The do-calculus is a well-known deductive system for deriving connections
between interventional and observed distributions, and has been proven complete
for a number of important identifiability problems in causal inference.
Nevertheless, as it is currently defined, the do-calculus is inapplicable to
causal problems that involve complex nested counterfactuals which cannot be
expressed in terms of the "do" operator. Such problems include analyses of
path-specific effects and dynamic treatment regimes. In this paper we present
the potential outcome calculus (po-calculus), a natural generalization of
do-calculus for arbitrary potential outcomes. We thereby provide a bridge
between identification approaches which have their origins in artificial
intelligence and statistics, respectively. We use po-calculus to give a
complete identification algorithm for conditional path-specific effects with
applications to problems in mediation analysis and algorithmic fairness.

本文提出了 potential outcome calculus (po-calculus) 作为 Do-Calculus 的一种推广，用于能够包容更加复杂的嵌套反事实，从而得到了一个完整的算法，并在介入分析和算法公正的问题中解决了条件路径特定效应的识别问题。

识别有条件的路径特定效应的潜在结果计算

A Potential Outcomes Calculus for Identifying Conditional Path-Specific  Effects

Mediation analysis seeks to infer how much of the effect of an exposure on an
outcome can be attributed to specific pathways via intermediate variables or
mediators. This requires identification of so-called path-specific effects.
These express how a change in exposure affects those intermediate variables
(along certain pathways), and how the resulting changes in those variables in
turn affect the outcome (along subsequent pathways). However, unlike
identification of total effects, adjustment for confounding is insufficient for
identification of path-specific effects because their magnitude is also
determined by the extent to which individuals who experience large exposure
effects on the mediator, tend to experience relatively small or large mediator
effects on the outcome. This chapter therefore provides an accessible review of
identification strategies under general nonparametric structural equation
models (with possibly unmeasured variables), which rule out certain such
dependencies. In particular, it is shown which path-specific effects can be
identified under such models, and how this can be done.

本文研究中介效应分析的路径特定效应识别策略，并提出了一种通用的非参数结构方程模型。