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This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.
Quantum logic. --- Algebraic logic --- Mathematical physics --- Quantum theory --- Logic. --- Logic, Symbolic and mathematical. --- Mathematical Logic and Foundations. --- Quantum Computing. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology --- Mathematical logic. --- Quantum computers. --- Computers
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This book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life. It reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.
Philosophy. --- Logic. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Mental philosophy --- Humanities --- Methodology --- Algebraic logic. --- Logic, Symbolic and mathematical --- Logic, Symbolic and mathematical. --- Computer science. --- Informatics
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This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science. Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants.
Topología --- Lógica simbólica y matemática --- Topology. --- Logic, Symbolic and mathematical. --- Algebra. --- Mathematical Logic and Foundations. --- Category Theory, Homological Algebra. --- General Algebraic Systems. --- Mathematical Applications in Computer Science. --- Discrete Mathematics. --- Mathematics --- Mathematical analysis --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Algebras, Linear --- Relation algebras. --- Algebra of relations --- Algebras, Relation --- Relational algebras --- Relations, Algebra of --- Algebraic logic --- Mathematical logic. --- Category theory (Mathematics). --- Homological algebra. --- Computer science—Mathematics. --- Computer mathematics. --- Discrete mathematics. --- Homological algebra --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Computer mathematics --- Electronic data processing
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This book constitutes the proceedings of the 17th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2018, held in Groningen, The Netherlands, in October/November 2018. The 21 full papers and 1 invited paper presented together with 2 invited abstracts and 1 abstract of a tutorial were carefully selected from 31 submissions. The papers are organized in the following topics: Theoretical foundations; reasoning about computations and programs; and applications and tools.
Computer science. --- Artificial intelligence. --- Logic design. --- Electronic data processing. --- Mathematical Logic and Formal Languages. --- Artificial Intelligence. --- Logics and Meanings of Programs. --- Programming Languages, Compilers, Interpreters. --- Programming Techniques. --- Numeric Computing. --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- 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 --- Informatics --- Science --- Automation --- Algebraic logic --- Logic, Symbolic and mathematical --- Mathematical logic. --- Computer logic. --- Programming languages (Electronic computers). --- Computer programming. --- Numerical analysis. --- Mathematical analysis --- Electronic computer programming --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Languages, Artificial --- Computer science logic --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Programming --- Machine theory. --- Compilers (Computer programs). --- Formal Languages and Automata Theory. --- Computer Science Logic and Foundations of Programming. --- Compilers and Interpreters. --- Numerical Analysis. --- 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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