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Reasoning about Actual Causes in Nondeterministic Domains -- Extended Version

Shakil M. Khan, Yves Lespérance, Maryam Rostamigiv

TL;DR

This work extends causal reasoning from deterministic to nondeterministic domains by embedding causation analysis in the nondeterministic situation calculus (NDSC). It introduces two agent-action notions—Certainly Causes and Possibly Causes—and shows how to perform regression-based reasoning about them via an extended regression operator R_ext, enabling analysis of which agent actions are causes across environment responses. The framework builds on and generalizes existing deterministic treatments (e.g., KL21) to handle nondeterminism, including a formal definition of nondeterministic causal settings and a pair of cause notions (PCauses, CCauses) with illustrative examples. The results offer a compact, regression-based method for computing actual causation in nondeterministic domains and point to future work on concurrency and epistemic aspects of causation, with potential practical implementations.

Abstract

Reasoning about the causes behind observations is crucial to the formalization of rationality. While extensive research has been conducted on root cause analysis, most studies have predominantly focused on deterministic settings. In this paper, we investigate causation in more realistic nondeterministic domains, where the agent does not have any control on and may not know the choices that are made by the environment. We build on recent preliminary work on actual causation in the nondeterministic situation calculus to formalize more sophisticated forms of reasoning about actual causes in such domains. We investigate the notions of ``Certainly Causes'' and ``Possibly Causes'' that enable the representation of actual cause for agent actions in these domains. We then show how regression in the situation calculus can be extended to reason about such notions of actual causes.

Reasoning about Actual Causes in Nondeterministic Domains -- Extended Version

TL;DR

This work extends causal reasoning from deterministic to nondeterministic domains by embedding causation analysis in the nondeterministic situation calculus (NDSC). It introduces two agent-action notions—Certainly Causes and Possibly Causes—and shows how to perform regression-based reasoning about them via an extended regression operator R_ext, enabling analysis of which agent actions are causes across environment responses. The framework builds on and generalizes existing deterministic treatments (e.g., KL21) to handle nondeterminism, including a formal definition of nondeterministic causal settings and a pair of cause notions (PCauses, CCauses) with illustrative examples. The results offer a compact, regression-based method for computing actual causation in nondeterministic domains and point to future work on concurrency and epistemic aspects of causation, with potential practical implementations.

Abstract

Reasoning about the causes behind observations is crucial to the formalization of rationality. While extensive research has been conducted on root cause analysis, most studies have predominantly focused on deterministic settings. In this paper, we investigate causation in more realistic nondeterministic domains, where the agent does not have any control on and may not know the choices that are made by the environment. We build on recent preliminary work on actual causation in the nondeterministic situation calculus to formalize more sophisticated forms of reasoning about actual causes in such domains. We investigate the notions of ``Certainly Causes'' and ``Possibly Causes'' that enable the representation of actual cause for agent actions in these domains. We then show how regression in the situation calculus can be extended to reason about such notions of actual causes.

Paper Structure

This paper contains 16 sections, 2 theorems, 42 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Situation Calculus (SC).
  4. Nondeterministic Situation Calculus (NDSC).
  5. Projection and Executability.
  6. Example.
  7. Actual Achievement Cause in the SC
  8. Example (Cont'd).
  9. Agent Actions as Causes in the NDSC
  10. Example (Cont'd).
  11. Reasoning about Achievement Causes
  12. Conclusion
  13. Technical Appendix
  14. First Application of $\mathcal{R}_\mathit{ext}$
  15. Second Application of $\mathcal{R}_\mathit{ext}$
  16. ...and 1 more sections

Key Result

Proposition 1

Figures (2)

  • Figure 1: Interconnections between locations
  • Figure 2: Executions of agent action sequence $\overrightarrow{\alpha_1}$.

Theorems & Definitions (10)

  • Definition 1: The Regression Operator
  • Definition 2
  • Definition 3
  • Definition 4: Primary Cause (KL21)
  • Definition 5: Actual Cause (KL21)
  • Proposition 1: Causes of $\varphi_1$ in $\sigma_1$
  • Definition 6: Nondeterministic Causal Setting
  • Definition 7: Possibly Causes
  • Definition 8: Certainly Causes
  • Proposition 2