Choice Functions with States of Mind

An agent is rational by dominance then states of mind (DSM) if he makes his decisions by, first, preselecting the alternatives that are not dominated by any other alternative in the choice set, and second, by choosing the preselected alternative corresponding to his state of mind. This state of mind is dependent on the previous choices he made. An agent is rational by states of mind then dominance (SMD) if he makes his decisions by, first, preselecting the alternatives corresponding to his state of mind and second, choosing the alternative that is not dominated. We give axiomatizations for SMD-rational or DSM-rational choice functions.