Combining Probabilistic, Causal, and Normative Reasoning in CP-logic

In recent years the search for a proper formal definition of actual causation -- i.e., the relation of cause-effect as it is instantiated in specific observations, rather than general causal relations -- has taken on impressive proportions. In part this is due to the insight that this concept plays a fundamental role in many different fields, such as legal theory, engineering, medicine, ethics, etc. Because of this diversity in applications, some researchers have shifted focus from a single idealized definition towards a more pragmatic, context-based account. For instance, recent work by Halpern and Hitchcock draws on empirical research regarding people's causal judgments, to suggest a graded and context-sensitive notion of causation. Although we sympathize with many of their observations, their restriction to a merely qualitative ordering runs into trouble for more complex examples. Therefore we aim to improve on their approach, by using the formal language of CP-logic (Causal Probabilistic logic), and the framework for defining actual causation that was developed by the current authors using it. First we rephrase their ideas into our quantitative, probabilistic setting, after which we modify it to accommodate a greater class of examples. Further, we introduce a formal distinction between statistical and normative considerations.