One of the fundamental problems in Artificial Intelligence is to perform complex multi-hop logical reasoning over the facts captured by a knowledge graph (KG). This problem is challenging, because KGs can be massive and incomplete. Recent approaches embed KG entities in a low dimensional space and then use these embeddings to find the answer entities. However, it has been an outstanding challenge of how to handle arbitrary first-order logic (FOL) queries as present methods are limited to only a subset of FOL operators. In particular, the negation operator is not supported. An additional limitation of present methods is also that they cannot naturally model uncertainty.

The theoretical analysis of the model is insufficient. For example, the author does not give an analysis of the full expressiveness of the model. That is, given any world with correct answers of some first-order logic queries W and false answers Wc, does there exist an assignment for model parameters that correctly classifies the entities in W and Wc? The reviewer is especially curious about the theoretical analysis of the proposed probabilistic negation operator because there are no comparative empirical results on answering queries with negation (all existing models cannot deal with negation). On EPFO queries, the author compared the proposed model only with two baselines.

The paper introduces a new method to query knowledge graphs via probabilistic embeddings based on the Beta distribution. The paper is well written and relevant to the NeurIPS community. All reviewers and the AC support acceptance of the paper for its contributions, notably since it proposes a novel and promising approach that enables logical negation and FOL queries on KG embeddings and as such extends the applicability of embeddings for KG inference tasks. However, please consider revising your paper to take feedback from reviewers into account e.g., in particular regarding the concerns raised related to empirical evaluation and theoretical analysis.

One of the fundamental problems in Artificial Intelligence is to perform complex multi-hop logical reasoning over the facts captured by a knowledge graph (KG). This problem is challenging, because KGs can be massive and incomplete. Recent approaches embed KG entities in a low dimensional space and then use these embeddings to find the answer entities. However, it has been an outstanding challenge of how to handle arbitrary first-order logic (FOL) queries as present methods are limited to only a subset of FOL operators. In particular, the negation operator is not supported.