Some results on theory revision

Abstract

The problem of Theory Revision is to “add” a formula to a theory, while preserving consistency and making only minimal changes to the original theory. A natural way to uniquely determine the process is by imposing an order of “epistemic entrenchment” on the formulae, as done by Gärdenfors and Makinson. We improve their results as follows: We define orders which generate unique revision processes too, but in addition, 1) have nice logical properties, 2) are independent of the theory considered, and thus well suited for iterated revision and computational purposes, 3) have a natural probabilistic construction. Next, we show that the completeness problems of Theory Revision carry over to a certain extent to an approach based on revising axiom systems. In the last section, we consider a more general situation: First, we will have only a partial order (on axioms) at our disposal. Second, the underlying logic will be non-monotonic. Ideas taken from defeasible inheritance will help us solve the problem.