Aligning different relations: the case of part-whole relations—LDK2017

Despite the best intentions, I did not get around to writing a post on the paper that I presented last week at the First International Conference on Language, Data and Knowledge 2017, 19-20 June, Galway, Ireland, and now Paul Groth also ‘beat’ me to it writing a nice conference report of it. On the bright side, it is an opportunity to say upfront I really enjoyed the conference and look forward to the next edition in 2019. The ESWC’17 organisers might be slightly disappointed that there was no special track on the multilingual semantic web after all, but I did get the distinct impression that the LDK17 authors might just all have gambled on LDK17—an opportunity to binge two days on all things natural language & Semantic Web—rather than on one track at an overpriced conference (despite the allure of it being A-rated).

So, what was my paper about that could have been submitted to either? I ended up struggling—and solving—an issue with aligning OWL object properties that were not simple 1:1 mappings, in a similar scope as our ESWC17 paper (introduced here) [4], but then with too many complications. Complications were due to the different conceptualisations of part-whole relations and that one of the requirements was to solve what to do with an object property (relation, relationship) that does not have a neat, single, label, and therewith neither fitting with the common OWL modelling paradigm nor with the recently agreed-upon ontolex-lemon model for linguistic annotations.

The start of all this sounded nice and doable: we need to generate natural language for healthcare, using, e.g., SNOMED CT, in local languages in South Africa, focussing on the largest one, being isiZulu. Medical terminologies are riddled with part-whole relations, so we sought to address that one (simple existentials already having been solved), availing of a standard list of part-whole relations (e.g. [1]). That turned out to be a non-trivial exercise, but doable eventually [2]. What wasn’t addressed in [2] was that some ‘common’ part-whole relations, such as membership and containment, weren’t like that in isiZulu, at all. Moreover, it wasn’t just a language issue, but ontological as well. The LDK17 paper “Representing and aligning similar relations: parts and wholes in isiZulu vs English” [3] describes this in some detail.

Here’s a (simplified) list of (assumed to be) common part-whole relations, which takes into account both transitivity differences and domain and range:

Now here’s the one based on the isiZulu language and some ontological analysis of that:

That is: there are both generalisations—some distinctions are not being made—and specialisations—some distinctions are made here but not elsewhere. For instance, ‘musician is part of some orchestra’ and ‘heart is part of some human’ (or vv.) is all done and described in the same way (ingxenye ‘part of’ and SC+CONJ for ‘has part’ [more about that below]). Yet, there is a difference between an individual (e.g., a voter) participating in some process and a collective (e.g., the electorate) participating in a process, or vv. The paper describes this more precisely, going into some detail regarding the differences in categories of domain and range and into the consequences on transitivity of mereological parthood.

The other ‘odd thing’—cf. current multilingual Semantic Web assumptions and technologies, that is—is that while the conceptualisation of ‘has part’ exists, it does not have a single label as in English (or in several other languages, such as heeft as deel), but it is dependent on the noun class of the noun of the class that play the part and play the whole in the relation. It combines the subject concord (~conjugation) of the noun class of the noun that plays the whole with a conjunction that is phonologically conditioned based on the first letter of the noun that plays the part; with verbalisation in the plural and three phonological cases, there are 18 possible strings all denoting ‘has part’. This still could be sorted with a language with inverses, provided the part-of direction has a name, like the ingxenye. This is not the case for containment, however. Instead of the relation (object property) having a name—be this a verb like ‘contained in’ or some noun phrase—it is the noun that plays the whole (the container, if you will) that gets modified. For instance, imvilophu ‘envelope’ and emvilophini denoting ‘contained in the envelope’, or, for individuals and locations, the city iTheku ‘Durban’ and eThekwini meaning ‘located in Durban’ (no typo—there’s some phonological conditioning I’m brushing over). While I have gotten used to such constructions, it generated some surprise among several attendees that one can have notions, concepts, views on or interpretations or descriptions of reality, that exist but do not have even one single string of text throughout to refer to regardless the context it is used.

The naming issue was solved by adding some arbitrary string as ‘name’ of the object property, and relating that to the function that verbalises that specific part-whole relation. The former issue, i.e., not all the same part-whole relations, required a bit more work, using ontology pattern alignments, by extending one correspondence pattern from the ODP catalogue and introducing a new one (see paper for the formal details), using the same broad framework of formalisation as proposed in [4].

All this was then implemented and aligned, and verified to not result in some unsatisfiable classes, object properties, or inconsistency (files). This also works in the isiZulu verbalisation tool we demo-ed at ESWC17 (described in the previous post) [5], all as part of the NRF-funded GeNI project.

Now, ideally, I already would have had the time to read the papers I flagged in my LDK17 conference notes with “check paper”. I haven’t yet due to end-of-semester tasks. So, on the basis of just a positive-seeming presentation, here are a few that are on the top of my list to check out first, for quite different reasons:

  • Interaction between natural language reading capabilities and math education, focusing on language production (i.e., ‘can you talk about it?’) [6], mainly because math education in South Africa faces a lot of problems. It also generated a lively discussion in the Q&A session.
  • The OnLiT ontology for linguistic [7] and LLODifying linguistic glosses [8] terminology (also: one of the two also won the best paper award).
  • Deep text generation, for it was looking at trying to address skewed or limited data to learn from [9], which is an issue we face when trying to do some NLP with most South African languages.

 

References

[1] Keet, C.M., Artale, A. Representing and Reasoning over a Taxonomy of Part-Whole Relations. Applied Ontology, 2008, 3(1-2):91-110.

[2] Keet, C.M., Khumalo, L. On the verbalization patterns of part-whole relations in isiZulu. 9th International Natural Language Generation conference (INLG’16), September 5-8, 2016, Edinburgh, UK. ACL.

[3] Keet, C.M. Representing and aligning similar relations: parts and wholes in isiZulu vs English. In: Gracia J., Bond F., McCrae J., Buitelaar P., Chiarcos C., Hellmann S. (eds) Language, Data, and Knowledge LDK 2017. Springer LNAI vol 10318, 58-73.

[4] Fillottrani, P.R., Keet, C.M. Patterns for Heterogeneous TBox Mappings to Bridge Different Modelling Decisions. 14th Extended Semantic Web Conference (ESWC’17). Springer LNCS. Portoroz, Slovenia, May 28 – June 2, 2017.

[5] Keet, C.M. Xakaza, M., Khumalo, L. Verbalising OWL ontologies in isiZulu with Python. 14th Extended Semantic Web Conference (ESWC’17). Springer LNCS. Portoroz, Slovenia, May 28 – June 2, 2017. (demo paper)

[6] Crossley, S., Kostyuk, V. Letting the genie out of the lamp: using natural language processing tools to predict math performance. In: Gracia J., Bond F., McCrae J., Buitelaar P., Chiarcos C., Hellmann S. (eds) Language, Data, and Knowledge LDK 2017. Springer LNAI vol 10318, 330-342.

[7] Klimek, B., McCrae, J.P., Lehmann, C., Chiarcos, C., Hellmann, S. OnLiT: and ontology for linguistic terminology. In: Gracia J., Bond F., McCrae J., Buitelaar P., Chiarcos C., Hellmann S. (eds) Language, Data, and Knowledge LDK 2017. Springer LNAI vol 10318, 42-57.

[8] Chiarcos, C., Ionov, M. Rind-Pawlowski, M., Fäth, C., Wichers Schreur, J., Nevskaya. I. LLODifying linguistic glosses. In: Gracia J., Bond F., McCrae J., Buitelaar P., Chiarcos C., Hellmann S. (eds) Language, Data, and Knowledge LDK 2017. Springer LNAI vol 10318, 89-103.

[9] Dethlefs N., Turner A. Deep Text Generation — Using Hierarchical Decomposition to Mitigate the Effect of Rare Data Points. In: Gracia J., Bond F., McCrae J., Buitelaar P., Chiarcos C., Hellmann S. (eds) Language, Data, and Knowledge LDK 2017. Springer LNAI vol 10318, 290-298.

Automatically finding the feasible object property

Late last month I wrote about the updated taxonomy of part-whole relations and claimed it wasn’t such a big deal during the modeling process to have that many relations to choose from. Here I’ll back up that claim. Primarily, it is thanks to the ‘Foundational Ontology and Reasoner enhanced axiomatiZAtion’ (FORZA) approach which includes the Guided ENtity reuse and class Expression geneRATOR (GENERATOR) method that was implemented in the OntoPartS-2 tool [1]. The general idea of the GENERATOR method is depicted in the figure below, which outlines two scenarios: one in which the experts perform the authoring of their domain ontology with the help of a foundational ontology, and the other one without a foundational ontology.

generator

I think the pictures are clearer than the following text, but some prefer text, so here goes the explanation attempt. Let’s start with scenario A on the left-hand side of the figure: a modeller has a domain ontology and a foundational ontology and she wants to relate class two domain classes (indicated with C and D) and thus needs to select some object property. The first step is, indeed, selecting C and D (e.g., Human and Heart in an anatomy ontology); this is step (1) in the Figure.

Then (step 2) there are those long red arrows, which indicate that somehow there has to be a way to deal with the alignment of Human and of Heart to the relevant categories in the foundational ontology. This ‘somehow’ can be either of the following three options: (i) the domain ontology was already aligned to the foundational ontology, so that step (2) is executed automatically in the background and the modeler need not to worry, (ii) she manually carries out the alignment (assuming she knows the foundational ontology well enough), or, more likely, (iii) she chooses to be guided by a decision diagram that is specific to the selected foundational ontology. In case of option (ii) or (iii), she can choose to save it permanently or just use it for the duration of the application of the method. Step (3) is an automated process that moves up in the taxonomy to find the possible object properties. Here is where an automated reasoner comes into the equation, which can step-wise retrieve the parent class, en passant relying on taxonomic classification that offers the most up-to-date class hierarchy (i.e., including implicit subsumptions) and therewith avoiding spurious candidates. From a modeller’s viewpoint, one thus only has to select which classes to relate, and, optionally, align the ontology, so that the software will do the rest, as each time it finds a domain and range axiom of a relationship in which the parents of C and D participate, it is marked as a candidate property to be used in the class expression. Finally, the candidate object properties are returned to the user (step 4).

While the figure shows only one foundational ontology, one equally well can use a separate relation ontology, like PW or PWMT, which is just an implementation variant of scenario A: the relation ontology is also traversed upwards and on each iteration, the base ontology class is matched against relational ontology to find relations where the (parent of the) class is defined in a domain and range axiom, also until the top is reached before returning candidate relations.

The second scenario with a domain ontology only is a simplified version of option A, where the alignment step is omitted. In Figure-B above, GENERATOR would return object properties W and R as options to choose from, which, when used, would not generate an inconsistency (in this part of the ontology, at least). Without this guidance, a modeler could, erroneously, select, say, object property S, which, if the branches are disjoint, would result in an inconsistency, and if not declared disjoint, move class C from the left-hand branch to the one in the middle, which may be an undesirable deduction.

For the Heart and Human example, these entities are, in DOLCE terminology, physical objects, so that it will return structural parthood or plain parthood, if the PW ontology is used as well. If, on the other hand, say, Vase and Clay would have been the classes selected from the domain ontology, then a constitution relation would be proposed (be this with DOLCE, PW, or, say, GFO), for Vase is a physical object and Clay an amount of matter. Or with Limpopo and South Africa, a tangential proper parthood would be proposed, because they are both geographic entities.

The approach without the reasoner and without the foundational ontology decision diagram was tested with users, and showed that such a tool (OntoPartS) made the ontology authoring more efficient and accurate [2], and that aligning to DOLCE was the main hurdle for not seeing even more impressive differences. This is addressed with OntoPartS-2, so it ought to work better. What still remains to be done, admittedly, is that larger usability study with the updated version OntoPartS-2. In the meantime: if you use it, please let us know your opinion.

 

References

[1] Keet, C.M., Khan, M.T., Ghidini, C. Ontology Authoring with FORZA. 22nd ACM International Conference on Information and Knowledge Management (CIKM’13). ACM proceedings, pp569-578. Oct. 27 – Nov. 1, 2013, San Francisco, USA.

[2] Keet, C.M., Fernandez-Reyes, F.C., Morales-Gonzalez, A. Representing mereotopological relations in OWL ontologies with OntoPartS. 9th Extended Semantic Web Conference (ESWC’12), Simperl et al. (eds.), 27-31 May 2012, Heraklion, Crete, Greece. Springer, LNCS 7295, 240-254.

FAIR’14 and ‘modelling relationships’ tutorial

After a weekend of ‘loadshedding’ (one of those South African euphemisms) I’m posting a few notes on the Forum on Artificial Intelligence Research 2014 (FAIR’14) that took place from 3-5 Dec 2014 at Stellenbosch University, which was organised by CAIR and co-located with the FASTAR/Espresso Workshop 2014, which, in turn, was co-located with PRASA, AFLaT, and RobMech 2014 in Cape Town. FAIR’14 consisted of a presentation by Sergei Obiedkov of the Higher School of Economics, Russia, a tutorial on modelling relationships in ontologies by me, and a course on computational social choice theory by Ulle Endriss from the ILLC, University of Amsterdam, The Netherlands.

While not quite relevant to my current research except for judgement aggregation at the end (for crowdsourcing), Ulle’s course was one of those events that made me think “[why didn’t/if only] I was exposed to this material before?!”, when I had to make choices as to what to study and specialise in (though, admitted, once knowing about the math with game theory and applying that to peace negotiations in my MA pdf, I still went on in CS with KR&R and ontologies). Ulle’s course combined socially relevant topics, such as the fair allocation of resources and voting systems, with solid, precise, logic- and math-based representations and computation. Besides the engaging content, he’s also good at teaching it. The content and slides are a condensed version of his MSc course on social choice theory and are available online here, which also has links to related reading material.

I tried to condense into 2 hours some aspects of modelling relationships in ontologies. It started with some problems and questions, proceeded to touching upon the nature of relations and some detail of the formal semantics, common relationships (with some detail about mereotopology), and closing with some practical modelling guidance and reasoner performance when modelling it one way or another. It being a tutorial, and not all participants had Protégé installed, I resorted to a peer instruction audience response system to incorporate interactively some questions about modelling some relationships. The slides are available online (though also here the text on the slides only partially reflect what I’ve talked about).

Other than that, there’s always the social component. Despite the weird time-warp that Stellenbosch town constitutes, it was really nice to catch up with former colleagues and to see the progress of postgrads of UKZN, to hear about the future of CAIR, and that it’s a small world even when meeting people new to me. And the food & wine was delicious. The train travel back to Cape Town took a bit longer than the schedule said it ought to be, but I recommend it nevertheless.

Part-whole relations, mereotopology and the OntoPartS tool

Part-whole relations are considered essential in knowledge representation and reasoning and, more practically, in ontology development and conceptual data modelling, especially in the subject domains of biology, medicine, geographic information systems, and manufacturing. In contrast to Ontology that sticks to one type of part-of, the modellers and subject domain experts have come up with a plethora of part-whole relations, some of which are considered real parthood relations and others only meronymic (or: due to imprecise natural language use). For instance, the Foundational Model of Anatomy has 8 basic locative part-whole relations [1], GALEN has come up with 26 part-whole relations [2], and in cognitive science and conceptual data modelling, it hovers around about 6 types [3,4]. They have been structured in a taxonomy of part-whole relations that makes a distinction between mereology and meronomy, transitivity and in- or non-transitivity, and the domain and range of the relationship [5], and some initial usage guidelines were proposed in [6].

But that’s not enough for the complex subject domains and demands on the representation and reasoning over the ontologies. This holds in particular when one has to represent that some things are contained in or located in something else. For instance, the way how Paris and France relate is somehow different from how the euro coin in your wallet relate to each other—the latter being an example of  (spatial) containment, but not structural part of—whereas in other case, the spatial containment of regions of space and the structural parthood of the objects occupying those regions do coincide, e.g., your heart in your body. Or consider representing that Alto Adige/Südtirol is a border province of Italy (bordering Austria), where we have to handle both the notion of administrative entities and connecting geographical regions. That is, handling regions and ‘things’ that occupy those regions (mereotopology).

Being more precise about how the things relate provides nice inferences. Take, e.g., NTPLI as ‘non-tangential proper located in’—a part is located in the whole but not at the boundary of it—and EnclosedCountry \equiv Country \sqcap \exists NTPLI.Country , with the following instances in our knowledge base NTPLI(Lesotho, South Africa) , Country(Lesotho) , and Country(South Africa) , then it deduces correctly that EnclosedCountry(Lesotho) , whereas with a mere ‘part-of’, we would not have been able to obtain this result.

Besides these examples, there are actual system requirements for, among others, annotating and querying multimedia documents and cartographic maps, such as annotating a photo of a beach where the area of the photo that depicts the sand touches the area that depicts the seawater so that, together with the knowledge that Varadero is a tangential proper part of Cuba, the semantically enhanced system can infer possible locations where the photo has been taken, or, vv., it can propose that the photo may depict a beach scene.

But how to cater for such things?

Let me summarise the three main basic problems that have to be resolved first:

  1. There is lack of oversight on plethora of part-whole relations, that include real parthood (mereology) parts with their locations (mereotopology), and other part-whole relations (from meronymy);
  2. The challenge to figure out which one to use when;
  3. The underspecified representation and reasoning consequences when one has to put up with less expressive languages for which technological infrastructure exists.

We propose to solve that in the following way, which is described in detail in [7] that recently got accepted at the 9th Extended Semantic Web Conference (ESWC’12).

The short answer for the reader who is not interested in all the theory, design, and evaluation, but just wants to model quickly: the OntoPartS tool guides you to choose the most appropriate relation and saves the selection into your OWL file.

Now for a slightly longer answer. First, we extend the taxonomy of part-whole relations of [5] with the novel addition of a taxonomy of formally defined mereotopological relations, which is driven by the KGEMT mereotoplogical theory of Varzi [8], resulting in a taxonomy of 23 part-whole relations—mereological, mereotopological, and meronymic ones—therewith ensuring a solid ontological and logic-based foundation.

Second, some things have to be simplified from the KGEMT theory to make it implementable in OWL, and we describe the design rationale and trade-offs so that OntoPartS can load OWL/OWL2-formalised ontologies, and, if desired, modify the OWL file with the chosen relation. Which OWL species is best suited obviously depends on your individual requirements, but from a representation & reasoning and mereotopology viewpoint, OWL 2 DL and OWL 2 RL seem to fit better than the other ones. (Note: there are papers on DL and representing spatial relations and on DL and parthood, and alternative representation choices are discussed in the paper, yet, as far as we are aware of, none deals with mereotopological relations in OWL or, more generally, in DL.)

Third, there is the ‘how to select’ from the 23 relations. To enable a quick selection of the appropriate relation, we avail of a simplified OWL-ized DOLCE ontology—well, just the taxonomy of categories—for the domain and range restrictions imposed on the part-whole relations and with that, we can let the user take shortcuts compared to a lengthy decision procedure. In this way, we reduced the selection procedure to 0-4 options based on just 2-3 inputs. All of this has been structured neatly in implementation-independent activity diagrams, and subsequently has been implemented; see also the demos, the tool, and the OWL version of the taxonomy of the 23 relations.

Last, we have tested OntoPartS with modellers in controlled experiments and it was shown to improve efficiency and accuracy in modeling of part-whole relations.

As mentioned, further details can be found in [7], Representing mereotopological relations in OWL ontologies with OntoPartS, which I co-authored with Francis Fernández-Reyes, with the Instituto Superior Politécnico “José Antonio Echeverría” (CUJAE), and Annette Morales-González, with the Advanced Technologies Application Center (CENATAV), both located in Cuba (the example on semantic annotation of multimedia with spatial relations comes straight from the image processing research being done at CENATAV). A tidbit of non-scientific information: the first version of the OntoPartS tool was developed as part of the mini-project that Francis, Annette (and Alexis, who is into fish fulltime now) had chosen to carry out for the ontology engineering course I taught at the University of Havana in 2010 (mentioned earlier here and here). For the paper, we added some more theory, minor refinements to the tool, and a user evaluation with several CUJAE and UKZN students and a few FUB colleagues (thanks again for their cooperation and interest). We’ve started work on additional features, so if you have any particular request, drop me a line.

References

  1. Mejino, J.L.V., Agoncillo, A.V., Rickard, K.L., Rosse, C.: Representing complexity in part-whole relationships within the foundational model of anatomy. In: Proc. of the AMIA Fall Symposium. pp. 450–454 (2003)
  2. http://www.opengalen.org/tutorials/crm/tutorial9.html up to http://www.opengalen.org/tutorials/crm/tutorial16.html/.
  3. Winston, M., Chaffin, R., Herrmann, D.: A taxonomy of part-whole relations. Cognitive Science 11(4), 417–444 (1987)
  4. Odell, J.: Advanced Object-Oriented Analysis & Design using UML. Cambridge: Cambridge University Press (1998)
  5. Keet, C.M., Artale, A.: Representing and reasoning over a taxonomy of part-whole relations. Applied Ontology 3(1-2), 91–110 (2008)
  6. Keet, C.M.: Part-whole relations in object-role models. In: Proc. of ORM’06, OTM Workshops 2006. LNCS, vol. 4278, pp. 1116–1127. Springer (2006)
  7. Keet, C.M., Fernández Reyes, F.C., Morales-González, A.: Representing mereotopological relations in OWL ontologies with OntoPartS. In Simperl, et al., eds.: Proc. of ESWC’12. LNCS, Springer (2012) 27-31 May 2012, Heraklion, Greece.
  8. Varzi, A.: Handbook of Spatial Logics, chap. Spatial reasoning and ontology: parts, wholes, and locations, pp. 945–1038. Berlin Heidelberg: Springer Verlag (2007)

Lecture notes for the ontologies and knowledge bases course

The regular reader may recollect earlier posts about the ontology engineering courses I have taught at FUB, UH, UCI, Meraka, and UKZN. Each one had some sort of syllabus or series of blog posts with some introductory notes. I’ve put them together and extended them significantly now for the current installment of the Ontologies and Knowledge Bases Honours module (COMP718) at UKZN, and they are bound and printed into lecture notes for the enrolled students. These lecture notes are now online and I will add accompanying slides on the module’s webpage as we go along in the semester.

Given that the target audience is computer science students in their 4th year (honours), the notes are of an introductory nature. There are essentially three blocks: logic foundations, ontology engineering, and advanced topics. The logic foundations contain a recap of FOL, basics of Description Logics with ALC, all the DL-based OWL species, and some automated reasoning. The ontology engineering block covers top-down and bottom-up ontology development, and methods and methodologies, with top-down ontology development including mainly foundational ontologies and part-whole relations, and bottom-up the various approaches to extract knowledge from ‘legacy’ representations, such as from databases and thesauri. The advanced topics are balanced in two directions: one is toward ontology-based data access applications (i.e., an ontology-drive information system) and the other one has more theory with temporal ontologies.

Each chapter has a section with recommended/required reading and a set of exercises.

Unsurprisingly, the lecture notes have been written under time constraints and therefore the level of relative completeness of sections varies slightly. Suggestions and corrections are welcome!

Better off with foundational ontologies

Various methods exist to commence with ontology development. Top-down ontology development has the underlying assumption that by using a foundational ontology, one can speed up ontology development and improve quality and interoperability of the domain ontology. Opponents complain that the foundational ontologies are too abstract, too expressive, too comprehensive for ‘simple’ or domain ontologies, and that it takes too much time to understand them in sufficient detail anyway. Informal assessment of these assumptions reveals ambiguous results either way, which are not only open to different interpretations but also such that foundational ontology usage is not foreseen in most methodologies.

So, what should an ontology developer do? The title of this blog post already suggests the answer to this question. It is fair to ask some follow-up questions: why should the developer use a foundational ontology and how and where does it make a difference?

Thus far, there were only theoretical answers to these questions, but no hard evidence to back it up. Sure, the OBO Foundry experiment is ongoing, but, as Ben already mentioned in a previous blog post comment, it is known that there is no empirical proof that validates the assumption. I tried to validate it in one way last year and only recently took the time to write it down. I had set up a controlled experiment with participants of the three ontology engineering courses I taught at the University of Havana and University of Computer Science, in Cuba, and CSIR Meraka in South Africa in 2010. 52 people participated in the experiment who developed 18 ontologies in groups, which were analysed on basic statistics (how many classes, relations, axioms were added), errors, language used, and other observations were noted. The raw data, i.e., the non-anonymised ontologies and some notes, are available upon request.

After a lecture about DOLCE, BFO, and part-whole relations, the lab session with the experiment started with the task to develop a computer ontology (for the time span of 24 hours to hand it in), with as options to start from scratch, to use DOLCE, BFO or GFO, and/or to use the taxonomy of part-whole relations, all made available in their OWLized versions.

One-third chose to start domain ontology development with an OWLized foundational ontology (6 out of 18 ontologies), being either DOLCE or the part-whole relations.

On average, those who commenced with a foundational ontology added more new classes and class axioms, and significantly less object properties than those who started from scratch. No one made the well-known novice error of confusing is-a with part-of, though the ones who did not use a foundational ontology spent some time inventing their own naming scheme for part-whole relations. There were some errors, but none had anything to do with using a foundational ontology or not (e.g., due to OWL 2 DL intricacies). None of the ontologies had the same definition for computer, but the ones that used a foundational ontology were obviously easier to harmonise.

More details—characterisation of participants, description of results, and discussion—are described in the technical report An empirical assessment of the use of foundational ontologies in ontology development [1] (a shorter version is under review at the moment). The comprehensive results show that the ‘cost’ incurred in spending time getting acquainted with a foundational ontology—in casu, DOLCE and a taxonomy of part-whole relations—compared to starting from scratch was more than made up for in size, understandability, and interoperability already within the limited time frame of the experiment.

Aside from further experimentation, the next step is to contemplate how this can be incorporated in extant ontology development methodologies, both in ‘high-level’ methodologies, such as the NeOn Methodology, and in ‘low level’ methodologies that focus on adding the entities, such as OntoSpec and along the line of the example for the African Wildlife Ontology tutorial ontology.

References

[1] C.M. Keet. An empirical assessment of the use of foundational ontologies in ontology development. KRDB Research Centre Technical Report KRDB10-6, Faculty of Computer Science, Free University of Bozen-Bolzano, Italy. December 2010.

Nontransitive vs. intransitive direct part-whole relations in OWL

Confusing is-a with part-of is known to be a common mistake by novice ontology developers. Each time I taught the ontology engineering course, I had included a session of 1-2 hours to explain some basic aspects of part-whole relations and, lo and behold, none of the participants made that mistake in the labs or mini-projects! One awkward thing did pop-up there and at other occasions, though, which had to do with modelling direct parthood that does not go well at the moment, to say the least, for a plethora of reasons. Inclusion of direct parthood is not without philosophical quarrels, and the more I think of it, the more I dislike the relation, but somehow the issue appears often in the context of part-whole relations in ontologies. The observed underlying modelling issue—representing intransitivity versus nontransitivity—holds for any OWL object property anyway, so I will proceed with the general case with an example about giraffes.

Preliminaries

First of all, to clarify terms in the post’s title: INtransitive means that for all x, y, z, if Rxy and Ryz then Rxz does not hold; formally \forall x, y, z (R(x,y) \land R(y,z) \rightarrow \neg R(x,z) and an option to state this in a Description Logic is to use role chaining: R \circ R \sqsubseteq \neg R NONtransitive means that we cannot say either way if the property is transitive or intransitive, i.e., in some cases is may be transitive but not in other occasions. Direct parthood is to be understood as follows: if some part x is a direct part of a y, then there is no other object z such that x is a part of z and z is a part of y; formally, \forall x,y (dpo(x, y) \equiv \neg \exists z (partof(x,z) \land partof(z,y))) . If direct parthood is in- or non-transitive is beside the point at this stage, so let us look now at what happens with it in an OWL ontology when one tries to model it one way or another.

The OWL ontology and the reasoner

Given that I used the African Wildlife Ontology as a tutorial ontology earlier and the theme appeals to people, I will use it again here. Depending on what we do with the direct parthood relation in the ontology, Giraffe is, or is not, classified automatically as a subclass of Herbivore. Herbivore is a defined class, equivalent to, in Protégé 4.1 notation, (eats only plant) or (eats only (is-part-of some plant)), and Giraffe is a subclass of both Animal and eats only (leaf or Twig). Leaves are part of a twig, twigs of a branch, and branches of a tree that in turn is a subclass of plant. The is-part-of is, correctly according to mereology, included in the ontology as being transitive. Instead of all the is-part-of and is-proper-part-of between plant parts and plants in the AfricanWildlifeOntology1.owl, we model them using direct-part. AfricanWildlifeOntology4a.owl has direct-part as sister object property to is-part-of, AfricanWildlifeOntology4b.owl has it as sub-object property of is-part-of, and neither ontology has any “characteristics” (relational properties) checked for direct-part. Before running the reasoner to classify the taxonomy, what do you think will happen with our Giraffe in both cases?

In AfricanWildlifeOntology4a.owl, Giraffe is still a mere direct subclass of Animal, whereas with AfricanWildlifeOntology4b.owl, we do obtain the (desired) deduction that Giraffe is a Herbivore. That is, we obtain different results depending on where we put the uncharacterized direct-part object property in the RBox. Why is this so?

By not clicking the checkbox “transitive”, an object property is non­-transitive, but not in-transitive. In fact, we cannot represent explicitly that an object property is intransitive in OWL (see OWL guide and related documents). If we put the object property at the top level (or, as in Protégé 4.1, as immediate subproperty of topObjectProperty), then we obtain the behaviour as if the property were intransitive (and therefore Giraffe is not classified as a subclass of Herbivore). However, the direct-part property is really nontransitive in the ontology. When direct-part is put as subproperty of is-part-of, then it inherits the transitivity characteristic from is-part-of and therefore Giraffe is classified as a Herbivore (because now leaf and Twig are part of plant thanks to the transitivity).

Obviously, it holds for any OWL/OWL2 object property that one cannot assert intransitivity explicitly, that an object property’s characteristics are inherited to its subproperties, and this kind of behaviour of nontransitive object properties depends on where you place it in the RBox—whether you like it or not.

How to go forward?

Direct parthood is called isComponentOf in the componency ontology design pattern and is a subproperty of isPartOf. Its inverse is called haspart_directly in the W3C best practices document on Simple Part-Whole relations [1], and is a subproperty of the transitive haspart. The componency.owl notes that isComponentOf is “hasPart relation without transitivity”, the ODP page’s “intent” of the pattern is that it is intended to “represent (non-transitively) that objects either are proper parts of other objects, or have proper parts”, and the W3C best Practices note that, unlike mereological parthood, it is “not transitive”. Hence, if you include either one in your OWL ontology, you will not obtain the intended behaviour. Therefore, I do not recommend using either suggestion.

Setting aside the W3C’s best practices motivation for inclusion of haspart_directly—easier querying for immediate parts, but for the ontology purist this ought not to be the motivation for its inclusion—it is worth digging a little deeper into the semantics of the direct parthood. Maybe a modeller actually wants to represent collections with their members, like each Fleet has as direct parts more than one Ship, or constitution of objects, like clay is directly part of some vase? In both cases, however, we deal with meronymic part-whole relations, not mereological ones (see [2] and references therein); hence, they should not be subsumed by the mereological part-of relation anyway. They can be modelled as sister properties of the part-of relation and have the intended nontransitive behaviour as in, e.g., the pwrelations.owl ontology with a taxonomy of part-whole relations (that can be imported into the wildlife ontology).

Alternatively, there is always the option to choose a sufficiently expressive non-OWL language to represent the direct parthood and the rest of the subject domain and use one of the many first/second order theorem provers.

References

[1] Alan Rector and Chris Welty. Simple Part-Whole relations in OWL ontologies. W3C Editor’s draft, 11 August 2005.

[2] C. Maria Keet and Alessandro Artale. Representing and Reasoning over a Taxonomy of Part-Whole Relations. Applied Ontology, 2008, 3(1-2): 91-110.