A conditional perspective of belief revision

Abstract

Belief Revision is a subarea of Knowledge Representation and Reasoning (KRR) that investigates how to rationally revise an intelligent agent's beliefs in response to new information. There are several approaches to belief revision, but one well-known approach is the AGM model, which is rooted in work by Alchourrón, Gärdenfors, and Makinson. This model provides a set of axioms defining desirable properties of belief revision operators, which manipulate the agent's belief set represented as a set of propositional formulas. A famous extension to the classical AGM framework of Belief Revision is Darwiche and Pearl's approach to iterated belief revision. They uncovered that the key to rational behavior under iteration is adequate preservation of conditional beliefs, i.e., beliefs the agent is willing to accept in light of (hypothetical) new information. Therefore, they introduced belief revision operators modifying the agent's belief state, built from conditional beliefs. Kern-Isberner fully axiomatized a principle of conditional preservation for belief revision, which captures the core of adequate treatment of conditional beliefs during the revision. This powerful axiom provides the necessary conceptual framework for revising belief states with sets of conditionals as input, and it shows that conditional beliefs are subtle but essential for studying the process of belief revision. This thesis provides a conditional perspective of Belief Revision for different belief revision scenarios. In the first part, we introduce and investigate a notion of locality for belief revision operators on the semantic level. Hence, we exploit the unique features of conditionals, which allow us to set up local cases and revise according to these cases, s.t., the complexity of the revision task is reduced significantly. In the second part, we consider the general setting of belief revision with respect to additional meta-information accompanying the input information. We demonstrate the versatility and flexibility of conditionals as input for belief revision operators by reducing the parameterized input to a conditional one for two well-known parameterized belief revision operators who are similarly motivated but very different in their technical execution. Our results show that considering conditional beliefs as input for belief revision operators provides a gateway to new insights into the dynamics of belief revision.