A Counterfactual Cause in Situation Calculus

TL;DR

This paper introduces a counterfactual-based notion of cause within the situation calculus, extending previous achievement cause concepts and relating them to Halpern and Pearl's causality framework.

Contribution

It proposes a new counterfactual approach to achievement cause in situation calculus, addressing limitations of previous definitions and analyzing its relation to existing causality theories.

Findings

The new cause notion generalizes to achievement cause in action histories.

It clarifies the relationship between different achievement cause definitions.

It discusses nuances of applying counterfactual causality to disjunctive goals.

Abstract

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. 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 goals, a common thorn in definitions of actual causes.