We study the identification of causal effects in the presence of different types of constraints (e.g., logical constraints) in addition to the causal graph. These constraints impose restrictions on the models (parameterizations) induced by the causal graph, reducing the set of models considered by the identifiability problem. We formalize the notion of constrained identifiability, which takes a set of constraints as another input to the classical definition of identifiability. We then introduce a framework for testing constrained identifiability by employing tractable Arithmetic Circuits (ACs), which enables us to accommodate constraints systematically. We show that this AC-based approach is at least as complete as existing algorithms (e.g., do-calculus) for testing classical identifiability, which only assumes the constraint of strict positivity. We use examples to demonstrate the effectiveness of this AC-based approach by showing that unidentifiable causal effects may become identifiable under different types of constraints.

翻译：本文研究在因果图之外存在不同类型约束（如逻辑约束）时因果效应的识别问题。这些约束对因果图所诱导的模型（参数化）施加限制，从而缩减了可识别性问题所考虑的模型集合。我们形式化了约束可识别性的概念，该概念将约束集作为经典可识别性定义的另一个输入。随后，我们引入一种基于可处理算术电路（AC）的框架来检验约束可识别性，该方法使我们能够系统性地处理各类约束。我们证明这种基于AC的方法在检验经典可识别性时至少与现有算法（如do-演算）具有同等完备性——后者仅假设严格正性约束。通过示例，我们展示了基于AC方法的有效性：在不同类型约束下，原本不可识别的因果效应可能变得可识别。