From Actions to Programs as Abstract Actual Causes

Causality plays a central role in reasoning about observations. In many cases, it might be useful to define the conditions under which a non-deterministic program can be called an actual cause of an effect in a setting where a sequence of programs are executed one after another. There can be two perspectives, one where at least one execution of the program leads to the effect, and another where all executions do so. The former captures a ''weak'' notion of causation and is more general than the latter stronger notion. In this paper, we give a definition of weak potential causes. Our analysis is performed within the situation calculus basic action theories and we consider programs formulated in the logic programming language ConGolog. Within this setting, we show how one can utilize a recently developed abstraction framework to relate causes at various levels of abstraction, which facilitates reasoning about programs as causes.