Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Non-Interventionist Approach to Causal Reasoning based on Lewisian Counterfactuals

Carlos Aguilera-Ventura, Xinghan Liu, Emiliano Lorini, Dmitry Rozplokhas

TL;DR

The paper develops a non-interventionist, Lewisian approach to causal reasoning by introducing a two-dimensional, computationally grounded semantics in which each state is a pair $S=(C,V)$ of a causal base and a propositional valuation. It proves that actual causation can be defined without interventions by translating Halpern-style notions into counterfactuals within this framework, and it establishes a concise model-checking formulation that is PSPACE-complete via reductions to and from QBF. The main theoretical contribution is a DAG-based reduction showing that the But condition and minimality of actual causes can be captured by counterfactuals alone, complemented by a solid computational approach to verification. The work has practical implications for explainable AI and automated causal property verification, and it points toward axiomatization, implementation, and temporal extensions as fruitful future directions.

Abstract

We present a computationally grounded semantics for counterfactual conditionals in which i) the state in a model is decomposed into two elements: a propositional valuation and a causal base in propositional form that represents the causal information available at the state; and ii) the comparative similarity relation between states is computed from the states' two components. We show that, by means of our semantics, we can elegantly formalize the notion of actual cause without recurring to the primitive notion of intervention. Furthermore, we provide a succinct formulation of the model checking problem for a language of counterfactual conditionals in our semantics. We show that this problem is PSPACE-complete and provide a reduction of it into QBF that can be used for automatic verification of causal properties.

A Non-Interventionist Approach to Causal Reasoning based on Lewisian Counterfactuals

TL;DR

The paper develops a non-interventionist, Lewisian approach to causal reasoning by introducing a two-dimensional, computationally grounded semantics in which each state is a pair of a causal base and a propositional valuation. It proves that actual causation can be defined without interventions by translating Halpern-style notions into counterfactuals within this framework, and it establishes a concise model-checking formulation that is PSPACE-complete via reductions to and from QBF. The main theoretical contribution is a DAG-based reduction showing that the But condition and minimality of actual causes can be captured by counterfactuals alone, complemented by a solid computational approach to verification. The work has practical implications for explainable AI and automated causal property verification, and it points toward axiomatization, implementation, and temporal extensions as fruitful future directions.

Abstract

We present a computationally grounded semantics for counterfactual conditionals in which i) the state in a model is decomposed into two elements: a propositional valuation and a causal base in propositional form that represents the causal information available at the state; and ii) the comparative similarity relation between states is computed from the states' two components. We show that, by means of our semantics, we can elegantly formalize the notion of actual cause without recurring to the primitive notion of intervention. Furthermore, we provide a succinct formulation of the model checking problem for a language of counterfactual conditionals in our semantics. We show that this problem is PSPACE-complete and provide a reduction of it into QBF that can be used for automatic verification of causal properties.
Paper Structure (24 sections, 7 theorems, 52 equations, 1 figure)

This paper contains 24 sections, 7 theorems, 52 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related Work
  3. Formal Framework
  4. Semantics
  5. Language
  6. Some Properties
  7. Actual Cause
  8. Equational States
  9. Interventions
  10. Formalization of Actual Cause
  11. Reduction to Counterfactuals
  12. Model Checking
  13. Conclusion
  14. Proof of Proposition \ref{['prop: validities']}
  15. Reduction to Counterfactuals
  16. ...and 9 more sections

Key Result

Proposition 1

Let $\varphi,\psi \in \mathcal{L}$, $\omega \in \mathcal{L}_{\mathsf{PROP}}$ and $p \in \mathbb{P}$. We have the following validities:

Figures (1)

  • Figure 1: Causal graph

Theorems & Definitions (27)

  • Definition 1: State
  • Definition 2: Model
  • Example 1: Videogame
  • Definition 3: Similarity relation between states
  • Definition 4: Language
  • Definition 5: Satisfaction relation
  • Example 2: Videogame continued
  • Proposition 1
  • Definition 6: Equational state
  • Definition 7: Exogenous and endogenous variables
  • ...and 17 more