What Is a Counterfactual Cause in Action Theories?

Since the proposal by Halpern and Pearl, reasoning about actual causality has gained increasing attention in artificial intelligence, ranging from domains such as model-checking and verification to reasoning about actions and knowledge. More recently, Batusov and Soutchanski proposed a notion of actual achievement cause in the situation calculus, amongst others, they can determine the cause of quantified effects in a given action history. While intuitively appealing, this notion of cause is not defined in a counterfactual perspective. In this paper, we propose a notion of cause based on counterfactual analysis. In the context of action history, we show that our notion of cause generalizes naturally to a notion of achievement cause.