Review Comment:
The paper presents a method to translates an OWL ontology in a latent space, using a methodology that is similar to Knowledge Graph Embeddings (KGEs). The problem of KGEs is that they capture only the topology of the graph without considering the semantics associated to the underlying ontology.
To this end, several approaches that target OWL ontologies have been presented. This paper considers one of them, which they call EmEL. It addresses an important limitation of EmEL, that is it is unable to represent efficiently onetomany and manytomany relations. The proposed solution consists of adding a special parameter (\sigma) to every relation. This new parameter moves away from a pointbased representation since \sigma can be used to encode an area in the latent space and this allows the method to represent onetomany and manytomany relations.
Although the extension is conceptually simple, the empirical evaluation shows that it leads to an improvement of the performance. This makes the presented contribution potentially interesting. Unfortunately, there are several problems with the current version of the manuscript to the point when I am not sure that someone could reproduce the method.
First of all, a general problem of the paper is that the quality of the writing is not always good. For instance, sentences are often not well constructed (e.g., a common problem seems to be an incorrect usage of the comma, starting with "but", and so on). There are also many typos and many concepts are not properly introduced. It appears to me that the paper was not properly proofread.
Moreover, the introduction does not describe what the actual contribution is, which is unusual in scientific publications. It also mentions terms like "connectionist" or "translation operator" without introducing them.
The related work section is very short, almost half of a page, which is surprising considering the amount of publications around this topic.
The preliminaries section fails to describe clearly the basic notions that are necessary to understand the paper. I believe that the paper can be understood only by a reader that is familiar with OWL and its terminology. To make it more understandable, an example would be extremely helpful to understand the notions of concepts, roles, and individuals. Also the chain operator could be better explained with an example. Also terms like ABox and TBox should be introduced.
Notice that initially the preliminaries uses OWL terms like concepts, roles, etc. Then, it starts using terms like entities, classes, and relations, but these are not defined. I think that also section 3.2 could be substantially improved by adding an example.
Section 4 has some important problems. Figures 1a and 1b are shown two pages later, which hinders the readability. The term "R" keeps getting redefined. First it is defined using a grammar (page 3, line 37), then as a member of N_R (page 4, line 27), then a member of the real numbers! (page 5, line 11). The definition of the loss in eq 1 does not seems to be correct since it suggests that there is a loss function for every (C,D) pair, since the function is defined for C and D. Notice that terms like C and D are not always reported in math mode. Another undefined concept is the one of nballs. Finally, Equation 7 contains a new term, called e_v, for which I could not find a definition.
Section 5 reports the actual contribution of the paper. Notice that this section is quite short, even not a full page. This section suffers from the same problems mentioned above. In page 6, line 45 it defines R as a member of \mathbb{R}', which I don't know what it is. The author mentions that they use the absolute value of \sigma in the regularization part of the loss, but in equation 9 there is no trace of the modulus of \sigma. At that point I realized that I would not be able to reproduce this method since too many things are missing or correctly defined. Fortunately, the authors do release the code although I think that a paper should be understandable without checking the related source code.
The evaluation reports many experiments but a general conclusion that I drew after reading it was that this method is not so much better than OWL2Vec (notice that the section mentions Table 6.1.1, which is not mentioned anywhere while Table 3 does not seem to be referenced in the text).
To conclude, if I take into account the problems related to the presentation and the relatively little gain reported in the experiments, I am not sure whether this work meets the minimum bar for acceptance in this journal. It is true that with a significant revision the paper could improve substantially, but it would require another extensive reviewing round and there would still be the problem of the relatively little gain compared to other state of the art methods.
