Proof Theories for Some Prioritized Consequence Relations

Handling a possibly inconsistent prioritized belief base can be done in terms of consistent subsets. Humans do not compute consistent subsets, they just start reasoning and when confronted with inconsistencies in the course of their reasoning, they may adjust their interpretation of the information. In logics this behaviour corresponds to the mechanisms of dynamic proof theories. The aim of this paper is to transform known consequence relations for inconsistent prioritized belief bases in terms of consistent subsets, into dynamic proof theories that are a more faithful representation of human reasoning processes.