logiques

Logiques is the study of principles of valid reasoning and demonstration. It covers formal systems that codify inferential rules and philosophical analyses of meaning, justification, and truth. The term is used in French to refer to logic in both mathematical and philosophical senses, and it can denote the field as a whole or specific logical traditions.

Historically, logic began with Aristotle's syllogistic, and was advanced through Frege's predicate logic, Boolean algebra, and the development of formal axiom systems in the 19th and 20th centuries. The emergence of model theory, proof theory, and set theory helped establish contemporary logic as a mathematical discipline, while non-classical logics broadened its scope to address questions of necessity, possibility, and computation.

Major branches include propositional logic, first-order logic, higher-order logic, and non-classical logics such as modal, temporal, intuitionistic, many-valued, fuzzy, and paraconsistent logics. The field also comprises proof theory, model theory, recursion theory, and the foundations of mathematics, with computational variants like lambda calculus and type theory playing central roles in computer science.

Applications span mathematics, computer science (including formal verification and programming languages), philosophy, linguistics, and artificial intelligence. Logic provides formal frameworks for analyzing arguments, validating proofs, structuring knowledge, and designing reliable computational systems, making it a foundational tool across disciplines.