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An Axiomatic Characterization of Causal Counterfactuals
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“Galles and Pearl [1] and Halpern [2] have given a complete axiomatization of structural counterfactuals, embracing both recursive and non-recursive models”
From The Deductive Approach to Causal Inference (2014) · cites this paper as [1]
Citations
Cites
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Rosenbaum, P. R., & Rubin, D. B. (1983) · Biometrika · doi:10.2307/2335942 · Cited by 3,495
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Causal diagrams for empirical research
PEARL, J. (1995) · Biometrika · doi:10.1093/biomet/82.4.669 · Cited by 2,355 · cited 11×
“[Balke and Pearl, 1995] A. Balke and J. Pearl.”
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Research works printed but not linked: 8
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Counterfactual Causality from First Principles?
Gößler, G., Sokolsky, O. V., & Stefani, J. (2017) · Electronic Proceedings in Theoretical Computer Science · doi:10.4204/eptcs.259.5 · Cited by 5
“On structural equations models [29] (SEM), [9] introduces three properties that hold in all (recursive and nonrecursive) SEM, two of which characterize manipulation (Pearl’s do operator) in the recursive case.”
A Regression Framework for Causal Mediation Analysis with Applications to Behavioral Science
Saunders, C. T., & Blume, J. D. (2019) · Multivariate Behavioral Research · doi:10.1080/00273171.2018.1552109 · Cited by 5
“Although one framework may lend itself to a specific research question, the SEM and PO frameworks are “logically equivalent,” a result proven formally by Galles and Pearl (1998).”
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Didier Dubois, A., & Prade, H. M. (2020) · Springer eBooks · doi:10.1007/978-3-030-06164-7_9 · Cited by 5
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“This logic has first been worked out by Galles and Pearl (1998) and Halpern (2000).”
MethodFormalizing Statistical Causality via Modal Logic
Kawamoto, Y., Sato, T., & Suenaga, K. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-43619-2_46 · Cited by 5
“We also remark that AX CP has axioms corresponding to the composition and effectiveness axioms introduced by Galles and Pearl [9].”
BackgroundResultStrongly Complete Axiomatization for a Logic with Probabilistic Interventionist Counterfactuals
Barbero, F., & Virtema, J. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-43619-2_44 · Cited by 5
Covariates and Causal Effects: The Problem of Context
Aliprantis, D. (2013) · Working paper · doi:10.26509/frbc-wp-201310r · Cited by 6
“I also adopt Galles and Pearl (1998)’s notation for Lewis’ conditional counterfactuals by denoting”
InfluentialCausal Models and Metaphysics—Part 2: Interpreting Causal Models
McDonald, J. (2024) · Philosophy Compass · doi:10.1111/phc3.13007 · Cited by 4
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“While there are differences in abstractions between them, there is formal equivalence (Galles and Pearl, 1998) in modeling counterfactuals (“What is the effect when the cause is intervened?”) and we refer the reader to (Pearl and Mackenzie, 2018) for a primer in causal modeling.”
BackgroundNazarov, D. M., Bayakhmetova, A. T., Bayakhmetova, L., & Bayakhmetova, L. (2022) · Mathematics · doi:10.3390/math10091415 · Cited by 7
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Backtracking through interventions: An exogenous intervention model for counterfactual semantics
Vandenburgh, J. (2022) · Mind & Language · doi:10.1111/mila.12447 · Cited by 4
Counterfactuals and dependencies on causal teams: expressive power and deduction systemsPreprint
Barbero, F., & Yang, F. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2004.00952 · Cited by 4
“We point out, however, that each of our deduction systems can be adapted to the case of unique-solution (possibly generalized) causal teams by replacing the Recur rule with an inference rule that expresses the Reversibility axiom from [5].”
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Ibeling, D., & Icard, T. (2021) · arXiv · doi:10.48550/arxiv.2107.08558 · Cited by 4
“If χU is finite, we obtain a familiar [13] sum formula pcf (yx, .”
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The Logic of Dynamical Systems Is Relevant
Hornischer, L., & Berto, F. (2025) · Mind · doi:10.1093/mind/fzaf012 · Cited by 3
Gallow, J. D. (2022) · Philosophical Perspectives · doi:10.1111/phpe.12174 · Cited by 3
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Barbero, F. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-56940-1_11 · Cited by 3
Towards an effective practice of learning from data and knowledge
Chen, Y., Huang, H., & Darwiche, A. Y. (2024) · International Journal of Approximate Reasoning · doi:10.1016/j.ijar.2024.109188 · Cited by 3
Operational Causality – Necessarily Sufficient and Sufficiently Necessary
Christel Baier, A., Dubslaff, C., Funke, F., Jantsch, S., Piribauer, J., & Ziemek, R. (2022) · Lecture notes in computer science · doi:10.1007/978-3-031-15629-8_2 · Cited by 3
“Halpern and Pearl express causal dependencies in structural equation models [63, 29, 30, 38] and employ the counterfactuality principle that has a rich history in philosophical theories of causal reasoning [46, 47, 58].”
The Language of Potential Outcomes
Sjölander, A. (2012) · Wiley series in probability and statistics · doi:10.1002/9781119945710.ch2 · Cited by 3
Team semantics for interventionist counterfactuals and causal dependencePreprint
Barbero, F., & Sandu, G. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1712.08661 · Cited by 3
“Galles and Pearl ([8]) consider the case of systems with unique solutions, defined as follows: 1) for fixed values of the exogenous variables, the system has a unique solution, and 2) each “intervened” system of equations obtained from the initial one replacing some equations of the form X := fX(PAX) with constant equ…”
BackgroundInfluentialProbabilistic Reasoning across the Causal HierarchyPreprint
Ibeling, D., & Icard, T. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2001.02889 · Cited by 3
“Axioms for causal conditionals interpreted over structural causal models are well understood (Galles and Pearl 1998; Halpern 2000; Pearl 2009; Zhang 2013; Ibeling and Icard 2019) and play a distinct role in causal reasoning tasks such as identification (Shpitser and Pearl 2008; Pearl and Barein-boim…”
BackgroundFiltering Semantics for Counterfactuals: Bridging Causal Models and Premise Semantics
Santorio, P. (2015) · Proceedings from Semantics and Linguistic Theory · doi:10.3765/salt.v24i0.2430 · Cited by 2
A Characterization of Lewisian Causal Models
Fang, J., & Zhang, J. (2023) · Lecture notes in computer science · doi:10.1007/978-3-031-45558-2_8 · Cited by 2
Multiteam Semantics for Interventionist Counterfactuals: Probabilities and Causation
Barbero, F., & Sandu, G. (2024) · Journal of Philosophical Logic · doi:10.1007/s10992-024-09777-0 · Cited by 2
“[13], [15]) the notation Yx(u) = y is used to express that, under the assumption that the (whole set of) exogenous variables U has values u, fixing some endogenous variables X to x forces the exogenous variables Y to take value y.”
Causal inference and inter-world laws
Wu, T.-Y. (2024) · Asian Journal of Philosophy · doi:10.1007/s44204-024-00206-2 · Cited by 2
“6 The following procedure for causal inference within SCM is based on the work of Galles and Pearl (1998), Pearl (2009, pp. 202–206), and Pearl et al., (2016, pp. 92–98).”
Identifying Causal Effects Under Functional Dependencies
Chen, Y., & Darwiche, A. Y. (2024) · Entropy · doi:10.3390/e26121061 · Cited by 2
“…2 can be thought of as specifying the function C = A ⊕ B and is therefore called a functional CPT. Functional CPTs are also known as (causal) mechanisms and are expressed using structural equations in structural causal models (SCMs) [Balke and Pearl, 1995, Galles and Pearl, 1998, Halpern, 2000].”
Statistics, Causality, and Graphs
Pearl, J. (1999) · Springer eBooks · doi:10.1007/978-3-642-58648-4_1 · Cited by 2
Self-citationLee, K. Y. (2015) · Logic in Asia: Studia logica library · doi:10.1007/978-3-662-48357-2_5 · Cited by 2
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Pearl, J. (2010) · Cited by 2
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Protzko, J. (2016) · Foundations of Science · doi:10.1007/s10699-016-9511-x · Cited by 2
“4 For example, the counterfactual model is logically equivalent to certain structural equation models (Galles and Pearl 1998).”
ResultPearl, J. (2011) · eScholarship (California Digital Library) · Cited by 2
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Thielscher, M. (1999) · Lecture notes in computer science · doi:10.1007/3-540-48238-5_11 · Cited by 2
“We will also show formally how, despite these di erences, the approach of [1, 4], if restricted to causal models without probabilities, is embedded in our proposal.”
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“In [5, 6], a complete axiomatization of structural counterfactuals, embracing both recursive and nonrecursive models, is given.”
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Goodman, J. E., Li, W., & Cox, L. A. (2021) · Global Epidemiology · doi:10.1016/j.gloepi.2021.100052 · Cited by 1
“These include counterfactual and potential-outcomes causation [13,14]; path analysis, causal networks, and structural equation models [15,16]; predictive causation [17,18]; quasi-experiment design and causal inference [19]; epidemiological and attributive causation [8,20]; interventional or manipulative causation [21,…”
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Dewey, D. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-35506-6_7
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Pearl, J. (2014) · Journal of Causal Inference · doi:10.1515/jci-2014-0028
“These auxiliary rules will rely on the composition axiom (Pearl, 2009, p. 229) X w = x =⇒ Y xw = Y w (9) which was shown to be sound and complete relative to recursive models (Galles and Pearl, 1998; Halpern, 1998).”
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Liu, T. P., Zhang, M. M., & Wang, Y. Y. (2013) · Advanced materials research · doi:10.4028/www.scientific.net/amr.756-759.3103
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Kuroki, M., & Kobayashi, F. (2012) · Japanese Journal of Biometrics · doi:10.5691/jjb.32.119
Proof Methods for Conditional and Preferential Logics of Nonmonotonic Reasoning
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“Although these variables are different, they are still related to each other by the consistency rule [11], [12]:”
BackgroundThe Correlation Argument for Reductionism
Clarke, C. J. (2018) · Philosophy of Science · doi:10.1086/701048
“For example, these axioms hold even on Woodward’s interventionist semantics for conditionals (Galles and Pearl 1998).”
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Schenone, P. (2018) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.1812.07414
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Metadata
- Authors
- Galles, D., & Pearl, J.
- Affiliations
- University of California, Los Angeles (US)
- Venue
- Foundations of Science
- Published
- 1998-01
- Volume
- 3
- Issue
- 1
- Pages
- 151-182
- ISSN
- 1233-1821 (ISSN-L)
- 1572-8471
- OpenAlex
- W1576238869
- Cited by
- 192
- References
- 49
- Citations by year
- 2026: 4 · 2025: 14 · 2024: 11 · 2023: 9 · 2022: 19 · 2021: 13 · 2020: 10 · 2019: 25 · 2018: 5 · 2017: 4 · 2016: 6 · 2015: 10 · 2014: 8 · 2013: 7 · 2012: 10
- FWCI
- 7.48
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- Foundations of Science (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy of Biology and Scientific Explanation
- Keywords
- counterfactuals, composition properties, reversibility, feedback, probabilistic graphical models, causal inference, axiomatization
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