Reviewer has chosen to be Anonymous

Summary of paper in a few sentences:

The authors propose a new link prediction approach for knowledge graphs that does not need a training phase, and that can provide interpretable explanations for each inference.It relies on the computation of Concepts of Nearest Neighbours (CNN) to identify clusters of similar entities based on common
graph patterns. Different rules are then derived from those graph patterns, and combined to predict new relationships. The authors conduct evaluations on standard benchmarks for link prediction, and find it is competitive compared to existing approaches.

Reasons to accept:

--Overall, the paper is well-written and presents a different way of looking at the problem of link prediction rather than proposing yet another embedding approach.
--The interpretability of the approach is a strong plus.
--The authors have been meticulous in putting up a webpage for the project and providing resources to use and replicate their work. I think this is a strong plus that deserves its due.
--There is a fair amount of experimental analysis and this is always a good thing in a paper.

Reasons to reject:

I think the paper makes a valid and different contribution to the field; hence, it should be accepted, even though it's not without some limitations, mainly that I am not confident that it can be applied to large-scale knowledge graphs due to its reliance anytime-computation. In contrast, embeddings are only linear in the total numbers of relations and entities.

Nanopublication comments:

Further comments:

--I am not sure it is wise to name the approach CNN, since the acronym has become synonymous with Convolutional Neural Networks. It may be difficult for people to find this paper, especially if all they remember is that it is called CNN.
--It would be good to address the scalability limitations in the beginning of the paper. It seems to me that storing the KG in memory is important for the practical merits of this approach. Either way, this needs to be mentioned somewhere in the introduction.
--I think the terminology and use of definitions and symbols can be simplified, and I encourage you to do so to make your theory more accessible.

By Heiko Paulheim https://orcid.org/0000-0003-4386-8195

Review Details

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Reviewer has chosen not to be Anonymous

Summary of paper in a few sentences:

The author presents an approach for knowledge graph completion, called "concepts of nearest neighbors". It is an anytime learning approach which learns patterns of neighbors and uses those for knowledge graph completion.

The paper is an extended version of an ESWC 2019 paper, as acknowledged by the author. Compared to that paper, there are no novel ideas, but a more extensive evaluation on more datasets and baselines, as well as a more detailed investigation of the impact of various parameters.

Reasons to accept:

The author compares against a variety of state of the art approaches and on more than one dataset. The comparison to AnyBURL is particularly interesting, yet not fully conclusive.

Reasons to reject:

Overall, the paper is written in a very confusing style. Although a running example is used, it is often hard to grasp the idea and the example per se. What would help is a big picture explaining how the different pieces (queries, answers, extensions, intensions, neighbors, inference, ...) fit together and how they are combined in order to produce a prediction. For the actual prediction part, I miss a pseudocode explaining how the approach actually computes an inference.

One major claim of the paper is that the inference is explainable. However, I find that claim problematic, in particular since the paper does not show examples of how such an explanation would be presented to a user. Just because the patterns learned are explicit, it does not mean that the inference itself is explainable. In fact, as the paper claims, many rules are combined into a final inference. Which one is then chosen as an explanation? Is there a difference whether the inference is created by one strong or by 100 weak rules?

Nanopublication comments:

Further comments: