Logics of belief change without linearity

Ever since [4]. systems of spheres have been considered to give an intuitiv e and elegant way to give a semantics for logics of theory- or belief- chan ge, Several authors [5.11] have considered giving up the rather strong assu mption that systems of spheres be linearly ordered by inclusion, These more general structures are called hypertheories after [8]. It is shown that no ne of the proposed logics induced by these weaker structures are compact an d thus cannot be given a strongly complete axiomatization in a finitary log ic, Complete infinitary axiomatizations are given for several intuitive log ics based on hypertheories that are not linearly ordered bq inclusion.