My basic approach to the frame problem, as presented in my thesis and in [Cos98d], gave a way to capture the default that actions have as few effects as possible. Last Summer, I extended this work in two ways. [Cos97a] looked at different approaches to the frame problem. I showed that, rather than assume that actions had as few effects, and as many preconditions as possible, one could assume that they had as few effects and as few preconditions as possible. The usual frame assumption allows new statements that remove preconditions, my new approach naturally allows adding preconditions.
Adding observations to plans is important. In [Cos97b] I showed that sometimes a ``deduction theorem'' could be established between two non-monotonic consequence relations. One relation is widely accepted to correctly model temporal projection, that is, when there is no information about any state other that the initial state. The other approach is the approach that I proposed in my thesis. I shows that for certain syntactic classes of observations A, if and only if . The idea of first doing temporal projection, and then adding in the observation has been suggested by Lifschitz, Sandewall and others. This result gave conditions when this approach correctly captures causal reasoning. My causal approach is more general as it does not insist that observations be separable from other information.
Most of my work in action has been in a formalism, the situation calculus, that does not allow concurrent, or continuous change. A joint paper with John McCarthy [CM98a] proposes a new formalism that allows both continuous change, concurrent action, and a much richer temporal structure. In particular, a benefit of the new formalism is that it does not assume that no other actions occur during a sequence of actions. It only assumes that no actions, that would effect the course of events described, happens. This allows non-interacting narratives to be conjoined consistently.
Following suggestions from my thesis committee, I investigated when the second order methods (circumscription) used in my thesis were axiomatizable and when they were decidable. [Cos98b] shows that as long as the fluents (propositional functions of situations) are unary the solutions to the frame problem are in a decidable fragment of second order logic. The paper also investigates how certain fluents which are not unary, such as block A is on block B, in situation S, On(A,B,S), can be recast into forms that are.