The complexity of model checking for belief revision and update

One of the main challenges in the formal modeling of common-sense reasoning is the ability to cope with the dynamic nature of the world. Among the approaches put forward to address this problem are belief revision and update. Given a knowledge base T, representing our knowledge of the "state of affairs" of the world of interest, it is possible that we are lead to trust another piece of information P, possibly inconsistent with the old one T. The aim of revision and update operators is to characterize the revised knowledge base T' that incorporates the new formula P into the old one T while preserving consistency and, at the same time, avoiding the loss of too much information in this process. In this paper we study the computational complexity of one of the main computational problems of belief revision and update: deciding if an interpretation M is a model of the revised knowledge base.