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Causal inference is a science with multi-disciplinary evolution and applications. On the one hand, it measures effects of treatments in observational data based on experimental designs and rigorous statistical inference to draw causal…

Methodology · Statistics 2022-09-05 Jingying Zeng , Run Wang

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…

Logic in Computer Science · Computer Science 2025-05-21 Carlos Aguilera-Ventura , Xinghan Liu , Emiliano Lorini , Dmitry Rozplokhas

Existing tools for explaining complex models and systems are associational rather than causal and do not provide mechanistic understanding. We propose a new notion called counterfactual explainability for causal attribution that is…

Machine Learning · Statistics 2025-10-07 Zijun Gao , Qingyuan Zhao

Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…

Logic · Mathematics 2024-04-29 Fredrik Engström

Interpretability research takes counterfactual theories of causality for granted. Most causal methods rely on counterfactual interventions to inputs or the activations of particular model components, followed by observations of the change…

Machine Learning · Computer Science 2024-07-08 Aaron Mueller

Many empirical studies estimate causal effects in environments where economic units interact through spatial or network connections. In such settings, outcomes are jointly determined, and treatment induced shocks propagate across…

General Economics · Economics 2026-01-05 Mariluz Mate

Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first…

Computation and Language · Computer Science 2025-03-18 Alihan Hüyük , Xinnuo Xu , Jacqueline Maasch , Aditya V. Nori , Javier González

We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…

Artificial Intelligence · Computer Science 2023-05-17 Benito van der Zander , Markus Bläser , Maciej Liśkiewicz

Team Semantics is a generalization of Tarskian Semantics that can be used to add to First Order Logic atoms and connectives expressing dependencies between the possible values of variables. Some of these extensions are more expressive than…

Logic · Mathematics 2021-05-13 Pietro Galliani

The impressive performance of recent language models across a wide range of tasks suggests that they possess a degree of abstract reasoning skills. Are these skills general and transferable, or specialized to specific tasks seen during…

Computation and Language · Computer Science 2024-04-01 Zhaofeng Wu , Linlu Qiu , Alexis Ross , Ekin Akyürek , Boyuan Chen , Bailin Wang , Najoung Kim , Jacob Andreas , Yoon Kim

We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…

Artificial Intelligence · Computer Science 2007-05-23 Joseph Y. Halpern , Judea Pearl

This work showcases a new approach for causal discovery by leveraging user experiments and recent advances in photo-realistic image editing, demonstrating a potential of identifying causal factors and understanding complex systems…

Computer Vision and Pattern Recognition · Computer Science 2021-08-23 Tao Li

In (Beckers, 2025) I introduced nondeterministic causal models as a generalization of Pearl's standard deterministic causal models. I here take advantage of the increased expressivity offered by these models to offer a novel definition of…

Artificial Intelligence · Computer Science 2025-03-12 Sander Beckers

Counterfactuals -- expressing what might have been true under different circumstances -- have been widely applied in statistics and machine learning to help understand causal relationships. More recently, counterfactuals have begun to…

Human-Computer Interaction · Computer Science 2024-04-08 Arran Zeyu Wang , David Borland , David Gotz

This paper presents a sound and completecalculus for causal relevance, based onPearl's functional models semantics.The calculus consists of axioms and rulesof inference for reasoning about causalrelevance relationships.We extend the set of…

Artificial Intelligence · Computer Science 2013-01-14 Blai Bonet

We describe the principles of counterfactual thinking in providing more precise definitions of causal effects and some of the implications of this work for the way in which causal questions in life course research are framed and evidence…

Applications · Statistics 2021-05-18 Bianca De Stavola , Moritz Herle , Andrew Pickles

We introduce a formalism for the evaluation of counterfactual queries in the framework of quantum causal models, generalising Pearl's semantics for counterfactuals in classical causal models, thus completing the last rung in the quantum…

Quantum Physics · Physics 2024-09-18 Ardra Kooderi Suresh , Markus Frembs , Eric G. Cavalcanti

We propose a formal model for counterfactual estimation with unobserved confounding in "data-rich" settings, i.e., where there are a large number of units and a large number of measurements per unit. Our model provides a bridge between the…

Econometrics · Economics 2025-04-03 Alberto Abadie , Anish Agarwal , Devavrat Shah

Counterfactual reasoning and contextuality is defined and critically evaluated with regard to its nonempirical content. To this end, a uniqueness property of states, explosion views and link observables are introduced. If only a single…

Quantum Physics · Physics 2009-11-10 Karl Svozil

Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions -- hypothetical…

Machine Learning · Computer Science 2025-10-28 Inwoo Hwang , Yushu Pan , Elias Bareinboim