Formalisées

Formalisées is the feminine plural past participle of the French verb formaliser, used as an adjective to indicate that a concept, model, rule, procedure or text has been made precise and unambiguous through a formal representation. In practice, something is formalisé when it is rewritten according to a formal language or a system of axioms, rules, and semantics.

In mathematics and logic, many theories are described as formalisées when their statements and proofs are presented in a formal calculus such as first-order logic, set theory, or type theory. A formalisation includes specifying syntax, semantics and inference rules, enabling mechanical verification or automated reasoning. In philosophy, the term is used to denote arguments or theories that have been reduced to formal structures to clarify assumptions and implications.

In computer science and information science, formalisations appear in formal methods, formal specification languages (for example Z, VDM, Alloy, or Coq) and formal semantics of programming languages; they support rigorous verification, correctness proofs, and tool-assisted development. In linguistics, grammar and syntax can be formalisées by means of formal grammars, automata, and tree-adjoining grammars. In the social sciences and administration, procedures are formalisées to ensure consistency and reproducibility.

Limitations include the potential for over-formalisation, increased complexity, and the risk of oversimplifying real-world phenomena that resist precise modelling. See also formalisation, langage formel, and méthode formelle.