The causal modelling approach has been one of the most prominent approaches to causation over recent decades. It appeals to functional causal models to characterize dependence between events represented by variables and values in causal systems. The crucial operation “intervention” in the models makes it possible to change values of variables and talk about a certain kind of counterfactuals, e.g. “if variable X were set to its value x, then variable Y would take value y.” We call the counterfactuals based on the intervention operation and expressed by variables with values causal counterfactuals. Halpern provided deterministic semantics for these counterfactuals and the corresponding axiomatic systems. This paper proposes probabilistic interpretations for causal counterfactuals in probabilistic causal models defined by Pearl, and studies their logics. An application of the probabilistic semantics is to interpret counterfactuals in counterfactual theories of actual causation, so as to obtain indeterministic versions of the theories. The new probabilistic accounts can be treated as the semantics for causal conditionals, for which I explore the validity of some common conditional properties.

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A Probabilistic Logic for Causal Counterfactuals

  • Jingzhi Fang

摘要

The causal modelling approach has been one of the most prominent approaches to causation over recent decades. It appeals to functional causal models to characterize dependence between events represented by variables and values in causal systems. The crucial operation “intervention” in the models makes it possible to change values of variables and talk about a certain kind of counterfactuals, e.g. “if variable X were set to its value x, then variable Y would take value y.” We call the counterfactuals based on the intervention operation and expressed by variables with values causal counterfactuals. Halpern provided deterministic semantics for these counterfactuals and the corresponding axiomatic systems. This paper proposes probabilistic interpretations for causal counterfactuals in probabilistic causal models defined by Pearl, and studies their logics. An application of the probabilistic semantics is to interpret counterfactuals in counterfactual theories of actual causation, so as to obtain indeterministic versions of the theories. The new probabilistic accounts can be treated as the semantics for causal conditionals, for which I explore the validity of some common conditional properties.