|Review Comment: |
I would like to thank the authors for this revision. In my opinion, all raised issues were corrected/improved or explained to clarify any doubts. There are a few minor issues listed below (in the order of appearance ) - and only a few of them go beyond typos or even only suggestions (which the authors may or not follow). I am confident that the authors manage to fix these easily, and that no further review would be required, i.e., the paper can be accepted.
- 3,l: "to the union of their set-representation." - plural "-s" missing at the end
- 4,l: "More formally, for each rule…let…"- maybe better: let each rule r\in P be of the form …"?
- 5,r: "organiz" - "e" missing
- 6,l: "This tree represents all the… In Figure 1 we report an example of such a tree…" - since Fig.1 does not show the complete tree, maybe it would be better to call it "a part of such a tree"?
- 6,r: Fig. 1 has two directed edges only: I guess not every edge is intended to be directed, but please consider using a consistent pattern, e.g., more arcs should (?) appear going into the various atom vertices with T(…), right?
- 8,l: in Algorithm 1 caption: "where Mat stores results previous materialization rounds…" - I assume "of" is missing?
- 8,r: in Example 6 "(Variables: x,y,z)" - I suppose variable should be lower-case?
- 8,r: the term "blocked" is only introduced on page 10, but used here already
-14,l: "and and"
-14,r: "(*)" is used for the second time as indicator (first time page 10); it's ok but maybe consider using a different symbol since Prop. 3 just refers to (*)?
-17,l: How can pre-materialization affect 44 out of 49 rules if there are only 44 left according to the info three paragraphs above?
-17,r: Now it "affects a further 30 rules…"? Is it 30 out of the 44 (or 49) rules? Please clarify what the "further" is referring to.
-17,r: "we chose two major duplicate sources…" - maybe better "pinpointed" or "determined" or "detected" since these were already there, i.e., it is nothing you deliberately chose?
-20,l: "although after a complete materialization reasoning is no longer needed…" - substitute "although" by "while"?
-23,l: "one and three order…" - "orders"
-23,r: "Virtuoso  supports … of a few (but not all) OWL rules" - First, I guess you mean OWL RL rules - and since your work does not support all OWL RL rules either, I think it would be nice to add just one short phrase which quantifies this a bit more.
-23,r: The same matter applies to Oracle : from the short description, it seems as if that work is basically the same as the authors which is probably not true nor what the authors want to transmit, i.e., differences should be stressed briefly (for approaches that are rather close in spirit).
-24,l: Maybe, my two previous complaints are covered by "none of these approaches supports a similar…" - but since it appears in a separate paragraph, it leaves the impression that this restriction only applies to references within that paragraph.
- throughout the paper: please check missing commas throughout the paper, e.g., there are quite a few instances of missing "," in the case of "if… , then"; also consider trying to separate quantifications (for each/all or even just for some technical term - see, e.g., Prop. 2 itself) in the formal parts to clarify the scope