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Proofs and Algorithms: An Introduction to Logic and Computability Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: An Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.
Algorithms. --- Computable functions. --- Electronic books. -- local. --- Logic. --- Logic, Symbolic and mathematical --- Algorithms --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Computer Science --- Mathematical Theory --- Computability theory --- Functions, Computable --- Partial recursive functions --- Recursive functions, Partial --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Algorism --- Computer science. --- Computers. --- Mathematical logic. --- Computer Science. --- Theory of Computation. --- Mathematical Logic and Formal Languages. --- Constructive mathematics --- Decidability (Mathematical logic) --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Algebra --- Arithmetic --- Methodology --- Foundations --- Information theory. --- Informatics --- Communication theory --- Communication --- Cybernetics --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Machine theory --- Calculators --- Cyberspace
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The development of programming languages has profoundly impacted our relationship with language, complexity and machines. By introducing the principles of programming languages, using the Java language as a support, Gilles Dowek provides the necessary fundamentals of this language as a first objective. It is important to realise that knowledge of a single programming language is not really enough. To be a good programmer, you should be familiar with several languages and be able to learn new ones. In order to do this, you’ll need to understand universal concepts, such as functions or cells, which exist in one form or another in all programming languages. The most effective way to understand these universal concepts is to compare two or more languages. In this book, the author has chosen Caml and C. To understand the principles of programming languages, it is also important to learn how to precisely define the meaning of a program, and tools for doing so are discussed. Finally, there is coverage of basic algorithms for lists and trees. Intended for students with some small experience of computer programming, learned empirically in a single programming language other than Java, students in both computer science and engineering will find this book a very welcome introduction to the principles of programming languages. Written for students this book presents what all scientists and engineers should know about programming languages.
Electronic books. -- local. --- Programming languages (Electronic computers). --- Programming languages (Electronic computers) -- Problems, exercises, etc. --- Programming languages (Electronic computers) --- Computer Science --- Engineering & Applied Sciences --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Computer science. --- Computer programming. --- Software engineering. --- Algorithms. --- Computer logic. --- Computer Science. --- Programming Languages, Compilers, Interpreters. --- Logics and Meanings of Programs. --- Algorithm Analysis and Problem Complexity. --- Programming Techniques. --- Software Engineering. --- Computer science logic --- Logic, Symbolic and mathematical --- Algorism --- Algebra --- Arithmetic --- Electronic data processing --- Languages, Artificial --- Computer software engineering --- Engineering --- Computers --- Electronic computer programming --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Informatics --- Science --- Foundations --- Programming --- Logic design. --- Computer software. --- Software, Computer --- Computer systems --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Machine theory --- Switching theory
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This book constitutes the refereed proceedings of the Joint 25th International Conference on Rewriting Techniques and Applications, RTA 2014, and 12th International Conference on Typed Lambda-Calculi and Applications, TLCA 2014, held as part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014. The 28 revised full papers and 3 short papers presented were carefully reviewed and selected from 87 submissions. The papers provide research results on all aspects of rewriting and typed lambda calculi, ranging from theoretical and methodological issues to applications in various contexts. They address a wide variety of topics such as algorithmic aspects, implementation, logic, types, semantics, and programming.
Computer science. --- Computer logic. --- Mathematical logic. --- Computer science --- Computers. --- Computer Science. --- Mathematical Logic and Formal Languages. --- Mathematics of Computing. --- Logics and Meanings of Programs. --- Symbolic and Algebraic Manipulation. --- Computing Methodologies. --- Mathematical Logic and Foundations. --- Mathematics. --- Logic design. --- Algebra --- Artificial intelligence. --- Logic, Symbolic and mathematical. --- Artificial Intelligence. --- Data processing. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Informatics --- Science --- Rewriting systems (Computer science) --- Computer science—Mathematics. --- Computer science logic --- Logic, Symbolic and mathematical --- Machine theory. --- Formal Languages and Automata Theory. --- Computer Science Logic and Foundations of Programming. --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Recursive functions --- Robotics
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Algorithms are probably the most sophisticated tools that people have had at their disposal since the beginnings of human history. They have transformed science, industry, society. They upset the concepts of work, property, government, private life, even humanity. Going easily from one extreme to the other, we rejoice that they make life easier for us, but fear that they will enslave us. To get beyond this vision of good vs evil, this book takes a new look at our time, the age of algorithms. Creations of the human spirit, algorithms are what we made them. And they will be what we want them to be: it's up to us to choose the world we want to live in.
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The design and implementation of programming languages, from Fortran and Cobol to Caml and Java, has been one of the key developments in the management of ever more complex computerized systems. Introduction to the Theory of Programming Languages gives the reader the means to discover the tools to think, design, and implement these languages. It proposes a unified vision of the different formalisms that permit definition of a programming language: small steps operational semantics, big steps operational semantics, and denotational semantics, emphasising that all seek to define a relation between three objects: a program, an input value, and an output value. These formalisms are illustrated by presenting the semantics of some typical features of programming languages: functions, recursivity, assignments, records, objects, ... showing that the study of programming languages does not consist of studying languages one after another, but is organized around the features that are present in these various languages. The study of these features leads to the development of evaluators, interpreters and compilers, and also type inference algorithms, for small languages.
Electronic -- Programming. --- Programming languages (Electronic computers) -- Semantics. --- Programming languages (Electronic computers). --- Programming languages (Electronic computers) --- Engineering & Applied Sciences --- Computer Science --- Semantics --- Computer programming. --- Computers --- Electronic computer programming --- Electronic data processing --- Electronic digital computers --- Programming (Electronic computers) --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Programming --- Computer science. --- Computers. --- Computer logic. --- Computer Science. --- Theory of Computation. --- Logics and Meanings of Programs. --- Coding theory --- Languages, Artificial --- Information theory. --- Logic design. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Machine theory --- Switching theory --- Communication theory --- Communication --- Cybernetics --- Semantics. --- Computer science logic --- Logic, Symbolic and mathematical --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Calculators --- Cyberspace
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Computation is revolutionizing our world, even the inner world of the 'pure' mathematician. Mathematical methods - especially the notion of proof - that have their roots in classical antiquity have seen a radical transformation since the 1970s, as successive advances have challenged the priority of reason over computation. Like many revolutions, this one comes from within. Computation, calculation, algorithms - all have played an important role in mathematical progress from the beginning - but behind the scenes, their contribution was obscured in the enduring mathematical literature. To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation. Along the way it invites us to reconsider the dialog between mathematics and the natural sciences, as well as the relationship between mathematics and computer science. It also sheds new light on philosophical concepts, such as the notions of analytic and synthetic judgment. Finally, it brings us to the brink of the new age, in which machine intelligence offers new ways of solving mathematical problems previously inaccessible. This book is the 2007 winner of the Grand Prix de Philosophie de l'Académie Française.
Mathematics --- Mathematics, Ancient. --- History --- History.
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This book constitutes the refereed proceedings of the 4th International Joint Conference on Automated Reasoning, IJCAR 2008, held in Sydney, Australia, in August 2008. The 26 revised full research papers and 13 revised system descriptions presented together with 4 invited papers and a summary of the CASC-J4 systems competition were carefully reviewed and selected from 80 full paper and 17 system description submissions. The papers address the entire spectrum of research in automated reasoning and are organized in topical sections on specific theories, automated verification, protocol verification, system descriptions, modal logics, description logics, equational theories, theorem proving, CASC, the 4th IJCAR ATP system competition, logical frameworks, and tree automata.
Automatic theorem proving --- Computer logic --- Information Technology --- Artificial Intelligence --- Artificial intelligence. --- Software engineering. --- Computer science. --- Logic design. --- Artificial Intelligence. --- Software Engineering/Programming and Operating Systems. --- Programming Techniques. --- Mathematical Logic and Formal Languages. --- Logics and Meanings of Programs. --- Software Engineering. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Machine theory --- Switching theory --- Informatics --- Science --- Computer software engineering --- Engineering --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Computer programming. --- Mathematical logic. --- Computer logic. --- Computer science logic --- Logic, Symbolic and mathematical --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computers --- Electronic computer programming --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Programming --- Artificial intelligence --- Computer science
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