结构方程系统与反事实——兼论传递性的充分条件集

The System of Structural Equation and Counterfactuals——Discussion on a Set of Sufficient Conditions of Transitivity

因果模型中反事实的分析是一种数学式的计算。以实际发生为基础,赋值内生变量,求解模型中的方程,可判断反事实语句的真值,验证变量间是否存在因果关系、反事实依赖关系。结构方程表示变量间的因果关系,解释反事实,智能体的行为可打破原有的因果结构,构建变量间的新联系,同时致使智能体的信念发生转变,产生实际世界的新认知。哈尔彭设定的因果关系传递性的充分条件集一定程度上可解释传递性的反例,模型的计算方法可以证明刘易斯依据反事实定义的因果关系具有传递性。变量{X_(1),…,X_(n-1),X_(n)}(n≥3)间的因果关系是传递的,当且仅当任意两个相邻变量X_(i-1)和变量X_(i)具有反事实依赖关系,且从X_(1)到X_(n)存在唯一因果路径。

Counterfactuals is a kind of mathematical calculation in the system of structural equation.Based on the actual situation,we can assign the value of endogenous variables,and solve equations in the model,which can judge the value of counterfactual sentences so as to verify whether there is a counterfactual dependence relationship between variables.Structural equations represent the causality of variables and explain counterfactual.The agent's intervention can not only break the original causal structure and build new connections among variables,but also change their belief and rebuild a new cognition of the world.The set of sufficient conditions for the transitivity of causality set by Halpern can explain the counterexample of transitivity to some extent,and the calculation method in the model can prove the transitivity of causality defined by Lewis according to counterfactuals.Causality is transitive among variables {X_(1),…,X_(n-1),X_(n)}(n≥3),i.e.any variable X_(i) is counterfactual and depends on variable X_(i-1).There is a unique causal path from X_(1) to X_(n).