Change, Change, Change: Three Approaches

We consider the frame problem, that is, char­ acterizing 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 re­ lated 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 as­ sumptions differ, which we show by giving ex­ amples. All agree on a small class of theories, those ax-iomatized by effect axioms and a class of sen­ tences we call compatible binary domain constraints. Further, for a similar class of theo­ ries a deduction theorem holds, allowing ob­ servations, or facts about particular situations, to be brought through the non-monotonic con­ sequence relation. This justifies approaches based on separating "observations" from "ef­ fects", and applying projection to the effects, to solve problems based on causality reasoning. 1 The Frame Problem Reasoning about change is central to much of common sense reasoning. To reason about change we clearly need to represent what changes after an action is completed. What is not so immediately obvious is that we also need to allow the reasoner to infer what does not change after an action. The simplest way to specify what changes and what does not would be to write each set down. However this seems wasteful, and worse, seems likely to introduce inconsistencies. It seems clear that just specifying what changes is sufficient—everything else doesn't change. We can generate the properties that do not change from the list of properties that do change. If we do this we are guaranteed that our lists will be consistent. Moreover, usually fewer things change than don't change, and thus we will have much less to specify. The idea that we need specify just the positive in­ stances of change has given rise to a problem: How do we generate all the instances of properties that stay the same? This is how I formulate the frame problem. …