This paper proposes a new identification strategy in causal effect estimation on a graph, and the identification strategy generalizes the framework of do-calculus. This paper shows a novel algorithm for searching an identifiable causal effect, which is an NP-hard problem. Authors also show the experimental results and provide their code for reproducing the results. One of the drawbacks of this paper is the complicated notation. For example, authors should define the do-calculus explicitly in their paper even though it is a well-known concept in this field, and we can understand the meaning after reading several pages. In addition to the above drawback, I could not understand the intuition of the rules of calculus. I think that authors should provide a more intuitive explanation about the each rule to justify them.

The author for the first time formulated the problem of causal effect identifiability in the presence of CSIs for binary variables, which is original. The manuscript is well structured and easy to follow; more details could be given for 5.2. The proofs for the rules are with good quality. Some more simulation results could be provided for a better understanding of the proposed algorithm. There are several concerns: 1. In 4.1, have all the rules been listed? 2. Will the greedy algorithm recover all the identifiable probability distributions? Although the problem is NP hard, can you provide a comparison of the greedy search result with an exhaustive search in the simulation? 3. How to identify the representatives of val(C)/~^s ? Is it through exhaustive search? Update: Thanks for the author for answering the questions. I think it is still not very clear to me what is the gap between the set of all identifiable causal effects and the rules identifiable using the rules listed in 4.1. But overall it is a very interesting work with good quality and I will keep my initial score.

This paper proposes an automated search procedure for identifying causal effects when context-specific independence relations are present in an observed distribution. Equipped with sufficient conditions for conditional independence statements (Boutiller et al. 1996) and LDAG representation (Pensar et al. 2015), a simple search algorithm is implemented. Overall, the paper is clearly written, and it was easy to follow theorems (clarity). However, it is hard to measure the novelty of the paper (originality), which I will discuss below. Hence, the proposed algorithm may be useful for some researchers, but its significance (impact) is unclear. It is nice to see the rules (basic probability axioms + (CS) independence) written clearly, which lead to the implementation of a search algorithm. However, there is nothing special about the rules. A set of sufficient criteria is implemented to check them in a sufficiently fast way. Is necessary (and sufficient) criteria impossible to provide even with a faithfulness assumption (or its modified version taking CSI into consideration)? The primary contribution, perceived and highlighted by the authors, seems to be the implementation of the search algorithm. However, the implementation cannot usually be an important factor to weigh in the acceptance of the paper. ** after rebuttal ** I somewhat disagree with the authors rebuttal in L39–41. Do-calculus *is* the result of basic probability axioms and conditional independence relations in a causal graph. (The authors proved it using LDAG w/ interventional nodes for Thm 2 in the appendix.) There is no reason to “prevent the need for … do-calculus.” But, I generally agree with the authors’ intention. Anyhow, I value the importance of the paper, and recommend the acceptance of the paper.