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This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions.
Artificial intelligence --- Mathematical theory of computation --- Computer programming / software development --- Software Engineering --- Artificial Intelligence --- Mathematical Logic and Formal Languages --- Logics and Meanings of Programs --- Formal Languages and Automata Theory --- Computer Science Logic and Foundations of Programming --- automata theory --- boolean functions --- computer programming --- first order logic --- formal languages --- formal logic --- logic programming --- model checking --- program verification --- semantics --- software architecture --- software design --- software quality --- software verification --- theorem provers --- theorem proving --- Computer programming / software engineering --- Computer architecture & logic design
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Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier--"Don't disturb my circles"--words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds--stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more. In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.
Mathematics --- Communication in mathematics. --- Math --- Science --- Language. --- History. --- Alasdair MacIntyre. --- Archimedes. --- Aristotle. --- Bleak House. --- Borel sets. --- Bourbaki. --- Carl Friedrich Gauss. --- David Hilbert. --- Emmy Noether. --- Enlightenment. --- G. E. R. Lloyd. --- Georg Cantor. --- Greece. --- Jean-Pierre Vernant. --- John Archibald Wheeler. --- K-ness. --- L'Algebra. --- Leo Perutz. --- Leopold Kronecker. --- Middlemarch. --- Paul Gordan. --- Plato. --- Rafael Bombelli. --- Robert Thomason. --- ThomasonДrobaugh article. --- Tom Trobaugh. --- abstraction. --- aesthetic contingency. --- algebra. --- automated theorem provers. --- axiomatic mathematics. --- belief. --- chiasmus. --- clues. --- cognitive meaning. --- compound machines. --- computational modeling. --- computer simulations. --- cubic equations. --- deductive mathematics. --- diagramma. --- dreams. --- energeia. --- epistemology. --- existential contingency. --- explanation. --- exploration mathematics. --- finiteness theorems. --- focalization. --- forensic rhetoric. --- formal models. --- geometry. --- ghost. --- ghostwriter. --- group. --- highest common factor. --- imaginary numbers. --- incommensurability. --- intuition. --- irony. --- literary narrative. --- literature. --- machine metaphor. --- mathematical argument. --- mathematical concepts. --- mathematical enquiry. --- mathematical line. --- mathematical modeling. --- mathematical models. --- mathematical objects. --- mathematical physics. --- mathematicians. --- mathematics. --- metanarratology. --- metaphor. --- myth. --- narrative analysis. --- narrative representation. --- narrative subjectivity. --- narrative. --- narratology. --- negative numbers. --- non-Euclidean epistemology. --- non-Euclidean geometry. --- non-Euclidean mathematics. --- non-Euclidean physics. --- non-Euclidean thinking. --- orthe. --- permutation groups. --- perspective. --- poetic storytelling. --- polynomial equations. --- proof. --- quantum mechanics. --- rational enquiry. --- rationality. --- reality. --- scientific inquiry. --- square roots. --- story generator algorithm. --- story grammars. --- story. --- storytelling. --- structural linguistics. --- symbols. --- theology. --- theorems. --- tragic mathematical heroes. --- truth. --- variste Galois. --- vestibular line. --- visions. --- visual line. --- vividness. --- Communication in mathematics
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