A theory is elaboration tolerant to the extent that new information can be incorporated with only simple changes. The simplest change is conjoining new information, and only conjunctive changes are considered in this paper. In general adding information to a theory should often change, rather than just enlarge, its consequences, and this requires that some of the reasoning be non-monotonic.
Our theories are narratives---accounts of sets of events, not necessarily given as sequences. A narrative is elaboration tolerant if new events, or more detail about existing events, can be added by just adding more sentences.
We propose a new version of the situation calculus which allows information to be added easily. In particular, events concurrent with already described events can be introduced without modifying the existing descriptions, and more detail of events can be added.
We can reason about theories, as well as in them. Many natural phenomena can be captured by theories, often by introducing a modality, true just of the theory. Rather than treat these phenomena as the sentences true in this modality, we can treat the entire theory or modality as an object. This point of view was proposed by McCarthy, who proposed calling these reified modalities contexts.
Contexts, viewed as theories or modalities, have structural properties, and associated natural structural operations, such as union and intersection. These structural properties are most naturally captured by an algebra, reminiscent of relation or dynamic algebra , a set of operations that can be applied to contexts to form new contexts.
Thus we can have a larger space of modalities than just those that are explicitly named. We add quantifiers that range over modalities, so that we can state propositions like, ``no context with the property P exists'', or ``all contexts obey Q''. We give an axiomatization of these quantifiers which we show is complete with respect to a natural semantics.
We introduce a new methodology for comparing non-monotonic treatments of change. We consider the elaboration tolerance of various proposals. The elaboration tolerance of a non-monotonic approach is defined as the elaborations, or changes, that can be made to the non-monotonic consequences, by conjoining on new information. The standard problem, the frame assumption, is capturing the tendency of properties to persist over time. We show that almost all approaches allow new effects to be added, and preconditions to be dropped. There are other ways of describing the world, and we investigate one in particular, assuming there are as few preconditions for an action as possible. This is equivalent to assuming that actions change properties as often as possible, if they ever change that property. We show that this assumption is in conflict with the usual frame assumption. We show that this methodology allows new effects to be added, and preconditions to be added. We show that this precondition assumption is naturally opposite to the frame assumption. We then show that this assumption can be naturally captured in a similar way to the frame problem, using circumscription.
We consider the frame problem, that is, characterizing the assumption that properties tend to persist over time. We show that there are at least three distinct assumptions that can be made. We show the first assumption, which have been widely studied, is not naturally captured by circumscription. The first assumption is, ``there is as little change as possible between one situation and the next''. This is closely related to temporal projection. The second assumption is that actions have as few effects as possible. This has arisen in causal approaches. We show this assumption cannot be captured by any circumscription policy, as it compares models with different domains. We consider a third assumption---there are as many frame axioms true as possible---which can be captured by circumscription. All three assumptions differ, which we show by giving examples. All agree on a small class of theories, those axiomatized by effect axioms and a class of sentences we call compatible binary domain constraints. Further, for a similar class of theories a deduction theorem holds, allowing observations, or facts about particular situations, to be brought through the non-monotonic consequence relation. This justifies approaches based on separating ``observations'' from ``effects'', and applying projection to the effects, to solve problems based on causality reasoning.
We can represent how to change our beliefs in the light of new information by using a conditional ``if A is the case, then we should accept B''. We propose that this belief change conditional should be defined as material implication when A is consistent with our current beliefs, and as a suitable counterfactual in the other case. We show that the resulting belief change system obeys the rationality postulates suggested by Alchourron, Gardenfors, and Makinson. To get an exact correspondence between systems of belief change thus defined in terms of counterfactuals, and systems based on rationality postulates, it is more intuitive to modify the usual ``closest possible world'' models of counterfactuals, so that different similarity measures centered at the same world are cotenable, and all worlds are ranked. Once this is done we can achieve a correspondence between finite sequences of belief changes using rationality postulates and models of a counterfactual. The valid counterfactual sentences do not constitute a possible state of belief. They do not decide enough sentences. However, we can specify a state of belief, by adding the additional sentences, that describe the fact that we believe no counterfactuals, save those that we have explicitly been told. This characterizes a ``tabula rasa'' or blank slate, upon which we can impose any belief change system, by revising it with the sentences that characterize the defaults of that belief change system.