Causal Theories of Action: A Computational Core

We propose a framework for simple causal theories of action, and study the computational complexity in it of various reasoning tasks such as determinism, progression and regression under various assumptions. As it turned out, even the simplest one among them, one-step temporal projection with complete initial state, is intractable. We also briefly consider an extension of the framework to allow truly indeterministic actions, and find that this extension does not increase the complexity of any of the tasks considered here.