Coherence and belief revision: models for revision functions without preservation

Abstract

In this thesis I investigate Gärdenfors' Triviality result which says that the Ramsey Test for conditionals and the AGM-theory of belief revision are incompatible. After an introduction into the theories of conditionals and belief revision I review the proof and its prerequisites, especially the Preservation Principle and the Monotonicity Principle. The Monotonicity Principle is a direct consequence of the Ramsey Test which means that incompatibility of Preservation and Monotonicity implies incompatibility between Preservation and the Ramsey Test. Contrary to Gärdenfors I argue that it is not the Monotonicity Principle - and thereby the Ramsey Test - that must be rejected but the Preservation Principle. On the grounds of a coherence theory of justification I argue that the Principle of Minimal Change of the AGM-theory does not necessarily have to be fulfilled. In order to incorporate a new belief into an agent's existing belief system it may be rational for this agent, to give up more beliefs than necessary to simply keep her beliefs logically consistent. As a consequence the Preservation Principle can be rejected. It can be rational to abandon some original beliefs even though they do not contradict the new belief. This is the case if they are objections to the new belief, that is it is not rational to accept the new belief and the objection at the same time. I then go on to develop a theory of belief revision that does not satisfy the Preservation Principle. This is done by modifying Groves' sphere semantics of belief revision. In this modified model we also consider a system of spheres. However, unlike in Groves' model we do not consider the smallest sphere intersecting [A] to determine the revised belief set but a sphere that is as least as large as the smallest one. I prove that in this theory of belief revision the Preservation Principle is not fulfilled, but all the other basic AGM-postulates are. We will also see that the Monotonicity Principle is consistent with this semantics.