Review Comment:
Ontologymediated query answering over temporal and inconsistent data
Contents

This article sonsider the issue of answering queries, formulated in a
temporal logic on top of conjunctive queries, on (possibly infinite)
sequences of knowledge bases, K_0, K_1,... where elements of the
sequence may be inconsistent. The temporal logic is linear time logic
(LTL) with a variety of operators looking to the future and the past;
the knowledge bases K_i= consist of a taxonomy T and
assertions (facts) A_i from a description logic (DL), which is either
DLLite_R or EL_\bot; these are prominent lowcomplexity description
logics related to OWL profiles.
Inconsistency of K_i is assumed to be due to the factual part A_i,
which may be tolerated by resorting to repairs for reasoning, i.e., to
subsets A'_i of A_i that restore consistency. To this end, according
to a regime, selected repairs are used for query answering.
The paper thus studies a setting that combines two aspects that have
been considered in the literature before: (1) temporal query answering
(with no special attention to inconsistency) and (2)
inconsistencytolerant reasoning for "atemporal" (ordinary) DL
knowledge bases. Specifically, it considers the widely used (a) AR
semantics, in which all inclusionmaximal subsets A'_i of A_i are
considered; (b) IAR semantics, in which the intersection of all
inclusionmaximal subsets A'_i is considered; and (c) brave
semantics, where some arbitrary inclusionmaximal subset A'_i is
considered to sufficient for deriving the query.
The main part of the paper is devoted to analyze and characterize the
computational complexity of answering Boolean temporal conjunctive
queries over sequences K_0,K_1, ... of knowledge bases for the three
semantics (a)(c) above, both in the setting of data complexity (where
just the data varies) and the combined complexity (general case). The
study considers restrictions on the queries, more specifically whether
negation is allowed or not, and on the dynamic nature of concepts and
roles, viz. whether they are rigid or susceptible to change. Furthermore,
the paper considers properties and reduction techniques that might be
exploited for practical implementations of query answering (e.g., to
eliminate rigid concepts and roles for query answering).
The authors report exact complexity characterizations for almost all
of the many cases considered, with very few exceptions. They reveal a
rich landscape of complexity from tractable (in few cases for IAR
semantics, under data complexity) to intractable up to conexptime
complete problems; as shown in several cases, inconsistency tolerance
does not increase the worst case complexity, and excluding negation
might lead to significant savings (unfortunately, perhaps not in data
complexity).
Evaluation

The results of this paper complement and extend previous results on
temporal and inconsistencytolerant query answering and are a
significant contribution to the literature. While the focus of the
paper is on temporal reasoning as such and less on stream reasoning in
the realm of dropping data, they provide a solid foundation as a
starting point for the development of suitable algorithms.
The derivation of the results is based on common techniques and
methods, which however are as in the case of the proof of Proposition
8.3 (type elimination to obtain a polynomial time algorithm) show
mastery in its use.
The paper is wellwritten and provides an ample exposition of
background and context, and puts the contributions in perspective. It
is clearly a research and theory oriented article, but I believe that
the results are accessible to a broader audience.
The technical results are formally stated and furnished with detailed
proofs or proof sketches; it appears from them that the results as
such are correct.
Overall, this is very informative and good article that should be
published. Below are some minor questions and comments which the
author mat consider in a final version.
Minor comments and corrections

page 2: "[19,20]. Ontologybased approaches for
stream reasoning often" Starting a new paragraph here would be
suggestive.
page 3: with respect of three > with respect to three
the achieved complexity results > the complexity results obtained.
page 4: the notation [[ 0,n]] for an interval is unusual; why no use
the common notation [0,n] ?
page 5: "We impose the constraint that the past operators..." please
say at this point why, or give a pointer to where this will be discussed.
page 7: "the impact rigid predicates can have on repairs." Adding
*which* might make the reading more natural.
page 8, proof of Prop. 3.5: Towards the end, you conclude that a^{I_i}
= a^{I_j} holds. However, it is not clear that the unique name
assumption by itself ensures that a is interpreted canonically (unless
you use Herbrand interpretation; perhaps I miss something.
page 8, "...TCQs that are rooted." Please briefly explain what this
means.
page 10, "Entailment under IAR semantics." Please explain or give a
hint why this procedure is useful, as this becomes apparent to the nonexpert only
later; as it stands, one would think it is not a good idea to compute
all the minimal inconsistent sets, as in general there can be clearly
exponentially many such sets.
page 11: axiom that involve two nonrigid > axiom that involves two nonrigid
"checking of L KBs" it would be better to use hyphen and
write "LKBs" here and in the rest of the paper.
page 13: proof of Proposition 6.9.: Please explain the intuition
behind the construction in the hardness parts, as this will help the
reader to grasp the idea faster. The formal argument that the
construction works may then be entirely left for the appendix; or
claimes are formulated that are proved in the appendix. By the way, it
is unclear what B_{3i} is.
page 14: proof of Proposition 6.10: "such that each x_j has either
only Pos or only Neg incoming edges" please explain what you mean with
"edges" (this might not be clear to nonexperts).
regarding the open case where no rigid concepts and roles do exist:
perhaps you can express an intuition or your expectation whether
this is still NPhard or gets tractable. It might be worthwhile to
link this to the case where only negationfree queries are
considered (where you show tractability) and explain, e.g. on an example,
why a similar method could not be extended to the case with
negation.
page 15, 16: Theorem 7.4, Proposition 7.6: Perhaps the details of the
proof an be outsourced to the appendix, and only the case discussed
that would not be routine. This may increase readability.
page 17: before Proposition 7.7: "." should be added.
Theorem 7.8: the two different cases should be separated using
"respectively," not to raise the impression that both properties
have to apply at the same time.
page 19: nondetermistic > nondeterministic
it would be helpful to illustrate the notion of propositional
abstraction on a simple example, so that a broader range of readers
can better grasp it.
page 20: "verification of Condition 3 or Condition 2 is linear in n"
it is not clear why this is linear in n, the number of time steps;
rather, the number of possible sets (there are polynomially many) is
relevant? What kind of data structures would be used?
page 22: the original algorithms omits > the original algorithm omits
"We say a PI is applied" if I am not mistaken, "PI" has not
been formally introduced.
page 23:
"then let a = x_{a'P_1,...,P_l}^{i_1...i_l}" this is confusing,
rather one should say that a must be of this form, and continue
with this
page 24: we break the proof > we split the proof (or "we divide
the proof")
"we obtain that \exists P^ (resp. \exists P^_2 ) is unsatisfiable"
please detail what you mean (as this might be not known the
nonexperts).
page 26: after Proposition 9.12, you write: "This is a remarkable
result, ..." However, the results seems not to be difficult to prove,
and it is also intuitive. So why should one call this "remarkable"?
page 28: for brave semantics which are relevant > for brave
semantics which is relevant
page 29: In [3], "C.F. Beckmann" should be "C. Folie"
page 30: Perhaps "omitted proofs" should be reformulated, as in some
cases you present complete versions of proofs for which
already detailed sketches were given (e.g., for Proposition
6.9). In order to avoid replication, you may consider to add
in the appendix the missing parts or make the informal claims
formal and prove them.
