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This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations. Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician's bookshelf.
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Chapters 2, 10, 26, 29, 30 and 37 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Computer science. --- Computer system failures. --- Software engineering. --- Programming languages (Electronic computers). --- Computer logic. --- Mathematical logic. --- Artificial intelligence. --- Computer Science. --- Mathematical Logic and Formal Languages. --- Software Engineering. --- Artificial Intelligence (incl. Robotics). --- Logics and Meanings of Programs. --- Programming Languages, Compilers, Interpreters. --- System Performance and Evaluation. --- Logic design. --- Computer system performance. --- Artificial Intelligence. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Machine theory --- Switching theory --- 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 software engineering --- Engineering --- Informatics --- Science --- Automatic theorem proving --- Computer failures --- Computer malfunctions --- Computer systems --- Failure of computer systems --- System failures (Engineering) --- Fault-tolerant computing --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Languages, Artificial --- 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 --- Failures --- Machine theory. --- Compilers (Computer programs). --- Electronic digital computers—Evaluation. --- Formal Languages and Automata Theory. --- Computer Science Logic and Foundations of Programming. --- Compilers and Interpreters. --- Compiling programs (Computer programs) --- Computer programs --- Programming software --- Systems software --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Recursive functions --- Robotics
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Computer science --- Proof theory --- Formal methods (Computer science) --- Logic, Symbolic and mathematical --- Mathematics --- Data processing
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The Open Logic Text is an open-source, collaborative textbook of formal meta-logic and formal methods, starting at an intermediate level (i.e., after an introductory formal logic course). Though aimed at a non-mathematical audience (in particular, students of philosophy and computer science), it is rigorous. The Open Logic Text is a collaborative project and is under active development. Coverage of some topics currently included may not yet be complete, and many sections still require substantial revision. We plan to expand the text to cover more topics in the future. We also plan to add features to the text, such as a glossary, a list of further reading, historical notes, pictures, better explanations, sections explaining the relevance of results to philosophy, computer science, and mathematics, and more problems and examples. If you find an error, or have a suggestion, please let the project team know. The project operates in the spirit of open source. Not only is the text freely available, we provide the LaTeX source under the Creative Commons Attribution license, which gives anyone the right to download, use, modify, re-arrange, convert, and re-distribute our work, as long as they give appropriate credit.
Humanities --- Mathematics --- Philosophy
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The Open Logic Text is an open-source, collaborative textbook of formal meta-logic and formal methods, starting at an intermediate level (i.e., after an introductory formal logic course). Though aimed at a non-mathematical audience (in particular, students of philosophy and computer science), it is rigorous. The Open Logic Text is a collaborative project and is under active development. Coverage of some topics currently included may not yet be complete, and many sections still require substantial revision. We plan to expand the text to cover more topics in the future. We also plan to add features to the text, such as a glossary, a list of further reading, historical notes, pictures, better explanations, sections explaining the relevance of results to philosophy, computer science, and mathematics, and more problems and examples. If you find an error, or have a suggestion, please let the project team know. The project operates in the spirit of open source. Not only is the text freely available, we provide the LaTeX source under the Creative Commons Attribution license, which gives anyone the right to download, use, modify, re-arrange, convert, and re-distribute our work, as long as they give appropriate credit.
Humanities --- Mathematics --- Philosophy
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