A Pattern for Periodic Intervals

A pattern for periodic non-convex intervals will make a worthwhile contribution, and a good start has been made. I have a few critiques, as follows:

• The paper would greatly benefit by at least one example, written in turtle, of an instance of a Periodic Interval.

• In the second bullet point under Section 3, the period of the interval “every Tuesday” is stated to be 6 days – shouldn’t that be 7 days? It seems more economical to refer to the period between starts than the actual gap, and corresponds with our commonplace phrasing wherein “every week” means every 7 days.

• I understand that ODPs should be distinct cases and small (as this is), but a periodic interval is only one case of a non-convex interval, and I would like to hear the authors’ views on other, “sibling” patterns so to speak. In other words to position it in a potential set of patterns that includes irregular periods and gaps.

• The example of I3 in Figure 1 would be a bit clearer if the gap and the interval were not identical; what is shown is an unusual case, e.g. for 2 days, every 4 days.

• Another way this pattern could be better contextualized is to discuss, even briefly, what some of the operators are we might want to compute against Periodic Intervals with. It would be good to know if there is some work under way or planned to develop reasoning software to interpret Periodic intervals. In other words, what is the necessary path to practical application?

This paper describes an ontology design pattern that extends the OWL-Time ontology with periodic intervals. While I am sure such a pattern would be useful in a number of applications, the authors do not make very convincing arguments that this is the case. The paper gives some real-world examples (e.g., classes taking place every Monday at a given time, or weekly TV shows), but it is not illustrated how existing ontologies would make use of this pattern.

While an OWL formalization is provided, the design choices made are not discussed or justified at all. One of these choices is the introduction of the hasPeriod and hasIntervalDurationPerPeriod properties, which are not quite intuitive for me and also not well illustrated in figure 2.

The paper suffers from many typos and grammatical issues, up to a point where some ideas of the relatively straight-forward ideas presented become hard to understand (e.g., on page 1: 'This type of time periods occurs naturally among systems requirement description.' I am not sure what the authors refer to here).

Moreover, some of the terms that would require some explanation are not explained at all, such as the notion of maximal convex subintervals introduced in the abstract (which is not even mentioned again in the remainder of the article).

In conclusion, this paper needs substantial revisions both in terms of the main ideas and the presentation.

This is a neat piece of work, which proposes a compact solution to a genuine problem. The proposal builds well on existing work. It is implied (through not fully demonstrated) that the solution has been effectively implemented.

However, I have a few concerns:

1. The most significant problem is that term 'period' is used to refer to only the gap between component intervals. This is inconsistent with the standard use of 'period', which covers a _complete_cycle_ i.e. a period is both the interval and gap! (see for example http://en.wikipedia.org/wiki/Periodic_function ). What the authors have called 'period' is actually 'duration of gap between (sub-)intervals'. In one sense this is only a minor issue of terminology, but it puts the proposed ontology outside all conventional treatments of periodic behaviour. Because of the strong precedent, I would suggest retaining the terminology, but
- correct the definitions (in section 2, paragraph 1)
- correct the examples (in section 3 requirement 2, it should read "What is the period of the interval 'every Tuesday of 2010'? Answer: 7 days"
With regard to the last: any pattern that recurs on a weekly cycle has a period of one week.

2. The title calls the work a 'pattern', and this terminology is repeated a number of times in the text. However, it does not appear to have the characteristics of a pattern, as it does not provide a solution to be applied recurrently (see, for example, Falbo et al. Ontology Patterns: Clarifying Concepts and Terminology, http://www.stlab.istc.cnr.it/documents/WOP2013/LongPapers/paper11.pdf ). Since the work is a small extension to an existing OWL ontology, it might better be called 'An ontology ...' or 'An ontology extension ...' or 'An extension of a standard ontology ...'.

Some other more minor issues:

- Section 1, paragraph 2, sentence 5 '... non-convex intervals are those that use time units in a repetitive way or refer to recurring periods.' Does 'repetitive' allow for irregular sequences of intervals? In common english repetitive is almost synonymous with 'periodic'. It might be better to make it clear that the general case covers both periodic and aperiodic sequences of intervals, though only the latter in considered in this paper.

- Figure 2 is incorrect in showing owl-time:DurationDescription as a subclass of owl-time:Interval - it is not modelled that way in the W3C Draft.

- In Section 3 a number of examples applications are given in words. It would be helpful to the reader to see example instances in code (at the moment we only have the class and property axioms, but no individuals).

- In the review of related work, it would be appropriate to also mention
- gridded data, which is a multi-dimensional generalization of periodic data
- ISO 8601 allows for denoting contiguous periodic intervals, e.g. R5/2008-03-01/P1Y2M, but not non-contiguous sequences.

This paper suggests a pattern for periodic intervals. The idea is very good: indeed it makes sense to model
weekdays, and other recurring time intervals. The pattern itself looks also promising. Authors define the parts of the periodic patterns to have "same duration & same gaps in between". This sounds an interesting approach and can clearly be applied to many periodic patterns.

My concern about this paper is the lack of clear examples of the use of the pattern. The Section 3 lists use cases but I wonder if the pattern can really be used to model all of them. For instance the first of them (Logic programming course). How will you model that it happens during the second semester? Perhaps the modeling is straightforward but an example (as a graph format or as turtle) would convince a reader more.

For this I propose the authors to do a major revision by showing via at least few examples of how to model actual cases (a few simple ones and a few complex ones) with the pattern. All in all I find this paper idea very good, it just needs to be better and more convincingly communicated / evaluated.

Minor details:
- the writing of the paper needs to be improved.
- For instance the last sentence of the 2nd paragraph has a strange "it is need to represent". Did you mean "it is needed to represent.."? Anyway, please rephrase that sentence to be more clear.
- 2nd page, first paragraph "ontology designed pattern" -> "ontology design pattern"?
- 2nd page, rephrase the sentence "…they are equally separated in time ..."
- 2nd page, 2 section make the reference to "this pattern" more clear (after reading the paper it is of course clear)
- 3rd page, "non-convex interval" -> "non-convex intervals"
- 3rd page, "this type of requirements" -> "these types of requirements"
- 4th page, "snipped" -> "snippet"?
- 5th page: the related modeling practices section looks somewhat superficial and would benefit of references to literature about modeling of time.