# Counterfactuals Modulo Temporal Logics

arXiv: https://arxiv.org/abs/2306.08916 · HTML: https://mlsanity.com/paper/2306.08916/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 15 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Reinforcement Learning With Temporal Logic Rewards](https://mlsanity.com/paper/1612.03471/) (2016)
- [A Composable Specification Language for Reinforcement Learning Tasks](https://mlsanity.com/paper/2008.09293/) (2020)
- [A Modification of the Halpern-Pearl Definition of Causality](https://mlsanity.com/paper/1505.00162/) (2015)
- [Temporal Logics for Hyperproperties](https://mlsanity.com/paper/1401.4492/) (2014)
- [Causality in Configurable Software Systems](https://mlsanity.com/paper/2201.07280/) (2022)
- [The Computational Complexity of Structure-Based Causality](https://mlsanity.com/paper/1412.3076/) (2014)
- [AutoHyper: Explicit-State Model Checking for HyperLTL](https://mlsanity.com/paper/2301.11229/) (2023)
- [Reasoning About Causal Models With Infinitely Many Variables](https://mlsanity.com/paper/2112.11362/) (2021)
- [Causes and Explanations: A Structural-Model Approach --- Part 1: Causes](https://mlsanity.com/paper/1301.2275/) (2013)
- [Probabilistic Hyperproperties of Markov Decision Processes](https://mlsanity.com/paper/2005.03362/) (2020)
- [Probabilistic causes in Markov chains](https://mlsanity.com/paper/2104.13604/) (2021)
- [HyperPCTL: A Temporal Logic for Probabilistic Hyperproperties](https://mlsanity.com/paper/1804.01853/) (2018)
- [The Hierarchy of Hyperlogics](https://mlsanity.com/paper/2005.05934/) (2020)
- [Causality-Based Game Solving](https://mlsanity.com/paper/2105.14247/) (2021)
- [Explaining Hyperproperty Violations](https://mlsanity.com/paper/2206.02074/) (2022)

## Built on by (most cited first, 1 of 1)

- [Sample-Efficient Learning of Probabilistic Causes for Reachability in Markov Decision Processes with Probabilistic Guarantees](https://mlsanity.com/paper/2606.29681/) (2026)

## Abstract (arXiv)

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.