In this paper we consider the three classes of choice functions satisfying the three significant axioms called heredity (H), concordance (C) and outcast (O). We show that the set of choice functions satisfying any one of these axioms is a lattice, and we study the properties of these lattices....

We first present the concept of duality appearing in order theory, i.e. the notions of dual isomorphism and of Galois connection. Then, we describe two fundamental dualities, the duality extension/intention associated with a binary relation between two sets, and the duality between implicational...

A classically rational subject is a maximiser: he chooses the best alternative(s) according to some utility function, a paradigm going back to the eighteenth century. One of the ways to overcome its well-known deficiences is to extend it to take into account insenitivity threshold as well as the...