“Just Because”: Taking Belief Bases Seriously

We formalize several ways of accounting, in the context of logically closed theories, for foundationalist intuitions that underlie change operations applying to belief bases. A positive and a negative concept of entrenchment is defined on the basis of the structure of a given, possibly prioritized belief base. Only the latter, more fine-grained concept proves to be appropriate for a successful attempt at approximating base changes on the theory level. We investigate the question as to which degree we can comply with the fundamental intuition expressed by the various Filtering Conditions that say that all (and only) beliefs that are believed “just because” a retracted belief was believed should be withdrawn.