Paraconsistent OWL and Related Logics
Review 1 by anonymous reviewer
I've checked the new version of the paper; it has been greatly improved with several examples, so I am now satisfied.
The reviews below are for the second round review, which resulted in an accept with minor revisions. The current manuscript is the subsequent revised submission.
Review 1 by anonymous reviewer
The authors addressed my issues and from my point of view the paper is fine now.
Review 2 by anonymous reviewer
Recommendation: New revision
The initial review raised several issues; in the following, each issue will be
revisited, along with a discussion of how the authors addressed them:
1) Confusion over what material is new w.r.t. other related publications:
The authors provided an adequate description of what is new in their response, and
appear to have updated the manuscript accordingly.
2) Empirical evaluation:
The small changes requested regarding clarifications were addressed satisfactorily.
The authors did not agree with the need to expand the content of this section, and offered
to remove the section completely. Though this is ultimately up to the authors, doing so would
perhaps compromise the amount of new material.
3) Examples and readability:
In their response, the authors claim that examples are short because this is a theoretical
paper and they are mainly used to show that properties do not hold. I would argue that the
fact that it is a theoretical paper actually means that examples are even more important, since
they help along the discussion and allow the reader to ground the more abstract parts.
Though whether or not to devise a running example (as originally suggested) is up to the authors,
revising the current ones (adding comments on what the example is conveying) and adding at least
one or two that focus on illustrating concepts (not using p, q, etc) is necessary to motivate the
presentation and make the paper readable by people who are not specialists in the topic.
4) Related work:
The discussion has been revised and extended, and is now greatly improved.
5) Other minor comments:
I still believe that the word "argument" as used in the manuscript is confusing; the
authors claim that other words like "conditional" or "implication" would be worse since
they may be confused by formal statements of a logic; however, the authors are doing
just that. The word "argument" could be confused with its use in the area of Argumentation
(as a dialectical form of reasoning, such as in the work of Anthony Hunter et al., and similar in
spirit to the work of Jaskowski now being cited by the authors). I may be completely misunderstanding
the authors' use of the term, but if this is the case, it only reinforces my point.
Apart from this, the other original minor comments have all apparently been adequately addressed.
I recommend a second revision in order to address point (3) above, i.e., commenting on the existing
examples and adding one or two illustrative ones.
The reviews below are for the original submission.
Review 1 by anonymous reviewer
The paper discusses paracosnistent OWL 2 and their profiles, based on Belnap’s four-valued logic.
The paper is well-written, self-contained and pleasant to read. While it appears as a summary of previous papers, I still think that it is worthwhile to publish it.
I’ve only some concerns on some Propositions that I think do not hold: specifically Propositions 33, 34, 36. However, they are of marginal interest. Anyway, in case I’m wrong, I'm sorry. In that case, counter argument my counter-examples. In case I’m right, just drop these propositions and place the counter-examples as examples.
Other minor corrections are in the annotated pdf as attachment.
I recommend: Accept with minor revision and I would like to see the author's revision.
The reviewer provided an annotated PDF document containing more details and corrections.
Review 2 by anonymous reviewer
Paper Title: Paraconsistent OWL and Related Logics
Auhors: Frederick Maier, Yue Ma, and Pascal Hitzler
Recommendation: Accept after major revision
This article starts out by arguing that reasoning over inconsistent OWL ontologies
is impossible due to the principle of explosion (every sentence in the language can be
derived from an inconsistent ontology). The approach adopted to remedy this is to extend
OWL DL and related logics to manage four truth values instead of the two classical ones.
Important results are shown to hold in the resulting logics, such as their soundness
relative to their classical variants, as well as consequence preservation. Finally, an
experimental evaluation is presented.
The paper is well written, well organized, and contains important results for reasoning
with inconsistent ontologies. My recommendation is motivated by two main concerns:
1) The material in the paper is heavily based on the past work of the authors; it is mentioned
at the end of Section 1 (and in other places as well) that it is a longer version of  and ,
and these are in turn based on  through ;  is also mentioned elsewhere as containing
some of the results described in this paper.
After carefully looking through these references, I was left wondering exactly what material
presented here is new. While it is clear that some parts are new, the novelty of others is
difficult to determine. Furthermore, some comments are rather confusing; an example of this is
the comment regarding reference  at the beginning of Section 6, which says that "This was a
point overlooked in the earlier work on SROIQ4 , and we discuss it here.". However, the
subsequent discussion was already present in .
Another such example can be found in Section 10, Page 21, where it says:
"SROIQ4 was first presented in , though there it lacks role chains, role assertions, and
\exists R.Self..."; again, these elements are included in the material in .
As part of the revision, the authors should address all such occurrences to avoid this kind of
Finally, could the authors please provide a detailed list of what material is new in this manuscript?
2) The empirical evaluation is somewhat weak for a journal paper. First of all, the authors
don't discuss any of the details about how the synthetic ontologies were created; please provide a
description of the process devised to do this so the reader has a better idea of how to interpret
The other concern is regarding the experiments themselves, which only measure the
time taken to classify the ontologies (which I assume means to infer the consistency and
properties such as superclasses and equivalence between classes; please clarify this in the
manuscript). I would expect to see a more complete set of experiments, with parameter variations
for the synthetic ontologies and some query answering tasks as well. The number of varied
parameters need not be great; choosing the two or three that the authors consider to have the most impact
on the running time for the task in question should be enough to convey a better picture than
the current experiments.
- Though the presentation and readability of the paper are good, the examples are quite short and
almost no discussion is provided. Perhaps adding a running example, with adequate discussion, that
ties together the presentation would help in this respect. Otherwise, the existing examples should
be expanded to address this.
- The discussion of related work focuses only on paraconsistent approaches to dealing with
inconsistency. There are other approaches in the Data Management literature that should at
least be mentioned here for completeness. These include the following, which are just representatives
of some alternative approaches; though some refer to relational databases or logical knowledge bases,
they are clearly related to the present work through well-known translations.
a) The knowledge base is regarded as a departure from some correct, consistent version. These
approaches prescribe changes to be applied in order to arrive at a "better" version. Some examples:
Grant and Hunter: "Measuring the Good and the Bad in Inconsistent Information". Proceedings of
Alchourron et al.: "On the logic of theory change: partial meet contraction and
revision functions". Journal of Symbolic Logic, 1985.
Falappa et al.: "On the evolving relation between Belief Revision
and Argumentation". Knowledge Engineering Review, 2011.
Reiter: "A Logic for Default Reasoning". Artificial Intelligence, 1980.
Martinez et al.: "Inconsistency Management Policies". Proceedings of KR 2008.
b) The knowledge base is considered to be an overspecified set of constraints, and "repairs" are
considered to be maximally consistent subsets of such constraints:
Arenas et al.: "Consistent Query Answers in Inconsistent Databases". Proceedings of PODS 1999.
Lembo et al.: "Inconsistency-tolerant Semantics for Description Logics". Proceedings of RR 2010.
Commenting on these alternatives would add to the manuscript's completeness.
Minor errors and typos:
- The use of the word "argument" on Page 1, Col.2 is not very clear. Perhaps "conditional"
or "implication" would be better.
- Page 4, Col. 1: "Below P and Q are ..." --> "Below, P and Q are ..."
- Awkward spacing in some formulas, see for instance the top of Col. 2 on Page 4.
There are other cases as well, especially with the = sign.
- In Def. 4, the composition operator is used without prior introduction.
- Page 14, right before Example 37: It says that "tractability is affected"; is it possible to
provide any insight on how much it is affected?
- Proposition 48 should refer to Table 9, otherwise H1, ... H4, B1, ..., B3 lacks context.
- Page 20, Col. 1: The phrase "This may be used..." could be rephrased to something like
"This argument supports the use of paraconsistent logics, and dispels the general doubts
that sometimes occur around these approaches.".
- Page 20, Col. 2:
"... the ALC fragment of SROIQ4 appears to identical to the logic described in ),
which are distinct from Patel-Schneider's ..." -->
"... the ALC fragment of SROIQ4 appears to be identical to the logic described in ),
which are distinct from those of Patel-Schneider's ...".
- Page 21, Col. 1: "... for translating his first order logic into FOL ..." --> (?)
"... for translating his logic into FOL ..."