Download or read book Mathematical Logic and Programming Languages written by Charles Antony Richard Hoare and published by Prentice Hall. This book was released on 1985 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Logic through Python written by Yannai A. Gonczarowski and published by Cambridge University Press. This book was released on 2022-07-31 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel's completeness theorem. A sneak peek to Gödel's incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed.

Download or read book Mathematical Logic for Computer Science written by Mordechai Ben-Ari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Aspects of Logic Programming Semantics written by Pascal Hitzler and published by CRC Press. This book was released on 2016-04-19 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the authors' own state-of-the-art research results, this book presents a rigorous, modern account of the mathematical methods and tools required for the semantic analysis of logic programs. It significantly extends the tools and methods from traditional order theory to include nonconventional methods from mathematical analysis that depend on topology, domain theory, generalized distance functions, and associated fixed-point theory. The authors closely examine the interrelationships between various semantics as well as the integration of logic programming and connectionist systems/neural networks.

Download or read book Logic for Computer Scientists written by Uwe Schöning and published by Springer Science & Business Media. This book was released on 2009-11-03 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Introduction to Formal Languages written by György E. Révész and published by Courier Corporation. This book was released on 2015-03-17 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers all areas, including operations on languages, context-sensitive languages, automata, decidability, syntax analysis, derivation languages, and more. Numerous worked examples, problem exercises, and elegant mathematical proofs. 1983 edition.

Download or read book Sets Logic and Maths for Computing written by David Makinson and published by Springer Science & Business Media. This book was released on 2012-02-27 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.

Download or read book Mathematical Logic written by H.-D. Ebbinghaus and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Download or read book Types and Programming Languages written by Benjamin C. Pierce and published by MIT Press. This book was released on 2002-01-04 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to type systems and programming languages. A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems—and of programming languages from a type-theoretic perspective—has important applications in software engineering, language design, high-performance compilers, and security. This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material. The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.

Download or read book The Formal Semantics of Programming Languages written by Glynn Winskel and published by MIT Press. This book was released on 1993-02-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although the treatment is elementary, several of the topics covered are drawn from recent research, including the vital area of concurency. The book contains many exercises ranging from simple to miniprojects.Starting with basic set theory, structural operational semantics is introduced as a way to define the meaning of programming languages along with associated proof techniques. Denotational and axiomatic semantics are illustrated on a simple language of while-programs, and fall proofs are given of the equivalence of the operational and denotational semantics and soundness and relative completeness of the axiomatic semantics. A proof of Godel's incompleteness theorem, which emphasizes the impossibility of achieving a fully complete axiomatic semantics, is included. It is supported by an appendix providing an introduction to the theory of computability based on while-programs. Following a presentation of domain theory, the semantics and methods of proof for several functional languages are treated. The simplest language is that of recursion equations with both call-by-value and call-by-name evaluation. This work is extended to lan guages with higher and recursive types, including a treatment of the eager and lazy lambda-calculi. Throughout, the relationship between denotational and operational semantics is stressed, and the proofs of the correspondence between the operation and denotational semantics are provided. The treatment of recursive types - one of the more advanced parts of the book - relies on the use of information systems to represent domains. The book concludes with a chapter on parallel programming languages, accompanied by a discussion of methods for specifying and verifying nondeterministic and parallel programs.

Download or read book The Haskell Road to Logic Maths and Programming written by Kees Doets and published by College Publications. This book was released on 2004 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long ago, when Alexander the Great asked the mathematician Menaechmus for a crash course in geometry, he got the famous reply ``There is no royal road to mathematics.'' Where there was no shortcut for Alexander, there is no shortcut for us. Still, the fact that we have access to computers and mature programming languages means that there are avenues for us that were denied to the kings and emperors of yore. The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming in Haskell. Haskell emerged in the 1990s as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvelous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures. This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book, the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others. This is the updated, expanded, and corrected second edition of a much-acclaimed textbook. Praise for the first edition: 'Doets and van Eijck's ``The Haskell Road to Logic, Maths and Programming'' is an astonishingly extensive and accessible textbook on logic, maths, and Haskell.' Ralf Laemmel, Professor of Computer Science, University of Koblenz-Landau

Download or read book Equational Logic as a Programming Language written by Michael J. O'Donnell and published by MIT Press (MA). This book was released on 1985 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes an ongoing equational programming project that started in 1975. Within the project an equational programming language interpreter has been designed and implemented. The first part of the text (Chapters 1-10) provides a user's manual for the current implementation. The remaining sections cover the following topics: programming techniques and applications, theoretical foundations, implementation issues. Giving a brief account of the project's history (Chapter 11), the author devotes a large part of the text to techniques of equational programming at different levels of abstraction. Chapter 12 discusses low-level techniques including the distinction of constructors and defined functions, the formulation of conditional expressions and error and exception handling. High-level techniques are treated in Chapter 15 by discussing concurrency, nondeterminism, the relationship to dataflow programs and the transformation of recursive programs called dynamic programming. In Chapter 16 the author shows how to efficiently implement common data structures by equational programs. Modularity is discussed in Chapter 14. Several applications are also presented in the book. The author demonstrates the versatility of equational programming style by implementing syntactic manipulation algorithms (Chapter 13). Theoretical foundations are introduced in Chapter 17 (term rewriting systems, herein called term reduction systems). In Chapter 19 the author raises the question of a universal equational machine language and discusses the suitability of different variants of the combinator calculus for this purpose. Implementation issues are covered in Chapters 18 and 20 focused around algorithms for efficient pattern matching, sequencing and reduction. Aspects of design and coordination of the syntactic processors are presented as well.

Download or read book Three Views of Logic written by Donald W. Loveland and published by Princeton University Press. This book was released on 2014-01-26 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first interdisciplinary textbook to introduce students to three critical areas in applied logic 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

Download or read book Mathematical Aspects Of Natural And Formal Languages written by Gheorghe Paun and published by World Scientific. This book was released on 1994-10-25 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains original reviews by well-known workers in the field of mathematical linguistics and formal language theory, written in honour of Professor Solomon Marcus on the occasion of his 70th birthday.Some of the papers deal with contextual grammars, a class of generative devices introduced by Marcus, motivated by descriptive linguistics. Others are devoted to grammar systems, a very modern branch of formal language theory. Automata theory and the algebraic approach to computer science are other well-represented areas. While the contributions are mathematically oriented, practical issues such as cryptography, grammatical inference and natural language processing are also discussed.

Download or read book Foundations of Logic Programming written by J. W. Lloyd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an account oC the mathematical Coundations oC logic programming. I have attempted to make the book selC-contained by including prooCs of almost all the results needed. The only prerequisites are some Camiliarity with a logic programming language, such as PROLOG, and a certain mathematical maturity. For example, the reader should be Camiliar with induction arguments and be comCortable manipulating logical expressions. Also the last chapter assumes some acquaintance with the elementary aspects of metric spaces, especially properties oC continuous mappings and compact spaces. Chapter 1 presents the declarative aspects of logic programming. This chapter contains the basic material Crom first order logic and fixpoint theory which will be required. The main concepts discussed here are those oC a logic program, model, correct answer substitution and fixpoint. Also the unification algorithm is discussed in some detail. Chapter 2 is concerned with the procedural semantics oC logic programs. The declarative concepts are implemented by means oC a specialized Corm oC resolution, called SLD-resolution. The main results of this chapter concern the soundness and completeness oC SLD-resolution and the independence oC the computation rule. We also discuss the implications of omitting the occur check from PROLOG implementations. Chapter 3 discusses negation. Current PROLOG systems implement a form of negation by means of the negation as failure rule. The main results of this chapter are the soundness and completeness oC the negation as failure rule.

Download or read book Foundations for Programming Languages written by John C. Mitchell and published by Mit Press. This book was released on 1996 with total page 846 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Programming languages embody the pragmatics of designing software systems, and also the mathematical concepts which underlie them. Anyone who wants to know how, for example, object-oriented programming rests upon a firm foundation in logic should read this book. It guides one surefootedly through the rich variety of basic programming concepts developed over the past forty years." -- Robin Milner, Professor of Computer Science, The Computer Laboratory, Cambridge University "Programming languages need not be designed in an intellectual vacuum; John Mitchell's book provides an extensive analysis of the fundamental notions underlying programming constructs. A basic grasp of this material is essential for the understanding, comparative analysis, and design of programming languages." -- Luca Cardelli, Digital Equipment Corporation Written for advanced undergraduate and beginning graduate students, "Foundations for Programming Languages" uses a series of typed lambda calculi to study the axiomatic, operational, and denotational semantics of sequential programming languages. Later chapters are devoted to progressively more sophisticated type systems.

Download or read book Logic Programming with Prolog written by Max A. Bramer and published by Springer Science & Business Media. This book was released on 2005-07-13 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for those who wish to learn Prolog as a powerful software development tool, but do not necessarily have any background in logic or AI. Includes a full glossary of the technical terms and self-assessment exercises.