  Since Pearl's seminal work on providing a formal language for causality, the
subject has garnered a lot of interest among philosophers and researchers in
artificial intelligence alike. One of the most debated topics in this context
regards the notion of actual causation, which concerns itself with specific -
as opposed to general - causal claims. The search for a proper formal
definition of actual causation has evolved into a controversial debate, that is
pervaded with ambiguities and confusion. The goal of our research is twofold.
First, we wish to provide a clear way to compare competing definitions. Second,
we also want to improve upon these definitions so they can be applied to a more
diverse range of instances, including non-deterministic ones. To achieve these
goals we will provide a general, abstract definition of actual causation,
formulated in the context of the expressive language of CP-logic (Causal
Probabilistic logic). We will then show that three recent definitions by Ned
Hall (originally formulated for structural models) and a definition of our own
(formulated for CP-logic directly) can be viewed and directly compared as
instantiations of this abstract definition, which allows them to deal with a
broader range of examples.
