Counterfactuals Modulo Temporal Logics
This work addresses the problem of automated symbolic counterfactual reasoning on infinite sequences for applications in formal verification and reinforcement learning, representing a novel extension of foundational causal theory.
The paper extends Lewis' counterfactual theory to handle infinite sequences like model checker counterexamples and RL trajectories by introducing a more relaxed similarity notion between worlds, two new counterfactual operators, and distance-minimizing versions. It proposes a logic combining temporal and counterfactual operators with decision procedures for satisfiability and trace-checking.
Lewis' theory of counterfactuals is the foundation of many contemporary notions of causality. In this paper, we extend this theory in the temporal direction to enable symbolic counterfactual reasoning on infinite sequences, such as counterexamples found by a model checker and trajectories produced by a reinforcement learning agent. In particular, our extension considers a more relaxed notion of similarity between worlds and proposes two additional counterfactual operators that close a semantic gap between the previous two in this more general setting. Further, we consider versions of counterfactuals that minimize the distance to the witnessing counterfactual worlds, a common requirement in causal analysis. To automate counterfactual reasoning in the temporal domain, we introduce a logic that combines temporal and counterfactual operators, and outline decision procedures for the satisfiability and trace-checking problems of this logic.