Review Comment:
The submission addresses the problem of partitioning the assertional part (ABox) of ontologies into smaller fragments that contain all the information necessary for reasoning. The problem has been studied before and is certainly relevant to the journal.
The presented approach, however, appears not to be entirely correct.
1. The definition of an equalityfree ontology requires that K \not\models a \approx b for all **individuals in K**. The authors then claim that "deduction of a property assertion between different named individuals in A should not be affected by their class assertions except via individual equality". Taking into account that the ontology language has number restrictions, the claim (if I interpret it correctly) is untrue: consider
R(a,b)
R <= S
A <= \exists P.\top
P <= S
A <= \leq 1 S.\top
It then only follows that S(a,b). If, however, we add A(a) to the ABox then we will also derive P(a,b) simply because both R and P are subroles of functional S.
Propositions 4.2 and 4.3 are based on the aforementioned claim and so, appear to be incorrect (tableau algorithms make no distinction between ABox individuals and special individuals introduced to satisfy the existential quantifiers).
2. Condition (3) cannot be sufficient because of the following example: let the TBox contain
A <= \forall R.A
and consider an ABox of the form
R(a_1,a_2), R(a_2,a_3),\dots, R(a_{n1}, a_n).
Then none of the ABox individuals is an instance of A (in every model). If, however, you add A(a_1) to the ABox, then **all** a_i will be instances of A in every model. Thus, the instance checking problem is not "local" (which also explains its Phardness in data complexity even in tractable languages like EL).
To sum up, I cannot see how the presented approach can work for SHIQ. It is no coincidence that the cited work (Wandelt and Moeller, 2012) deals only with SHI (no number restrictions resolves item 1 above) and looks at paths of ABox individuals (rather than the starlike configurations of in the submission, item 2). On the other hand, the presented approach might work perfectly for DLLite.
So, the submission cannot be accepted in the present form.
COMMENTS
 The use of "class" and "role is somewhat inconsistent: it is concepts and roles in DLs, and classes and properties in OWL.
 The claim that a \approx b is not supported in SHIQ is strange  it can be added without any change in the complexity (simply rename all b's into a's and remove the equality). The explanation (nominals are illegal in SHIQ) is stranger still (and perhaps it is related to item 1 above).
 The role of justified entailment is not entirely clear in the submission.
Some typos and minor remarks are listed below.
abstract: solving the tractability problem sounds very much like giving an affirmative answer to P v NP
p 1, par 1: terminologies are not "concepts and roles"  the sentence needs rephrasing
p 2, par 1: "knowledge data" is a strange term
p 2, par 2: "up to exponential worstcase complexity" is imprecise because OWL 2 is based on SROIQ, which is N2ExpTimecomplete
p 2, par 3: "where although" is ungrammatical
p 3, line 2: there are three options in the preceding sentence and it is not quite clear what "the latter" refers to
p 3, par 2: "a closure of all facts" is a new term, which is not defined
p 3, item 1: "sound and complete facts" also needs clarification
p 4, par 1: "SHIQ is extended from ALC" sounds strange
p 4: "\sqsusbeteq is reflexive and transitive" is a strong assumption
p 4, Def 2.3: tuple > pair
p 5, Def 2.4: \Delta is nonempty and is referred to as the domain (not "referred to as a nonempty domain")
p 5, above Def 2.5: "at least one contradiction" needs clarifying
p 5, after Def 2.6: something else is usually understood by the classification problem (computing the complete lattice of concepts and roles)
p 6, Def 2.9: is said to be in simple form
p 7, after Def 3.2: a criter*ion* (and a criterion is by definition a necessary and sufficient condition, so there is no need to write that)
p 9, footnote 1: the operation \circ is not allowed in TBox axioms (according to Definition 2.1 and below the sentences below it)
p 11, line 2: "the set of decidable and distinct Rneighbors"  what exactly is a decidable neighbor?
p 16, line 1: author*s*
p 17, Def 6.1: font in (T,A) and , instead of \cup in line 4
p 19: Java *h*eap and \mathcal in ALF
p 20, last par: *more* than 90%
p 24, Table 4: brackets around h and s should be removed
p 24: the claim that modular resigning can change the complexity "from exponential to (approximately) polynomial" is rather bold
