logique mathématique L2
Mathematique L2 · DEUXIEME ANNÉE L2
3 chapitres · 0 séance
Description à venir.
Au programme
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Paradoxes (Antinomies)
Par Mr Aissaoui Mohammed
Abstract This chapter introduces the concept of paradoxes (antinomies) in mathematics and logic. We explore classical examples such as the Liar Paradox, Russell’s Paradox, and the Barber Paradox, examining their underlying structures and the contradictions they reveal. The chapter highlights how these paradoxes have contributed to the development of modern logic, set theory, and the foundations of mathematics.
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Proportional calculus
Par Mr Aissaoui Mohammed
Abstract Propositional calculus is a fundamental formal system used to represent and analyze logical reasoning. This chapter introduces propositions, logical connectives, truth tables, logical equivalences, tautologies, and contradictions. We also study logical implications, normal forms, and methods for establishing the validity of logical arguments. These concepts provide an essential foundation for further studies in logic, mathematics, computer science, and artificial intelligence.
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Propositional language
Par Mr Aissaoui Mohammed
Abstract Propositional language provides a formal framework for expressing and analyzing logical statements. This chapter introduces the basic elements of propositional language, including propositional variables, logical connectives, well-formed formulas, and the construction of compound propositions. We examine how natural-language statements can be translated into symbolic expressions and how their logical structure can be analyzed using truth tables and logical equivalences. These concepts form a fundamental basis for the study of mathematical logic and formal reasoning.