Review Comment:
This paper focuses on the query answering and entailment problem, according to OWLHorst semantics, over a collection of contextualized RDF triples (i.e., quads) whereby interoperability between different contexts is enabled through a set of bridge rules which are firstorder rules with existential heads. The author adapted OWLHorst semantics to these quad systems akin to the semantics of Distributed Description Logics. For this formalism, the author then:
(i) showed the undecidability of conjunctive query entailment (CQE) of unrestricted quad systems;
(ii) proposed a fragment called safe quad systems for which combined complexity is 3ExpTimecomplete based on a certain safety criteria;
(iii) identified Horn fragment of safe quad systems for which combined complexity of CQE is ExpTimecomplete and its more restricted variant whose combined complexity of CQE is NPcomplete;
(iv) showed that data complexity is Pcomplete for safe quad systems and their fragments mentioned in (ii) and (iii) above.
This paper is definitely relevant to the journal. I also did not spot any problems in terms of correctness of the results. Discussion on related work is adequate. The results contain novel contribution for theoretical foundations of contextualized reasoning over RDF triples. In general, the paper merits an acceptance but some improvements are needed as discussed below.
One main issue which can be seen as a weakness of this paper is the safety criteria which is formulated as a procedural definition based on the procedure with which decidability is established. Essentially, a quad system is safe iff its dchase does not contain two different blank nodes whose origincontext is the same such that one is a descendant of the other. That is, the dchase would always terminate because dchase never performs a recursive generation of blank nodes using other blank nodes with the same origincontext. Then, the author employed dchase itself as a decision procedure for query answering over safe quad system. On a first glance, this would seem trivial since one can almost say that this is the same as saying that reasoning over a language that satisfies a conditon C is decidable where C is the statement "the reasoning procedure terminates". I think the author should clarify in the paper whether this is indeed trivial. Moreover, the author should also clarify that deciding safety is possibly not easy since it is done using the tripleexponential dchase procedure itself, and this would distinguish this framework from other earlier approaches using conditions on dependency graph which, I believe, are easier to check. It would also be much more useful if there is a discussion that clarify whether a safety criteria that is independent of the dchase procedure is very difficult or impossible to obtain.
I also suggest the author to include a discussion on the implication of the safety criteria from user's point of view. More precisely, if I am a user who wishes to model some domain knowledge using this contextualized framework, then I would most likely not know whether my knowledge base is safe or not in advance. Using the proposed idea from the author, the (only?) way to check whether my knowledge base is safe or not is by running dchase on it and there is no simpler guidance that I can use while developing the knowledge base to avoid unsafety in the first place.
On the other hand, I would also say that making the definition procedural like above does not necessarily mean that everything else does not have any merit because the author was able to obtain the remaining, more precise, complexity results (not just decidability). The author should also make a more pointed discussion on this aspect.
The next issue is regarding the complexity of the Hornfragment. Isn't it the case that this fragment can be directly translated into Datalog (ground facts from the triples and rules from the bridge rules)? If yes, I suspect that this translation is sufficient to derive ExpTimecompleteness of combined complexity and PTimecompleteness of data complexity without going through analysis on dchase; (the author cited the relevant paper from Dantsin, etal, but only for ExpTimehardness of combined complexity). If not, it would be better if the author clarifies why using only such a translation would not work.
Another issue is related to inconsistency handling. From the introduction, the author seemed to alluded that with his framework, knowledge can be fed into separate reasoner (based on context) so that it prevents inconsistencies which may happen if the reasoning is done on the union of all triples in all the contexts. First of all, "to prevent incosistency" might not be a correct term here (inconsistency is a property of the knowledge base, not the reasoning approach). I would think it is more appropriate to say "to ensure reasoning can still be performed although union of all triples is inconsistent". Moreover, there is no section in the paper that addresses this issue more precisely. From the presentation, it is rather difficult to see whether dchase procedure actually handles this.
Typo/Presentation:
Section 4, p13, right column, the paragraph between the statements about condition of unSafeTest(Q,R) and R^{safe}(Q_C) should be rewritten using shorter sentences (i.e., avoid using a long sentence with too many subsentence which makes it difficult to read).
Section 6, p16, right column, in the 2nd paragraph with heading "Data Integration"
"... employs the super weakacyclicity to ensure decidability. It can straightforwardly noted that ..." ===> It can be straightforwardly noted that
"... This is because when a quadsystem is unsafe, requires skolem blanknode ... " ===> This is because when a quadsystem is unsafe, it requires Skolem blanknode/
