Some Logical Properties of Nonmonotonic Causal Theories

The formalism of nonmonotonic causal theories (Giunchiglia, Lee, Lifschitz, McCain, Turner, 2004) provides a general-purpose formalism for nonmonotonic reasoning and knowledge representation, as well as a higher level, special-purpose notation, the action language $\mathcal{C}+$, for specifying and reasoning about the effects of actions and the persistence (‘inertia') of facts over time. In this paper we investigate some logical properties of these formalisms. There are two motivations. From the technical point of view, we seek to gain additional insights into the properties of the languages when viewed as a species of conditional logic. From the practical point of view, we are seeking to find conditions under which two different causal theories, or two different action descriptions in $\mathcal{C}+$, can be said to be equivalent, with the further aim of helping to decide between alternative formulations when constructing practical applications.