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What Is a Counterfactual Cause in Action Theories?

Daxin Liu, Vaishak Belle

TL;DR

The paper introduces a counterfactual analysis of achievement causality within a modalized situation-calculus framework, denoted by $ abla$ and built on a Basic Action Theory $\\Sigma$. It defines minimal counterfactual achievement causes across action histories, including narrative-prefix variants that use a Filter to preserve executability when testing counterfactuals. The work relates the proposed notion to Batusov and Soutchanski's achievement-cause account and discusses informal connections to Halpern and Pearl's actual causality, highlighting nuances with disjunctive goals and preemption. It also identifies limitations in interleaved non-atomic competing events and argues for the utility of a uniform action-theory approach, with promising applications to planning and robotics (e.g., GOLOG). Future directions include epistemic extensions and practical integration into robot programming and action-language frameworks.

Abstract

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. 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 to definitions of actual causes.

What Is a Counterfactual Cause in Action Theories?

TL;DR

The paper introduces a counterfactual analysis of achievement causality within a modalized situation-calculus framework, denoted by and built on a Basic Action Theory . It defines minimal counterfactual achievement causes across action histories, including narrative-prefix variants that use a Filter to preserve executability when testing counterfactuals. The work relates the proposed notion to Batusov and Soutchanski's achievement-cause account and discusses informal connections to Halpern and Pearl's actual causality, highlighting nuances with disjunctive goals and preemption. It also identifies limitations in interleaved non-atomic competing events and argues for the utility of a uniform action-theory approach, with promising applications to planning and robotics (e.g., GOLOG). Future directions include epistemic extensions and practical integration into robot programming and action-language frameworks.

Abstract

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. 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 to definitions of actual causes.
Paper Structure (14 sections, 1 theorem, 5 equations)

This paper contains 14 sections, 1 theorem, 5 equations.

Table of Contents

  1. Introduction
  2. A Modal Logic of Action and Change
  3. Syntax
  4. Semantics
  5. Basic Action Theory
  6. Projection by Regression
  7. Counterfactual Achievement Cause
  8. Minimal Cause
  9. Minimal Cause in Narratives
  10. Relation with Batusov and Soutchanski's Achievement Cause
  11. Relation with HP Definition of Causality
  12. Limitation of the Proposed Achievement Cause
  13. Related Work
  14. Conclusion

Key Result

theorem 1

Given a causal setting $\mathcal{C} = \langle z, \phi \rangle$, let $\mathit{BSChain}(\mathcal{C})$ be achievement causal chain of $\mathcal{C}$ by Definition def:bs18, $z'$ be the cause of $\phi$ wrt $\Sigma$ and $z$ as Definition def:acn, then $\mathit{BSChain}(\mathcal{C}) \subseteq \mathit{Chai

Theorems & Definitions (10)

  • definition 1: Truth of Formulas
  • definition 2: Minimal cause
  • definition 3: Length-based minimality
  • definition 4: Fluent-based minimality
  • definition 5: Plan-and-effect minimality
  • definition 6: Achievement cause for narratives
  • definition 7: Actual achievement cause batusov2018situation
  • theorem 1
  • proof
  • definition 8