A Counterfactual Cause in Situation Calculus

Perhaps the most popular modern formulation of actual causality is the HP account by Halpern and Pearl. Recent advancement has focused on extension of HP account to lift its limited expressiveness, in particular, Batusov and Soutchanski proposed a notion of actual achievement cause in the situation calculus, a rich first-order formalism of actions and changes. Among other things, the first-order nature allows for determining the cause of quantified effects in a given action history therein. While intuitively appealing, Batusov and Soutchanski's account 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. We analyze the relationship between our notion of the achievement cause and the achievement cause by Batusov and Soutchanski. Finally, we relate our account of cause to Halpern and Pearl's account of actual causality. Particularly, we note some nuances in applying a counterfactual viewpoint to disjunctive effects, a common thorn in definitions of actual causes.