Causality and Minimal Change Demystified

The Principle of Minimal Change is prevalent in various guises throughout the development of areas such as reasoning about action, belief change and nonmonotonic reasoning. Recent literature has witnessed the proposal of several theories of action that adopt an explicit representation of causality. It is claimed that an explicit notion of causality is able to deal with the frame problem in a manner not possible with traditional approaches based on minimal change. However, such claims remain untested by all but representative examples. It is our purpose here to objectively test these claims in an abstract sense; to determine whether an explicit representation of causality is capable of providing something that the Principle of Minimal Change is unable to capture. Working towards this end, we provide a precise characterisation of the limit of applicability of minimal change.