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Computer science --- Algorithmes --- Graphes, Théorie des --- Informatique --- Logique mathématique --- Mathematics. --- Mathématiques
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Humanities and religion --- Religion and the humanities --- Logique --- Logic. --- Atomism. --- Epicurus --- Criticism and interpretation. --- Logique mathématique --- Philosophie --- Gassendi, Pierre, --- Contributions in philosophy of nature --- Philosophy --- Early works to 1800 --- Renaissance --- Psychological aspects --- Gassendi, Pierre --- Views on ethics --- Logique.
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Explores the nature of mathematical proof in a range of historical settings, providing the first comprehensive history of proof.
Mathematics, Ancient --- Proof theory --- Logic, Symbolic and mathematical --- Ancient mathematics --- Mathematics --- Logic of mathematics --- Mathematics, Logic of --- Philosophy. --- History. --- Prova, Teoria de la. --- Matemàtica --- Lògica de la matemàtica --- Matemàtica, Lògica de la --- Demostració, Teoria de la --- Lògica matemàtica --- Filosofia. --- Histoire des mathematiques --- Logique mathematique --- Theorie de la preuve
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Il y a cent ans paraissait un ouvrage de logique qui a marqué considérablement les études dans ce domaine tout au long du XXe siècle, soit que l'on en poursuivit le projet, soit, au contraire, que l'on en critiqua la démarche. Les Principia Mathematica de Russel et Whitehead sont donc une oeuvre majeure sur laquelle il n'était pas inutile de revenir en ce début du XXIe siècle. Certes la question à laquelle ils étaient censés répondre, c'est-à-dire celle d'un fondement rigoureux et solide des mathématiques sur la logique formelle paraît aujourd'hui dépassée. Les travaux de Gödel dans les années trente du siècle précédent ont d'une certaine façon mis fin aux ambitions du formalisme et du logicisme tels qu'ils s'exprimaient dans cet ouvrage. Cependant, de nombreuses autres questions ont été soulevées par ce texte que l'ouvrage ici présenté tente d'élucider. Les articles qui le composent reprennent, entre autres, le débat qui opposa à la démarche de Russel aussi bien l'intuitionnisme que les travaux de Lesiewski. Le travail présenté ici montre combien demeure aujourd'hui vivante la philosophie de la logique française ce dont on peut se réjouir.
Logic, Symbolic and mathematical --- Mathematics --- Logique symbolique et mathématique --- Mathématiques --- Philosophy --- Philosophie --- Russell, Bertrand, --- Whitehead, Alfred North, --- Logic, symbolic and mathematical --- Logique symbolique et mathématique --- Mathématiques --- Mathematics - Philosophy --- Russell, Bertrand, - 1872-1970. - Principles of mathematics --- Whitehead, Alfred North, - 1861-1947 - Principia mathematica --- Russell, bertrand (1872-1970) --- Whitehead, alfred north (1861-1947) --- Logique mathématique --- Contribution aux mathématiques --- Fondements
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Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems. The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic for the verification of concurrent programs. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking. There are 150 exercises with answers available to qualified instructors. Documented, open-source, Prolog source code for the algorithms is available at http://code.google.com/p/mlcs/ Mordechai (Moti) Ben-Ari is with the Department of Science Teaching at the Weizmann Institute of Science. He is a Distinguished Educator of the ACM and has received the ACM/SIGCSE Award for Outstanding Contributions to Computer Science Education. His other textbooks published by Springer are: Ada for Software Engineers (Second Edition) and Principles of the Spin Model Checker.
Mathematical logic --- wiskunde --- Mathematical logic. --- Mathematical Logic and Formal Languages. --- Mathematical Logic and Foundations. --- Logic, Symbolic and mathematical. --- Computer logic --- Logique mathématique --- Logique informatique --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism
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In his attempt to give an answer to the question of what constitutes real knowledge, Kant steers a middle course between empiricism and rationalism. True knowledge refers to a given empirical reality, but true knowledge has to be understood as necessary as well, and so consequently, must be a priori. Both demands can only be reconciled if synthetic a priori judgments are possible. To ground this possibility, Kant develops his transcendental logic. In Frege’s program of providing a logicistic basis for true knowledge the same problem is at issue: his logicist solution places the quantifier into the position of the basic element connected to the truth of a proposition. As the basic element of a theory of logic, it refers at the same time to something in reality. Mołczanow argues that Frege’s program fails because it does not pay sufficient attention to Kant’s transcendental logic. Frege interprets synthetic a priori judgments as ultimately analytic, and thus falls back onto a Leibnizian rationalism, thereby ignoring Kant’s middle course. Under the title of the transcendental analytic of quantification Mołczanow discusses Frege’s concept of quantification. For Frege, the proper analysis of number words and the categories of quantity raises problems which can only be solved, according to Mołczanow, with the help of Kant’s transcendental logic. Mołczanow’s book thus deserves its places in the series Critical Studies in German Idealism because it provides a further elaboration of Kant’s transcendental logic by bringing it into conversation with contemporary logic. The result is a new conception of the nature of quantification which speaks to our time.
Logic, Symbolic and mathematical. --- Frege, Gottlob, --- Kant, Immanuel --- Logic, Symbolic and mathematical --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Kant, I. --- Kānt, ʻAmmānūʼīl, --- Kant, Immanouel, --- Kant, Immanuil, --- Kʻantʻŭ, --- Kant, --- Kant, Emmanuel, --- Ḳanṭ, ʻImanuʼel, --- Kant, E., --- Kant, Emanuel, --- Cantơ, I., --- Kant, Emanuele, --- Kant, Im. --- קאנט --- קאנט, א. --- קאנט, עמנואל --- קאנט, עמנואל, --- קאנט, ע. --- קנט --- קנט, עמנואל --- קנט, עמנואל, --- كانت ، ايمانوئل --- كنت، إمانويل، --- カントイマニユエル, --- Kangde, --- 康德, --- Kanṭ, Īmānwīl, --- كانط، إيمانويل --- Kant, Manuel, --- Frege, G. --- Fu-lei-ko, --- Frege, Friedrich Gottlob, --- פרגה, גוטלוב, --- Frege, Friedrich Ludwig Gottlob, --- Kant, Immanuel, --- Référence (philosophie) --- Calcul des prédicats. --- Quantificateurs (logique mathématique) --- Logique --- Philosophie.
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