Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)





First Advisor

Dr. HAWKE Peter Michael

Second Advisor

Prof. ZHANG Jiji


Probabilistic actual causation is a theory about actual causal relations in probabilistic scenarios. Compared with general (or type) causal connections, actual (or token, singular) causation involves specific and actual events occurring in a particular time and space. Halpern and Pearl proposed three mathematical definitions on actual causation via structural equation models (or causal models). Fenton-Glynn extended one of their definitions into a probabilistic version by following the probability-raising principle in the tradition of theorizing about probabilistic causation. The basic idea of this principle is that a cause shall raise the probability of its effect. He adopted interventional probabilities to analyse actual causation in causal Bayesian networks. According to Pearl, interventional probabilities of the form P(Y = yX=x) are used to form type-level causal claims, while it is counterfactual probabilities of the form P(Y = yX=x | X = x1, Y = y1) that help us characterize token-level causal relations as the conditionalization part takes actual situations into account; the more facts we condition upon, the closer we come to actual causation. In this dissertation, we modify Fenton-Glynn’s probabilistic definition of actual causation in probabilistic causal models by employing counterfactual probability raising instead of his interventional probability raising. Our new definitions PAC and PAC’ are capable of dealing with a number of probabilistic versions of causal examples in which Fenton-Glynn’s definition fails, such as voting, overlapping, trumping, etc. Alternatively, we can exploit elaborate and plausible counterfactual definitions of actual causation, once counterfactuals are interpreted probabilistically, essentially we turn the deterministic theories of actual causation into their indeterministic versions. That can be seen as the second or new approach to defining probabilistic actual causation compared with the traditional straightforward probability-raising approach. In order to realize this idea, we propose a probabilistic semantics for causal counterfactuals in probabilistic causal models using counterfactual probabilities. Causal counterfactuals or interventional sentences have the form [X ←x]Y = y with the meaning “if X is manipulated to take value x, Y has value y.” Causation definitions in the causal modeling framework take interventional sentences as counterfactuals. Our proposed semantics for [X ← x]Y = y is its corresponding counterfactual probability being very high (e.g. P(Y = yX=x | e) = 1). For this semantics, we provide a sound and complete axiomatization. Based on this logical result, Halpern’s latest definition of actual causation can be translated as a probabilistic version by interpreting interventional statements in it with our semantics. The difference between definitions from this approach and the traditional one turns out to be the extent of probability increase, namely, slight (traditional approach) or significant (new approach) probability raising. We compare the logical properties of our conception PAC of probabilistic actual causation and the new indeterministic version of Halpern’s latest actual causation by treating these two definitions as the semantics for causal conditionals.



Recommended Citation

Fang, J. (2022). On probabilistic reasoning of actual causation (Doctor's thesis, Lingnan University, Hong Kong). Retrieved from