# mathematical logic for computer science

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## Mathematical Logic For Computer Science

**Author :**Mordechai Ben-Ari

**ISBN :**9781447141297

**Genre :**Mathematics

**File Size :**83. 32 MB

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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.

## Mathematical Logic For Computer Science

**Author :**Mordechai Ben-Ari

**ISBN :**9781447103356

**Genre :**Computers

**File Size :**56. 60 MB

**Format :**PDF, Docs

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This is a mathematics textbook with theorems and proofs. The choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. In order to provide a balanced treatment of logic, tableaux are related to deductive proof systems. The book presents various logical systems and contains exercises. Still further, Prolog source code is available on an accompanying Web site. The author is an Associate Professor at the Department of Science Teaching, Weizmann Institute of Science.

## Mathematical Logic For Computer Science

**Author :**M. Ben-Ari

**ISBN :**1852333197

**Genre :**Computers

**File Size :**55. 51 MB

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Including theorems and proofs, this book presents logical systems such as Propositional calculus; Predicate calculus; Resolution; Hoare logic; Z; and, Temporal logic.

## Mathematical Logic For Computer Science

**Author :**Lu Zhongwan

**ISBN :**9789814497565

**Genre :**Mathematics

**File Size :**47. 34 MB

**Format :**PDF

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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:

## Mathematical Logic In Computer Science

**Author :**B. Dömölki

**ISBN :**UOM:39015037748327

**Genre :**Mathematics

**File Size :**41. 90 MB

**Format :**PDF

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## Logic For Computer Scientists

**Author :**Uwe Schöning

**ISBN :**9780817647636

**Genre :**Mathematics

**File Size :**25. 70 MB

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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.

## Logic In Computer Science

**Author :**Michael Huth

**ISBN :**9781139453059

**Genre :**Computers

**File Size :**81. 75 MB

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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.

## Mathematical Logic For Computer Science

**Author :**Zhongwan Lu

**ISBN :**9810230915

**Genre :**Mathematics

**File Size :**81. 21 MB

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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.

## A Course On Mathematical Logic

**Author :**Shashi Mohan Srivastava

**ISBN :**9781461457466

**Genre :**Mathematics

**File Size :**85. 74 MB

**Format :**PDF

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This is a short, modern, and motivated introduction to mathematical logic for upper undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in getting acquainted with logic and would like to learn Gödel’s incompleteness theorems should find this book particularly useful. The treatment is thoroughly mathematical and prepares students to branch out in several areas of mathematics related to foundations and computability, such as logic, axiomatic set theory, model theory, recursion theory, and computability. In this new edition, many small and large changes have been made throughout the text. The main purpose of this new edition is to provide a healthy first introduction to model theory, which is a very important branch of logic. Topics in the new chapter include ultraproduct of models, elimination of quantifiers, types, applications of types to model theory, and applications to algebra, number theory and geometry. Some proofs, such as the proof of the very important completeness theorem, have been completely rewritten in a more clear and concise manner. The new edition also introduces new topics, such as the notion of elementary class of structures, elementary diagrams, partial elementary maps, homogeneous structures, definability, and many more.

## Three Views Of Logic

**Author :**Donald W. Loveland

**ISBN :**9781400848751

**Genre :**Mathematics

**File Size :**28. 49 MB

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Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses