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Manuel de logique moderne classique pour étudiants et chercheurs du supérieur, cet ouvrage présente la méthode du calcul des séquents (les groupes L). Celle-ci est une méthode de décision syntaxique ou une théorie de la démonstration utilisée par Joseph Dopp pour construire six systèmes logiques. Chacun de ces systèmes utilise des schémas d'introduction d'un opérateur dans l'antécédent ou dans le conséquent pour l'engendrement ou la démonstration des théorèmes en conformité avec les règles et les opérateurs logiques : l'implication, la conjonction, la disjonction, la négation, la négation stricte et le schéma f. Cet ouvrage présente ces systèmes logiques, les analyse, les explicite et les enrichit des exercices d'illustration résolus pour faciliter au lecteur l'approfondissement et la maîtrise de la méthode des séquents.

Logique mathématique. --- Théorie de la démonstration. --- Logic, Symbolic and mathematical. --- Proof theory.

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Logic, Symbolic and mathematical. --- Logique mathématique. --- Proof theory. --- Théorie de la démonstration --- Computational complexity. --- Complexité de calcul (informatique) --- Algorithmique --- Complexite

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"Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed 'scratch work' sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and, of course, mathematicians. Perfect for self-study, an introduction to proofs course, or as a supplementary text for a discrete mathematics course or foundations of computing course. Systematic and thorough, showing how several techniques can be combined to construct a complex proof. Covers logic, set theory, relations, functions, and cardinality" [Publisher]

Logic, Symbolic and mathematical --- Mathematics --- Proof theory --- Logique mathématique --- Théorie de la démonstration --- Logic, Symbolic and mathematical - Textbooks --- Mathematics - Textbooks --- Proof theory - Textbooks --- Logique mathématique --- Théorie de la démonstration

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Logic, Symbolic and mathematical --- Logique mathématique --- Proof theory --- Théorie de la démonstration --- Computational complexity --- Complexité de calcul (informatique) --- Logique mathématique --- Théorie de la démonstration --- Complexité de calcul (informatique)

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A collection of essays from distinguished contributors looking at why it is that mathematical proof is given precedence over other forms of mathematical justification.

Proof theory. --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Logic, Symbolic and mathematical --- Logic symbolic and mathematical --- Logique mathématique. --- Proof theory --- Théorie de la démonstration. --- Logique mathématique. --- Théorie de la démonstration.