This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations of logic programming.

Author: Uwe Schöning

Publisher: Springer Science & Business Media

ISBN: 9780817647636

Category: Mathematics

Page: 168

View: 797

This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations of logic programming. The classic text is replete with illustrative examples and exercises. It presents applications and themes of computer science research such as resolution, automated deduction, and logic programming in a rigorous but readable way. The style and scope of the work, rounded out by the inclusion of exercises, make this an excellent textbook for an advanced undergraduate course in logic for computer scientists.

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs.

Author: Jean H. Gallier

Publisher: Courier Dover Publications

ISBN: 9780486780825

Category: Computers

Page: 528

View: 817

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.

Mathematical logic is essentially related to computer science. This book describes the aspects of mathematical logic that are closely related to each other, including classical logic, constructive logic, and modal logic.

Author: Zhongwan Lu

Publisher: World Scientific

ISBN: 9810230915

Category: Mathematics

Page: 244

View: 561

Mathematical logic is essentially related to computer science. This book describes the aspects of mathematical logic that are closely related to each other, including classical logic, constructive logic, and modal logic. This book is intended to attend to both the peculiarities of logical systems and the requirements of computer science.In this edition, the revisions essentially involve rewriting the proofs, increasing the explanations, and adopting new terms and notations.

Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics.

Author: Anita Wasilewska

Publisher: Springer

ISBN: 9783319925912

Category: Computers

Page: 535

View: 976

Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science contains intuitive introductory chapters explaining the need for logical investigations, motivations for different types of logics and some of their history. They are followed by strict formal approach chapters. All chapters contain many detailed examples explaining each of the introduced notions and definitions, well chosen sets of exercises with carefully written solutions, and sets of homework. While many logic books are available, they were written by logicians for logicians, not for computer scientists. They usually choose one particular way of presenting the material and use a specialized language. Logics for Computer Science discusses Gentzen as well as Hilbert formalizations, first order theories, the Hilbert Program, Godel's first and second incompleteness theorems and their proofs. It also introduces and discusses some many valued logics, modal logics and introduces algebraic models for classical, intuitionistic, and modal S4 and S5 logics. The theory of computation is based on concepts defined by logicians and mathematicians. Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics. Important applications derived from concepts of logic for computer technology include Artificial Intelligence and Software Engineering. In addition to Computer Science, this book may also find an audience in mathematics and philosophy courses, and some of the chapters are also useful for a course in Artificial Intelligence.

The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking.

Author: Mordechai Ben-Ari

Publisher: Springer Science & Business Media

ISBN: 9781447141297

Category: Mathematics

Page: 346

View: 317

Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems. The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic for the verification of concurrent programs. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking.

Author: Mauricio Ayala-RincónPublish On: 2017-02-04

This book provides an introduction to logic and mathematical induction which are the basis of any deductive computational framework.

Author: Mauricio Ayala-Rincón

Publisher: Springer

ISBN: 9783319516530

Category: Computers

Page: 150

View: 969

This book provides an introduction to logic and mathematical induction which are the basis of any deductive computational framework. A strong mathematical foundation of the logical engines available in modern proof assistants, such as the PVS verification system, is essential for computer scientists, mathematicians and engineers to increment their capabilities to provide formal proofs of theorems and to certify the robustness of software and hardware systems. The authors present a concise overview of the necessary computational and mathematical aspects of ‘logic’, placing emphasis on both natural deduction and sequent calculus. Differences between constructive and classical logic are highlighted through several examples and exercises. Without neglecting classical aspects of computational logic, the authors also highlight the connections between logical deduction rules and proof commands in proof assistants, presenting simple examples of formalizations of the correctness of algebraic functions and algorithms in PVS. Applied Logic for Computer Scientists will not only benefit students of computer science and mathematics but also software, hardware, automation, electrical and mechatronic engineers who are interested in the application of formal methods and the related computational tools to provide mathematical certificates of the quality and accuracy of their products and technologies.

This book is intended to attend to both the peculiarities of logical systems and the requirements of computer science.In this edition, the revisions essentially involve rewriting the proofs, increasing the explanations, and adopting new ...

Author: Lu Zhongwan

Publisher: World Scientific

ISBN: 9789814497565

Category: Mathematics

Page: 256

View: 770

Mathematical logic is essentially related to computer science. This book describes the aspects of mathematical logic that are closely related to each other, including classical logic, constructive logic, and modal logic. This book is intended to attend to both the peculiarities of logical systems and the requirements of computer science. In this edition, the revisions essentially involve rewriting the proofs, increasing the explanations, and adopting new terms and notations. Contents:Prerequisites:SetsInductive Definitions and ProofsNotationsClassical Propositional Logic:Propositions and ConnectivesPropositional LanguageStructure of FormulasSemanticsTautological ConsequenceFormal DeductionDisjunctive and Conjunctive Normal FormsAdequate Sets of ConnectivesClassical First-Order Logic:Proposition Functions and QuantifiersFirst-Order LanguageSemanticsLogical ConsequenceFormal DeductionPrenex Normal FormAxiomatic Deduction System:Axiomatic Deduction SystemRelation between the Two Deduction SystemsSoundness and Completeness:Satisfiability and ValiditySoundnessCompleteness of Propositional LogicCompleteness of First-Order LogicCompleteness of First-Order Logic with EqualityIndependenceCompactness, Löwenheim–Skolem, and Herbrand Theorems:CompactnessLöwenheim-Skolem's TheoremHerbrand's TheoremConstructive Logic:Constructivity of ProofsSemanticsFormal DeductionSoundnessCompletenessModal Propositional Logic:Modal Propositional LanguageSemanticsFormal DeductionSoundnessCompleteness of TCompleteness of S4, B, S5Modal First-Order Logic:Modal First-Order LanguageSemanticsFormal DeductionSoundnessCompletenessEquality Readership: Computer scientists. keywords:

In this book, a combination of survey chapters and applications work is presented--particularly concentrating on lamda-calculus, typed functional programming, and theorem provers

Author: Piergiorgio Odifreddi

Publisher:

ISBN: UOM:39015018916067

Category: Computers

Page: 430

View: 838

The application of mathematical logic to computer science continues to be of major importance in the development of more advanced systems. In this book, a combination of survey chapters and applications work is presented--particularly concentrating on lamda-calculus, typed functional programming, and theorem provers

This book offers a more substantive and rigorous approach to logic that focuses on applications in computer science.

Author: Rex Page

Publisher: MIT Press

ISBN: 9780262039185

Category: Computers

Page: 304

View: 649

An introduction to applying predicate logic to testing and verification of software and digital circuits that focuses on applications rather than theory. Computer scientists use logic for testing and verification of software and digital circuits, but many computer science students study logic only in the context of traditional mathematics, encountering the subject in a few lectures and a handful of problem sets in a discrete math course. This book offers a more substantive and rigorous approach to logic that focuses on applications in computer science. Topics covered include predicate logic, equation-based software, automated testing and theorem proving, and large-scale computation. Formalism is emphasized, and the book employs three formal notations: traditional algebraic formulas of propositional and predicate logic; digital circuit diagrams; and the widely used partially automated theorem prover, ACL2, which provides an accessible introduction to mechanized formalism. For readers who want to see formalization in action, the text presents examples using Proof Pad, a lightweight ACL2 environment. Readers will not become ALC2 experts, but will learn how mechanized logic can benefit software and hardware engineers. In addition, 180 exercises, some of them extremely challenging, offer opportunities for problem solving. There are no prerequisites beyond high school algebra. Programming experience is not required to understand the book's equation-based approach. The book can be used in undergraduate courses in logic for computer science and introduction to computer science and in math courses for computer science students.

- A. Nerode: Some Lectures on Intuitionistic Logic.- R.A. Platek: Making Computers Safe for the World. An Introduction to Proofs of Programs. Part I. - G.E. Sacks: Prolog Programming.- A. Scedrov: A Guide to Polymorphic Types.

Author: Steven Homer

Publisher: Springer

ISBN: 3540527346

Category: Mathematics

Page: 170

View: 695

The courses given at the 1st C.I.M.E. Summer School of 1988 dealt with the main areas on the borderline between applied logic and theoretical computer science. These courses are recorded here in five expository papers: S. Homer: The Isomorphism Conjecture and its Generalization.- A. Nerode: Some Lectures on Intuitionistic Logic.- R.A. Platek: Making Computers Safe for the World. An Introduction to Proofs of Programs. Part I. - G.E. Sacks: Prolog Programming.- A. Scedrov: A Guide to Polymorphic Types.

Designed primarily as an introductory text on logic for computer science, this well-organized book deals with almost all the basic concepts and techniques that are pertinent to the subject.

Author: SINGH, ARINDAMA

Publisher: PHI Learning Pvt. Ltd.

ISBN: 9789387472440

Category:

Page: 432

View: 458

Designed primarily as an introductory text on logic for computer science, this well-organized book deals with almost all the basic concepts and techniques that are pertinent to the subject. It provides an excellent understanding of the logics used in computer science today. Starting with the logic of propositions, it gives a detailed coverage of first order logic and modal logics. It discusses various approaches to the proof theory of the logics, e.g. axiomatic systems, natural deduction systems, Gentzen systems, analytic tableau, and resolution. It deals with an important application of logic to computer science, namely, verification of programs. The book gives the flavour of logic engineering through computation tree logic, a logic of model checking. The book concludes with a fairly detailed discussion on nonstandard logics including intuitionistic logic, Lukasiewicz logics, default logic, autoepistemic logic, and fuzzy logic. The Second Edition includes applications of compactness theorem to many interesting problems relevant to mathematics and computer science. It also presents the undecidability of first order logic, inexpressibility of truth, and incompleteness of Peano's Arithmetic in a comprehensive and lively manner. Besides students of Computer Science, those offering courses in Mathematics and Philosophy would greatly benefit from this study. KEY FEATURES • Provides numerous worked-out examples which not only illustrate the concepts and theory developed, but also give a lead to the succeeding notions. • Exercises at the end of each section aim at reinforcing and mastering the techniques, raising issues and preparing background for further development of the subject. • Problems of theoretical nature, which are important for learning the subject, are included at the end of each chapter. • The reader is constantly provoked toworkout the details, promoting interactive learning.

The coverage of model-checking has been substantially updated. Further exercises have been added. Internet support for the book includes worked solutions for all exercises for teachers, and model solutions to some exercises for students.

Author: Michael Huth

Publisher: Cambridge University Press

ISBN: 9781139453059

Category: Computers

Page:

View: 513

Recent years have seen the development of powerful tools for verifying hardware and software systems, as companies worldwide realise the need for improved means of validating their products. There is increasing demand for training in basic methods in formal reasoning so that students can gain proficiency in logic-based verification methods. The second edition of this successful textbook addresses both those requirements, by continuing to provide a clear introduction to formal reasoning which is both relevant to the needs of modern computer science and rigorous enough for practical application. Improvements to the first edition have been made throughout, with extra and expanded sections on SAT solvers, existential/universal second-order logic, micro-models, programming by contract and total correctness. The coverage of model-checking has been substantially updated. Further exercises have been added. Internet support for the book includes worked solutions for all exercises for teachers, and model solutions to some exercises for students.

This book constitutes the refereed proceedings of the 7th International Workshop on Deontic Logic in Computer Science, DEON 2004, held in Madeira, Portugal, in May 2004.

Author: Alessio Lomuscio

Publisher: Springer Science & Business Media

ISBN: 9783540221111

Category: Computers

Page: 274

View: 457

This book constitutes the refereed proceedings of the 7th International Workshop on Deontic Logic in Computer Science, DEON 2004, held in Madeira, Portugal, in May 2004. The 15 revised full papers presented together with the abstracts of 2 invited talks were carefully reviewed and selected for inclusion in the book. The papers are devoted to the relationship between normative concepts and computer science, artificial intelligence, organization theory, and law; in addition to these topics, special emphasis is placed on the relationship between deontic logic and multiagent systems.

This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory.

This volume presents the refereed proceedings of the 11th International Conference on Deontic Logic in Computer Science, DEON 2012, held in Bergen, Norway, in July 2012.

Author: Thomas Agotnes

Publisher: Springer

ISBN: 3642315690

Category: Mathematics

Page: 215

View: 297

This volume presents the refereed proceedings of the 11th International Conference on Deontic Logic in Computer Science, DEON 2012, held in Bergen, Norway, in July 2012. The 14 revised papers included in the volume were carefully reviewed and selected from 29 submissions. Topics covered include logical study of normative reasoning, formal analysis of normative concepts and normative systems, formal specification of aspects of norm-governed multi-agent systems and autonomous agents, normative aspects of protocols for communication, negotiation and multi-agent decision making, formal representation of legal knowledge, formal specification of normative systems for the management of bureaucratic processes in public or private administration, and applications of normative logic to the specification of database integrity constraints.

This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2020, held in Deerfield Beach, FL, USA, in January 2020.

Author: Sergei Artemov

Publisher: Springer

ISBN: 3030367541

Category: Mathematics

Page: 287

View: 434

This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2020, held in Deerfield Beach, FL, USA, in January 2020. The 17 revised full papers were carefully reviewed and selected from 30 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.

An understanding of logic is essential to computer science. This book provides a highly accessible account of the logical basis required for reasoning about computer programs and applying logic in fields like artificial intelligence.

Author: Steve Reeves

Publisher: Addison Wesley Publishing Company

ISBN: UOM:39015018522071

Category: Computers

Page: 260

View: 851

An understanding of logic is essential to computer science. This book provides a highly accessible account of the logical basis required for reasoning about computer programs and applying logic in fields like artificial intelligence. The text contains extended examples, algorithms, and programs written in Standard ML and Prolog. No prior knowledge of either language is required. The book contains a clear account of classical first-order logic, one of the basic tools for program verification, as well as an introductory survey of modal and temporal logics and possible world semantics. An introduction to intuitionistic logic as a basis for an important style of program specification is also featured in the book.