Résumé
Generalised quantifiers, which include Henkin's branching quantifiers, have been introduced by Mostowski and Lindström and developed as a substantial topic application of logic, especially model theory, to linguistics with work by Barwise, Cooper, Keenan.
In this paper, we mainly study the proof theory of some non-standard quantifiers as second order formulae. Our first example is the usual pair of first order quantifiers (for all / there exists) when individuals are viewed as individual concepts handled by second order deductive rules. Our second example is the study of a second order translation of the simplest branching quantifier: "A member of each team and a member of each board of directors know each other", for which we propose a second order treatment.