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A causal claim is any assertion that invokes causal relationships between variables, for example that a drug has a certain effect on preventing a disease. Causal claims are established through a combination of data and a set of causal…

Artificial Intelligence · Computer Science 2012-07-19 Judea Pearl

A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has…

Reasoning about observed effects and their causes is important in multi-agent contexts. While there has been much work on causality from an objective standpoint, causality from the point of view of some particular agent has received much…

Artificial Intelligence · Computer Science 2019-11-01 Shakil M. Khan , Mikhail Soutchanski

The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This…

Quantum Physics · Physics 2020-05-28 Holger F. Hofmann

Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those…

Artificial Intelligence · Computer Science 2014-08-08 Joseph Y. Halpern

Pearl observes that causal knowledge enables predicting the effects of interventions, such as actions, whereas descriptive knowledge only permits drawing conclusions from observation. This paper extends Pearl's approach to causality and…

Artificial Intelligence · Computer Science 2025-07-08 Kilian Rückschloß , Felix Weitkämper

Reasoning about actual causes of observed effects is fundamental to the study of rationality. This important problem has been studied since the time of Aristotle, with formal mathematical accounts emerging recently. We live in a world where…

Artificial Intelligence · Computer Science 2026-02-17 Shakil M. Khan , Asim Mehmood , Sandra Zilles

We describe and contrast two distinct problem areas for statistical causality: studying the likely effects of an intervention ("effects of causes"), and studying whether there is a causal link between the observed exposure and outcome in an…

Statistics Theory · Mathematics 2021-04-02 A. Philip Dawid , Monica Musio

A recent trend of fair machine learning is to define fairness as causality-based notions which concern the causal connection between protected attributes and decisions. However, one common challenge of all causality-based fairness notions…

Machine Learning · Computer Science 2019-10-29 Yongkai Wu , Lu Zhang , Xintao Wu , Hanghang Tong

In this work, we argue for the importance of causal reasoning in creating fair algorithms for decision making. We give a review of existing approaches to fairness, describe work in causality necessary for the understanding of causal…

Artificial Intelligence · Computer Science 2018-05-16 Joshua R. Loftus , Chris Russell , Matt J. Kusner , Ricardo Silva

The probability of causation (PC) is often used in liability assessments. In a legal context, for example, where a patient suffered the side effect after taking a medication and sued the pharmaceutical company as a result, the value of the…

Statistics Theory · Mathematics 2024-09-17 Hanmei Sun , Chengfeng Shi , Qiang Zhao

The precise definition of causality is currently an open problem in philosophy and statistics. We believe causality should be defined as functions (in mathematics) that map causes to effects. We propose a reductive definition of causality…

Artificial Intelligence · Computer Science 2023-07-18 Tianyi Miao

Causality plays an important role in daily processes, human reasoning, and artificial intelligence. There has however not been much research on causality in multi-agent strategic settings. In this work, we introduce a systematic way to…

Artificial Intelligence · Computer Science 2025-02-20 Sylvia S. Kerkhove , Natasha Alechina , Mehdi Dastani

The concept of causality has a controversial history. The question of whether it is possible to represent and address causal problems with probability theory, or if fundamentally new mathematics such as the do calculus is required has been…

Machine Learning · Statistics 2021-12-13 Finnian Lattimore , David Rohde

The starting point of the present paper is Bell's notion of local causality and his own sharpening of it so as to provide for mathematical formalisation. Starting with Norsen's (2007, 2009) analysis of this formalisation, it is subjected to…

Quantum Physics · Physics 2011-08-22 M. P. Seevinck , J. Uffink

Existing algorithms for explaining the outputs of image classifiers are based on a variety of approaches and produce explanations that frequently lack formal rigour. On the other hand, logic-based explanations are formally and rigorously…

Artificial Intelligence · Computer Science 2026-02-20 David A Kelly , Hana Chockler

Causal models defined in terms of a collection of equations, as defined by Pearl, are axiomatized here. Axiomatizations are provided for three successively more general classes of causal models: (1) the class of recursive theories (those…

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

Explanations are a fundamental element of how people make sense of the political world. Citizens routinely ask and answer questions about why events happen, who is responsible, and what could or should be done differently. Yet despite their…

Computation and Language · Computer Science 2025-12-04 Paulina Garcia-Corral

Causal reasoning is a cornerstone of how humans interpret the world. To model and reason about causality, causal graphs offer a concise yet effective solution. Given the impressive advancements in language models, a crucial question arises:…

Computation and Language · Computer Science 2024-06-25 Sirui Chen , Mengying Xu , Kun Wang , Xingyu Zeng , Rui Zhao , Shengjie Zhao , Chaochao Lu

Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world…

Artificial Intelligence · Computer Science 2015-04-27 Pedro A. Ortega