Ontology of Units of Measure and Related Concepts

Paper Title: 
Ontology of Units of Measure and Related Concepts
Hajo Rijgersberg, Mark van Assem and Jan Top
This paper describes the Ontology of Units of Measure and Related Concepts (OM), an OWL ontology of the domain of quantities and units of measure. OM enables to make quantitative research data more explicit, so that data can be integrated, verified, repoduced, etcetera. The various options for modelling the domain are discussed. For example, physical quantities can be modeled either as classes, instances or properties. The design choices made are based on use cases from our own projects and general experience in the field. The use cases have been implemented as tools and web services. OM is compared to QUDT, another active effort for an OWL model in this domain. We note possibilities for integration of these efforts. We also discuss the role OWL plays in our approach.
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Manuscript has been accepted for publication in the fourth round. It was accepted with minor revision in round three, following a previous accept with minor revision. The third round reviews are below, followed by the reviews for second and initial rounds.

Third round reviews:

Review 1 by Simon Scheider

The paper is in principle fit for publication. But I still have some minor issues, some of which reappear because they have not been addressed carefully enough in the new version. There is also one issue about exact copy of formulations, I will return to this at the bottom.

- Regarding measurement theory: I see the argument to use the established wording of practicioners, and I am also not insisting on Suppes' terminology. However, this doesn't mean that terms should be used in an ambiguous fashion that ignores useful distinctions. For example, "Ratio scales such as the Kelvin scale..." (p. 3) "We have based it [OM] on the standard sources used by physicists,..." "What is called a scale type in measurement theory is a scale in the technical standards" (p.2) The first cited sentence implies that "scales" are exactly the scales of measurement theory (i.e. your units of measurement). The other two sentences imply that "scales" are rather scale types like ratio, nominal a.s.o. Please decide on one kind of usage. This reappears at other places in the paper. Btw., it shows how useful the clear distinctions in measurement theory are, since this gets easily confused. And the fact that this is also confused in technical standards is a good argument against sticking to the standards.

- Why do essential terms of OM, such as quantity kinds (and also scales and scale types) not reappear in the overview in Fig.1 ?

- Literature is still very meager.

- The authors do not discuss what it means for OM users that OM is static and how dynamics can be accounted for. This is not an issue with DOLCE integration on p. 10 (it only shows up there), but a primary design decision of OM, which needs to be addressed independently at a central place. The authors refer on p. 10 to some other ontology OQR without reference or explanation.

- I noticed that the authors addressed some of the issues in the last round of review by copying exact formulations from the reviewer texts. For example, "Dolce qualities include all kinds of observable properties, also quantitatively measurable ones" (p.10, bottom) "Dolce qualities are temporally indexed, because their values can change over time" (p. 10) "but whether there is a scale that represents the values of a given Dolce quality" p. 10. If this is an invitation to become co-author of the paper, I must reject because I am a reviewer ;). Kidding aside: Please use your own formulation, which will require exploring the underlying ideas on your own.

Review 2 by Michael Compton

The authors have addressed all my previous concerns. I consider the paper ready for publication, excepting two small issues.

Firstly, at the top of page 10 you state "under OWL semantics OM's transitive generalization" - however you mean QUDT's generalization, don't you.

The only remaining issue is that the text uses om:commonly_used_unit, but this seems to be the om-1.7 term, while om-1.8 uses om:unit_of_measure. It will probably be fine to still refer to the common units throughout the text, but you should indicate that that is the intention of om:unit_of_measure.

As a side comment on this, you have updated the text (as per my previous review) on OWL2 and included a discussion on punning, which is appropriate given how om:unit_of_measure is used. It did make me wonder, however, about UC2 and for example om:Length, which has specified a number of common units. Your tool suggests common units if a user has indicated that the application area is astronomy, does it do the same if the user indicates that the measurement is a Breadth or Radius?

I ask because punning allows no reasoning across the multiple uses of a name (as you already point out), hence the om:unit_of_measure axioms for Length are not implied for om:Breadth, etc., meaning that your notion of commonly used units doesn't propagate down the concept hierarchy. This is easily enough simulated by taking the om:unit_of_measure for a Quantity as the union of that for all its super-Quantities, but this is reasoning done outside OWL (or by simulating it using object properties for the role hierarchy and role composition).

If your tool already does this sort of reasoning then you should update Section 6 (OWL DL compatibility) which argues that reasoning is not required for om:unit_of_measure. If however that text referred only to application areas, then no update is needed and take this only as a side comment.

Review 3 by anonymous reviewer

just few comments on the comparison with DOLCE

p.10 "The class Quality in DOLCE can not be de- fined as a superclass of OM class om:Quantity just like that; there are clear differences between these two classes"

have you considered the idea to map om:Quantity to the class Region in DOLCE?

p.10 "Firstly, DOLCE qualities are temporally indexed because their value can change over time, whereas the relation om:phenomenon is binary and thus "static" for a phenomenon. In our view, time de- pence should be expressed as a relation between mul- tiple quantities, time being one of them. "

actually "time" is a quality in DOLCE, namely Temporal Location

p.10 "A second differ- ence between OM and DOLCE is that DOLCE qual- ities include all kinds of observable properties, also
quantitatively measurable ones. The essential point is not the distinction between quantitative and qualitative concepts, but whether there is a scale that represents the values of a given DOLCE quality [8]. Qualities can be grouped together in DOLCE through spaces. Spaces can be constructed taking into account units of mea- surement. These kinds of spaces have a complex struc- ture because a metric is needed, but in principle they can be represented in DOLCE. So, relating quantities in OM and qualities in DOLCE is not straightforward and must be investigated."

It seems to me that you can conclude that DOLCE is more general because, differently from OM, it can represent both qualitative and quantitative knowledge

p.10 " What certainly can be related to DOLCE is a phenomenon such as the class Fruit in Figure 2 by making it a subclass of Endurant in that ontology."

this can be a very tricky point if we take into account time
if an apple changes color between t1 and t2, how many entities there are? In DOLCE we have one single endurant, the apple, and its color that change position in the color space from t1 and t1. But, following four dimensionalism, it is possible to consider that what we are measuring at t1 and t2 are two different entities, two different temporal slices. In this case, the apple is not an endurant, but a perdurant composed by all these temporal slices

Second round reviews:

Review 1 by Simon Scheider

The paper proposes an ontology of units of measure. The authors discuss the OWL design choices made based on use case requirements. Most salient features of the approach include: the systematic treatment of prefixes for expressing (sub)multiples; accouning for synonymous labels and application areas; formal checks of quantity formulas and units allowable for a quantity; as well as specification of commonly used units.

The paper is well written and its ontological choices are convincingly argued for based on use cases. The ontology seems already quite robust and mature. For example, it accounts for synonymous and improper use of terms and integrates many well known former attempts.

I consider the paper fit for publication, provided that the following issues are somehow addressed by the authors: 1) improper use of some measurement theoretic concepts and terminology, and 2) an open question regarding foundational concepts relating to DOLCE and 3) a quite meager set of references to relevant literature. In detail:

1) The paper shows a quite common but improper use of some terms like "measurement scale" and "unit of measurement". In the standard volume about measurement theory (Suppes et al. "Foundations of Measurement", for a more condensed reading, see Suppes, Zinnes: "Basic measurement theory"), a "scale" is defined as a homomorphic mapping from some empirical relational system of measurement to some formal number system. The formal system (not the scale!) may have free parameters (sometimes also called "datums") in choosing the meaning of some of its number instances. An example for a scale is the "meter" scale for measuring lengths, where "1" has a fixed meaning. Thus, a scale already fixes all free parameters of the formal system. In contast, "scale types", such as "ratio" or "interval" are equivalence classes of particular scales under some admissible scale transformations. The latter map choices of the free parameters into each other.
The authors use the term "scale" in the paper in order to denote "scale type", and reserve the (too narrow) term "unit of measurement" to denote "scale". The drawback of this usage is that it conceptually narrows down measurement to certain types, such as ratio. Ratio scales need only "units (number 1)" to fix the meaning of all numbers. Units are the most prominent parameters and can be prefixed. But there are many others, e.g.: "absolute scales" (for counting) do no have any free parameters or units; "ordinal scales" have a free parameter for every single one of its numbers, not only for "1". It would be good to draw these distinctions and reserve the term unit for the meaning of the number 1.
The distinctions discussed above are often confused or improperly used in the text: "In case of conversion between absolute scales also an offset is required, as the zero points may differ" (p.6): What the authors mean here are interval scales, not absolute scales! "Most scales have uniquely defined zero points" (p.6): is this really an empirical fact? "Units of measure in turn can be defined in terms of quantities" (p.2): Units of measure cannot be (formally) defined at all. Instead, they are free parameters that need to be fixed by some observable standard phenomenon. Instead, one could state explictly that scales have unique scale types, but quantities as well as scale types can have more than one scale.

2) On page 4, it is claimed that OM can be grounded in foundational ontologies like DOLCE, e.g., by defining "quantity" as subclass of "quality". However, DOLCE qualities are temporally indexed for good reasons, because their values can change over time, whereas the relation "om:phenomenon" is binary and thus "static" for a phenomenon. This seems an important design choice, which is not discussed at all, and which makes OM incompatible with DOLCE. On page 10, "the former [DOLCE quality] is qualitative and the latter is quantitative [OM quantity]". But DOLCE qualities include all kinds of observable properties, also quantitatively measurable ones. The essential point is not the distinction between quantitative and qualitative (which is spurious anyway), but rather the question whether there is a number scale (with appropriate scale type) that represents the values of a given DOLCE quality (compare "reference space" in the reference "Probst" given below).

3) There is plenty of literature on general ontological considerations of observation and measurement that would be relevant: besides measurement theory (see above), you may have a look into (Masolo 2010: Founding properties on measurement. FOIS 2010: 89-102) or (Probst, F. (2008) Observations, Measurements and Semantic Reference Spaces. Journal of Applied Ontology). A general view on how to fix datums of measurement scales and observations is dicussed in: (Scheider et al. 2009: Grounding Geographic Categories in the
Meaningful Environment). There are other existing approaches for ontologically driven datum conversions (see e.g. Schade (2010): Ontology-Driven Translation of Geospatial Data).

Review 2 by Michael Compton

The paper has been revised in line with comments from all reviewers. As stated in my original review, I feel that the paper provides a very nice overview of the issues of representing units, uses cases and discussion relating OM back to these points in terms of design decisions and modelling.

The paper is largely ready for publication, though the issues below should be addressed.

- (The editors may have an opinion on this point) The paper uses references as parts of sentences: for example, "which we describe in [6]". To me this is non-standard and I rather expect the reference to not be part of the sentence: for example, more like "as we have described previously [6]" or some such construction.

- Placement of footnotes is inconsistent: sometimes written "abc.^3" and other times "abc^3.". Footnotes are normally placed after punctuation.

- The given url for the OM ontology, http://www.wurvoc.org/vocabularies/om-1.8/, doesn't download a valid ontology for me (version 1.7 seems ok). Check this.

- Similarly, the footnote http://www.cs.vu.nl/~mark/om on page 6 is not reachable.

- Those two issues meant that the comments and example at the top of page 6 were not able to be checked - I didn't fully understand the last paragraph on page 5/first paragraph on page 6, in relation to instances not being able to specify commonly_used_unit. It was unclear how that was enforced.

- Also on page 6, in "Checking datasets", it first states that the checking isn't possible in OWL and then shows how to do it in OWL. It's eventually clear what you mean - just fix up the wording of the first sentence.

- The Discussion section spends some time explaining why the ontology can't be represented in OWL1, but I couldn't find a clear statement earlier in the paper that OM was an OWL 2 ontology, or what DL is required to express it. Please add.

Review 3 by anonymous reviewer

Most of the comments in my review of the previous version of the paper have not been taken into account. The only point that has been addressed regards the link with the ontology DOLCE (actually DOLCE is cited for the first time at page 4, but no introduction and no reference are provided). With respect to this point I have some additional comments. In which sense the qualities of DOLCE are "qualitative" (as opposed to "quantitative")? In DOLCE, individual qualities are always completely specified properties of specific objects (determinate properties in philosophical terms), 'the exact shade of color of a given object', 'the exact length of a given object", etc. Individual qualities inhering in different objects are 'grouped together' via the the regions in the spaces, i.e. individual qualities not perfectly resembling, i.e. resembling at a given degree, can be mapped to the same region (e.g. 'the being carmine of object 1' and 'the being magenta of the object 2' can both be mapped to the red region if in the corresponding space there are no more specific regions). Regions (and spaces) but not individual qualities allow for abstraction (and different/incompatible classifications). Actually I don't understand also the comment about the structures of qualia. The regions of a given space can be constructed taking into account units (of measurement). These kinds of spaces have a complex structure because a metric is needed but in principle they can be represented in DOLCE that however can also represent simpler qualitative spaces (e.g. cognitive color spaces).

The reviews below are from the initial submission of the manuscript, which was accepted with revisions.

Review 1 by Werner Kuhn

This is a well written description of a decent ontology of measurement units and related concepts. It contains good use cases and the ontology development appears to have been driven, though apparently not evaluated explicity, by them. The authors are keen to provide accessible tools using the ontology, which is great.

A weakness of the presentation is the narrow discussion of related ontologies. In the paper, only QUDT is discussed (though in detail and with good arguments) and only a pointer is given to a discussion elsewhere of Gruber's EngMath. At least a summary of that discussion should be added, for the paper to be self-contained. And then, there are other attempts, at least MUO (http://forge.morfeo-project.org/wiki_en/index.php/How_to_use_MUO), but probably more.

Regarding the excellent QUDT discussion, this should not remain one sided and I hope the journal can request a comment from the QUDT authors, ideally leading to some sort of joining forces, as the present authors seem to suggest (or at least to a documented "agree to disagree").

A significant weakness of the work, not only of the presentation, is the lacking alignment with a foundational ontology. Particularly in a cross-cutting area like measurements, it is a big and hardly justifiable loss for interoperability to provide only an insular ontology, without links to basic vocabulary taken from, for example, DOLCE (which is particularly strong on this topic). A direct consequence of this omission is the rather questionable as well as unclear use of the term "metrological concept" (MC) for a measurable aspect of a phenomenon. To my knowledge, MC means something else in metrology (a measurement design or method). In ontology, there are solid theories about qualities (or other measurement concepts) that this work should be linked to in order to become more broadly applicable (for example, also in the sensor web area). This lack of foundations is the (only) reason for my average rating of methodology, as the rest of the rationale and procedure seems very solid.

Independently of how the MC is called, a clarification of whether the phenomenon is included in the concept or not would help.

In general, the literature review is skimpy, though this may be a bit less harmful for an ontology description paper, as long as other existing ontologies are covered.

Details in the text:
- "measurements consist of..." - this may better say "minimally of", as measurements can consist of much more than the four elements given (for example, precision, instrument data, time stamps etc.).
- "velocity is a specific kind of speed" - but not in the sense of being a sub-class!
- "base units are mutually independent" - not really (e.g., meter is defined through second)
- "each MC has a measurement scale" - not really (it can have several or the scale can be undefined)
- "ambiguities in SI" - please give an example
- "encoded in use cases" is a strange formulation.

Spelling etc:
- you seem to have adopted english spelling (metre) for some, and US (meter) for other aspects, please clarify;
- etcetera is not a word (either et cetera, or etc., but why use it at all?)
- interms should be in terms
- check your use of the term "extent" - I think you mean "amount" in some cases
- "shipping" is also not what you use it for
- "absolute temperatures" for Celsius etc. is a misnomer
- "does does" - repeated word
- "of their to their" ?
- "other For example" misses a period.

Review 2 by anonymous reviewer

This well written paper describes an "ontology" able to model different aspects of measurement. The ontology presented is quite simple and the ontological choices are not really discussed. This is a pity because at the end the proposed ontology sounds as the result of introspection, while some relevant analysis are already present in the literature. Indeed, the paper seems more focused on the usage of the proposed ontology to match the requirements coming from the use cases considered in a specific project. I don't know whether papers of type "Description of Ontology" must be more practical than theoretical. If it is the case I accept the paper otherwise it requires major revisions. In any case, I think that the paper could greatly improve, if the following two aspects are addressed in detail:

(1) Clarify/address foundational/theoretical aspects of the proposed ontology of measurement also in the light of what exist in the literature.
(2) Point out in a clear way the reasoning advantages/disadvantages of alternative models, i.e. in which tasks one model is better than the other one.

(1) From the *foundational* point of view the paper is quite superficial. The idea of reifying "quantities" is already present in some foundational (top-level) ontologies that are already available. For example DOLCE deeply analyzes these reified entities (called individual qualities) and their relations with "phenomenons" and "measures" taking into account change and the temporal dimension of measurement (an important aspect, actually I think one of the most critical and challenging aspect of measurement, aspect ignored in the present paper). I think that "Quantity is a class that represents combinations of the elements MC and phenomenon" (section 4) is not a very precise characterization.

In addition, some extensions of DOLCE take into account:

(1.a) a formal comparison among the different "MCs-as-classes" vs. "MCs-as-instances" vs. "MCs-as-properties" options

Masolo C.; Borgo, S., 2005, Qualities in Formal Ontology. In the proceedings of the Ws Foundational Aspects of Ontologies (FOnt 2005), Koblenz, Germany, Sept. 2005.

[This work does not address units of measurement, but the proposed frameworks are general enough to allow to classify (a more general process than measurement) phenomena along the same dimension (quantity) according to different measurement instruments. E.g. the color of an object can be measured according to different measurement instruments that organize the measures in structurally different ways, i.e. measurement results does not differ only because of the units of measurement; instead they refer to different metrics, i.e. they are structured in different ways. This can be an interesting extension of your work]

(1.b) the epistemological and empirical aspects of measurement (a quite important metrological topic) by explicitly introducing observations in the process of measurement

Kuhn, W., 2009. A Functional Ontology of Observation and Measurement. K. Janowicz, M. Raubal, and S. Levashkin (Eds.): GeoSpatial Semantics · Third International Conference (GeoS 2009), Mexico City, 3-4 December 2009. Springer-Verlag Lecture Notes in Computer Science 5892: 26–43.

Probst, F. (2008) Observations, Mesurements and Semantic Reference Spaces. Special Issue: Ontological Foundations for Conceptual Modeling. Journal of Applied Ontology.

(2) Section 4 "They are compatible in that rules may be formulated to automatically translate one in the other. Which perspective should be preferred then depends on practical concerns, e.g. which perspective allows useful reasoning (in the chosen representation language) not easy to realize in another perspective. We return to this issue in the Discussion."
Honestly I find the final discussion quite disappointing. There are no practical examples that show in which cases the modeling strategy chosen by OM "works better than" the one chosen by QUDT (and vice versa). I'm not talking about the fact, for example, that OM, but not QUDT, allows for labels, unit conversions. I'm interested in understanding if, for example, there are some practical advantage/disadvantages is representing QuantityKinds as classes instead than instances or to have a QuantityValue separated by the Unit (as in QUDT). I think that this kind of discussion is interesting for modeling strategies in general, not only in the domain of measurement. Therefore I strongly encourage the authors to consider this more general aspect.

Other remarks.
(A) I find the sentence in section 3

"It should for example be possible to state that "the viscosity of ketchup is around 70.000cps". This requires relating a phenomenon to a MC, a numerical value and a unit"

quite misleading. I don't see a phenomenon here, the sentence does not refer to a specific amount of ketchup. I see here something more general, like "all the amounts of ketchup have a viscosity around 70.000cps". How does the author represent this kind of knowledge (for me this is partially linked to "average" measures)? Note that, curiously, in figure 1 the authors introduce ex:diam1, ex:mass1, but ex:apple instead of ex:apple1. Why? ["around" is another interesting aspect of "qualitative aspects of" measurement that is not addressed in the paper]

(B) "An intensional description of the allowed units for a quantity can be given using OWL restrictions." (sect 4). What is an intensional description here? The term "intensional" is used in philosophy and logic with a quite precise meaning.

© Section 4, subsection Labels. I think that the linguistic aspects need to be clearly separated from the conceptual and ontological ones. The fact that the proposed model allows for using alternative names for the same "concept" has no ontological impact. The same mechanism can be easily introduced in models based on a completely different ontology.

(D) Section 5. "Instances of Quantity link to a QuantityValue, a QuantityKind and (presumably) a phenomenon to represent a complete measurement." Why presumably? In addition, in fig.2, there is an arrow from phenomena to quantities and not from quantities to phenomena, is that correct?

(E) Section 6. "Secondly, how to represent measures with just a number rather than a number with a unit. An example is the countable quantity (e.g. number of apples)." There is a huge literature in philosophy and in ontological research about unity criteria that underline any counting process. Note however that counting is in general considered a quite different process withe respect to measurement.

(F) Section 6, Integration."Another option is to allow both models to co- exist but harmonize them such that one is automatically translatable into the other." Conceptually, the two models seem to me quite close, they mostly differ because of their "technical implementations" (quantity-classes vs. quantity-instances). I'm not able to see what are the difficulties in doing this translation. Maybe the authors can discuss this point in more detail, pointing out difficulties.

Review 3 by Michael Compton

This paper (submitted as a "Description of Ontologies" paper) describes an ontology of units and quantities - the Ontology of Units of Measure and Related Concepts (OM).

In alignment with the "Description of Ontologies" call, this paper gives a brief outline of the ontology, the key design principles and choices, use cases and a comparision with the QUDT ontology. The paper clearly points out where the ontology is available and how it is versioned.

The paper is well written and spells out clearly the issues and technical requirements in this area as well as use cases that require much of the introduced material. Section 2 gave a nice overview of the domain and the relevant issues.

The description of the ontology is well written, it discusses various modelling options and the consequences as well as linking the discussion to the presented use cases.

However, while readable, I felt that Section 4, would be better served by diagrams showing the key relationships discussed or examples that intuitively demonstrated the discussed material. Having everything buried in text was hard to navigate. The given figures (1 and 2) seemed to be far too simple (for 1) and far too much syntax (for 2) to properly support the text - though I appreciate that figure 1 is also used as a point of comparison with QUDT.

There are other units ontology that could at least be referenced or discussed.

The four listed contributions are overly ambitious, especially given the brevity of the discussion for contribution 3. I would say more that highlihghting and discussing the modeling choices with QUDT as an example comparator is the contribution (i.e. somewhere between the listed second and third contributions). Also, presenting the domain, use cases and ontology and modelling choices as a cross referenced package seems to be the other, and worthy, contribution.

The article is in general well written, but contains some English errors (such as " OM enables to make" in the abstract). Needs a careful edit and proof read.

In summary this is a well written article that describes an ontology and various modelling choices. It satisfies the requirements for a "Description of Ontologies" article.