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

TL;DR

This paper introduces a new semantics for counterfactuals that models causality without interventions, using a decomposition of states into propositional and causal components, and provides computational tools for verification.

Contribution

It offers a novel non-interventionist formal semantics for causal reasoning based on Lewisian counterfactuals, with a PSPACE-complete model checking approach.

Findings

Semantics formalizes actual cause without interventions

Model checking for the semantics is PSPACE-complete

Reduction to QBF enables automatic verification

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.