Review Comment:
### Overview:
This paper deals with the DISPONTE framework for probabilistic description logics  the framework itself was introduced by the authors in previous work  that adopts the distribution semantics, where axioms are annotated with probability values and an independence assumption is made. The main contributions of the paper are the presentation of the BUNDLE algorithm for query answering over DISPONTE KBs and a brief experimental evaluation of said algorithm, though versions of these were already presented in the RR 2013 version of this article.
### Main Comments:
I have several concerns with the current version of this manuscript, which are mainly related with (1) how the authors portray the relationship between their work and the related formalisms they refer to, and (2) the amount of new material present in this extended version wrt the conference (RR 2013) paper.
(1) In Section 7 (Related Work), the authors present a discussion of an extensive body of related work. However, in my opinion they fail to adequately portray the relationship between their work and some of the references. For instance, on Page 18, the second to last paragraph ("DISPONTE differs from Heinsohn (1994) ...") states that DISPONTE "minimally extends the language and provides a unified framework for representing different types of probabilistic knowledge: from assertional to terminological knowledge". It's not at all clear why minimally extending the language is an important feature; regarding the other characteristic, the authors themselves state that there are other works that allow both assertional and terminological knowledge to be probabilistic. The comparison with these works is therefore quite weak.
Continuing in this vein, though perhaps more serious in nature, the comparison with Nilsson's probabilistic logic is flawed. The authors refer to the fact that in the Nilsson approach, there is no independence assumption being made and that therefore probabilistic conclusions must be weaker. Indeed, independence assumptions are not made in this logic  however, ground instances can be added to the KB in order to express that probabilistic independence holds for these cases. Consider, for instance:
p(a): [0.4,0.4]
p(b): [0.25.0.25]
p(a) ^ p(b): [0.1,0.1]
Atoms p(a) and p(b) are therefore constrained to be independent.
Though this is perhaps not an elegant way to express things, it seems as appropriate as the authors' claim that their framework can handle situations in which independence does not hold. With respect to this last point, the authors state that their approach can do so "possibly introducing new atoms if needed"  this statement deserves a more detailed explanation (perhaps an example), including an estimate of the growth of the KB due to these extra atoms. Though the reference to the fact that BNs can be encoded with PLPs under the distribution semantics is appropriate (since BNs are known to be able to encode any probability distribution), I don't see the relevance of the other references, since it is not clear if they are making independence assumptions or not.
Finally (for this point), the comment about the intervals vs. point probabilities is also inadequate as it stands, since interval probabilities generalize point probabilities, so the formalism is not forced to use the full generality of the approach.
As a final point in the matter of related work, the last paragraph of the section deals with the approaches by d'Amato et al. (2008) and Gottlob et al. (2011); the authors claim that DISPONTE provides a "tighter" integration of probability in ontologies as we do not rely on an additional graphical model". According to the authors' own account, these papers appear to generalize DISPONTE by allowing annotations to refer to a probabilistic model that is more general than the one they use (one Boolean random variable per axiom, under the independence assumption). The fact that DISPONTE's stricter assumptions allows axioms to directly be annotated with probabilities is really of no consequence to the tightness of the integration. In relation to this, the comment on tightness brought to mind some related work work on tightly integrated probabilistic ontologies by some of the same authors that should probably be included when talking about tightness of integration.
(2) Regarding the amount of new material presented in this extended version, it is not clear to me that it is significantly enough, since the main framework, inference mechanisms, BUNDLE algorithm, and experiments are aleady included in the conference paper (the experiments are different, however). In an eventual revision, please include a pointbypoint description of what's new in the journal version to avoid confusion in this regard.
### Other comments:
The experiments section could be expanded to make it more comprehensive. For instance, a study on data complexity (where the ABox is varied and the TBox is fixed) seems to be a most important evaluation that is not present. In real world settings, it is often that case that the largest portions of ontological KBs are the ABoxes, so this would be more relevant than the experiments performed for running time.
In Section 4, why to the authors include proofs of theorems that they attribute to other authors?
### Minor issues and typos:
 Please include QED marks (white boxes) to mark the end of proofs.
 Page 17: "hundred of thousand" > "hundreds of thousands"
 Page 18: what does "upper ontology" mean?
 Page 19: "considers a probabilistic" > "consider a probabilistic"
 Page 22: "In Table 2 we reported" > "In Table 2 we report"

Comments