Conditional irrelevance in belief change

This thesis presents an approach to incorporating qualitative assertions of conditional irrelevance into belief change, in order to address the limitations of existing work which considers only unconditional irrelevance. These assertions serve to enforce the requirement of minimal change to existing beliefs, while also suggesting a route to reducing the computational cost of belief change by excluding irrelevant beliefs from consideration. Our approach uses modified multivalued dependencies to represent domain-dependent conditional irrelevance assertions. We consider these assertions as capturing a property of the underlying domain, and consequently assume that a knowledge engineer has specified a collection of conditional irrelevance assertions to be taken into account during belief change. We introduce two related notions of what it means for a conditional irrelevance assertion to be taken into account by a belief revision or contraction operator: partial and full compliance. We also show that partially (and fully) compliant belief revision and contraction operators are interdefinable via the Levi and Harper identities. Further, we provide characterisations of partially and fully compliant belief revision operators in terms of semantic conditions on their associated faithful rankings. Using these characterisations, we show that partially and fully compliant belief revision operators exist. Finally, we compare our approach to existing work on unconditional irrelevance in belief change.