Belief Revision: A Computational Approach

In order to reason about the real world, intelligent systems must have ways of dealing with incomplete and inconsistent information. This issue is addressed in the study of nonmonotonic reasoning, truth maintenance and database update. Belief revision is a formal approach which is central to these areas. This thesis describes a computational approach to the logic of belief revision developed by Alchourrón, Gärdenfors and Makinson (AGM), culminating in the first implementation of an AGM belief revision system. The implementation is based on classical first-order logic, and for any finitely representable belief state, it efficiently computes expansions, contractions and revisions satisfying the AGM postulates for rational belief change. The epistemic state is represented by a finite entrenchment base, from which the full belief set may be derived by logical closure, and the entrenchment relation can be generated via the construction of a unique most conservative entrenchment. The entrenchment construction is motivated by considerations of evidence and by connections with truth maintenance and nonmonotonic reasoning. A minimal change policy is presented as the solution to the entrenchment revision problem. The belief change algorithms and design decisions are described in detail, with examples of the system’s operation on some standard problems in the AI literature. Two extensions of the system are also described: firstly, an entrenchment generation algorithm which allows the AGM system to simulate the behaviour of the assumption-based truth maintenance system (ATMS); and secondly, a modification to the most conservative entrenchment in order to implement nonmonotonic reasoning using defaults with exceptions.