In this paper we propose a logical system combining the update logic of A. Baltag, L. Moss and S. Solecki (to which we will refer to by the generic term BMS, [BMS04]) with the belief revision theory as conceived by C. Alchourron, P. Gardenfors and D. Mackinson (that we will call the AGM theory, [GardRott95]) viewed from the point of view of W. Spohn ( [Spohn90], [Spohn88]). We also give a proof system and a comparison with the AGM postulates.