, Hubert Comon. A Case Study of the Completion Procedure: Proving Ring Commutativity Problems, Deepak Kapur and Hantao Zhang. Computations in Regular Rewriting Systems I and II, Girard Huet and JeanJacques Levy. Unification and ML Type Reconstruction, Paris Kanellakis, Harry Mairson, and John Mitchell. Automatic Dimensional Analysis, Mitchell Wand. Logic Programming. Logic Programming Schemes and Their Implementations, Keith Clark. A Near-Horn Prolog for Compilation, Donald Loveland and David Reed. Unfold/Fold Transformations of Logic Programs, P. A. Gardner and J. C. Shepherdson. An Algebraic Representation of Logic Program Computations, Andrea Corradini and Ugo Montanari. Theory of Disjunctive Logic Programs, Jack Minker, Arcot Rajasekar, and Jorge Lobo. Bottom-Up Evaluation of Logic Programs, Jeffrey Naughton and Raghu Ramakrishnan. Absys, the First Logic Programming Language: A View of the Inevitability of Logic Programming, E. W. Elcock.

Logic, Language, Information, and Computation

Alexandra Silva,Renata Wassermann,Ruy de Queiroz
Logic Language Information and Computation Book PDF

Author : Alexandra Silva,Renata Wassermann,Ruy de Queiroz
Publisher : Springer Nature
Page : 435 pages
File Size : 44,5 Mb
Release : 2021-10-05
Category : Philosophy
ISBN : 9783030888534

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Logic, Language, Information, and Computation by Alexandra Silva,Renata Wassermann,Ruy de Queiroz Pdf

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 27th Workshop on Logic, Language, Information and Communication, WoLLIC 2021, Virtual Event, in October 2021. The 25 full papers presented included 6 invited lectures were fully reviewed and selected from 50 submissions. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation.

Logic, Computation and Rigorous Methods

Alexander Raschke,Elvinia Riccobene,Klaus-Dieter Schewe
Logic Computation and Rigorous Methods Book PDF

Author : Alexander Raschke,Elvinia Riccobene,Klaus-Dieter Schewe
Publisher : Springer Nature
Page : 367 pages
File Size : 47,5 Mb
Release : 2021-06-04
Category : Computers
ISBN : 9783030760205

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Logic, Computation and Rigorous Methods by Alexander Raschke,Elvinia Riccobene,Klaus-Dieter Schewe Pdf

This Festschrift was published in honor of Egon Börger on the occasion of his 75th birthday. It acknowledges Prof. Börger's inspiration as a scientist, author, mentor, and community organizer. Dedicated to a pioneer in the fields of logic and computer science, Egon Börger's research interests are unusual in scope, from programming languages to hardware architectures, software architectures, control systems, workflow and interaction patterns, business processes, web applications, and concurrent systems. The 18 invited contributions in this volume are by leading researchers in the areas of software engineering, programming languages, business information systems, and computer science logic.