Counterfactuals Modulo Temporal Logics

24 pages•Published: June 3, 2023

Abstract

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.

Keyphrases: causality, counterfactuals, decidability, modal logic, temporal logic

In: Ruzica Piskac and Andrei Voronkov (editors). Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 94, pages 181--204

Links:	https://easychair.org/publications/paper/sWZw
	https://doi.org/10.29007/qtw7