Modelling issues and choices in the development of the Data Mining OPtimization ontology

The Data Mining OPtimization ontology (DMOP) is a sizeable ontology with about 600 classes, over 1000 subclass axioms, more than 100 object properties, 40 object sub-property axioms and about 10 property chains, and thus uses several SROIQ/OWL 2DL features. The ontology contains detailed knowledge represented about data mining tasks, algorithms, hypotheses (mined models or patterns), workflows, and data with its characteristics. Such detailed knowledge is required to meet its high-level aim: to support informed decision-making in the knowledge discovery process. While the ontology can be used as a reference by data miners, its primary purpose—at least, the main motivation why it was developed—is automation of algorithm and model selection that relies heavily on semantic meta-mining [1] (ontology-based meta-analysis where data mining experiments are conducted, annotated, and mined and analysed, and from that patterns are extracted about data mining performance). Unlike other data mining ontologies, DMOP helps proposing not just any set of valid workflows, but optimal workflows, thanks to all this detailed knowledge about data mining. (DMOP was developed in the EU FP7 e-lico project and is used in such a system that proposes relatively optimal workflows.)

DMOP’s development was no trivial exercise, however, and several modeling problems popped up that required use of OWL 2 DL features and started to stretch the recent performance improvements of the automated reasoners. A summary of the ontology and a description, discussion, and solution of those issues—or: the choices we made for version 5.3 of the ontology—is described in our OWLED’13 paper Modeling issues and choices in the Data Mining OPtimization Ontology [2], which was co-authored with Agnieszka Lawrynowicz (from uni of Poznan, who will present the paper at OWLED’13), Claudia d’Amato (uni of Bari), and Melanie Hilario (uni of Geneva, Axone, and e-lico coordinator).

The main issues we describe in the paper are about meta-modelling and punning, property chains, aligning DMOP to a foundational ontology, and qualities and attributes (and data properties). The meta-modelling topic arose primarily because of the ontological status of Algorithm: is it a class or an instance, and what are the consequences of modeling it either way? Generally, one would consider an algorithm to be an instance, and it can have zero or more implementations that are also instances. In addition, it can take types of inputs (data mining data sets) and outputs (data mining hypotheses), but one cannot assert an axiom that involves both an instance and a class other than instantiation (which is not applicable for an algorithm’s input and output).  In the end, we settled for OWL 2’s punning feature (for details and arguments, refer to the paper).

There is a brief section about property chains, its issues, and that they were resolved. A detailed description how this was done, as well as a generalization of and theoretical foundation for it, was described in my EKAW’12 paper [3] (there’s an informal introduction in an earlier blog post). There were chains that caused undesirable deductions, which are resolved in v5.3 of DMOP using the tests described in [3]. The chains themselves do not exceed the use of three object properties, i.e., two on the left-hand side of the inclusion, yet some nifty desirable inferences can be made now.

Linking DMOP to a foundational ontology does introduce several modelling issues besides the linking of DMOP classes and properties to the categories and relationship in the chosen foundational ontology. These include whether to import or to extend the foundational ontology (normally: import); whether the whole foundational ontology should be imported or only a relevant section of it (i.e., the need for module extraction); harmonize any expressiveness issues (e.g., the foundational ontology may be too expressive for the purpose of the domain ontology); and what to do with any possible differences in ‘modeling philosophies’ between the two ontologies (e.g., data properties). We ended up importing DOLCE-lite. Linking the data mining classes to DOLCE categories was performed manually, where most of them (like algorithm, software, strategy, task, and optimization problem) were asserted as subclasses of dolce:non-physical-endurant, and their characteristics and parameters are subclasses of dolce:abstract-quality.

A tricky representation issue concerns the ‘attributes’ of entities, such as that each FeatureExtractionAlgorithm has a transformation function that is either linear or non-linear. I’m skipping the arguments here in the blog post (it deserves its own one, and see also the paper), and I jump to the choices we made. Instead of using OWL’s data properties, we went for the ‘foundational ontology way’ of dealing with attributes, where an attribute is not a binary relation between a class and a data type, but an entity itself (subsumed by dolce:quality) that, in turn, is related to a space dolce:region. There is where DOLCE stops, but we needed the data types, so we added a data property hasDataValue from dolce:region to the data type anyType. A section of the ontology is depicted graphically in the next figure.

A section of DMOP with a partial representation of DMOP’s ‘attributes’ (Source: [2]).

For instance, a ModelingAlgorithm has as quality exactly one LearningPolicy (so, LearningPolicy is a subclass of dolce:quality), this LearningPolicy has as quale exactly one abstract region Eager-Lazy, and that Eager-Lazy has as data value at most one anyType data type to record the value of the learning policy of a modeling algorithm. Although this is more cumbersome than with data properties, it makes the ontology much more reusable for a broader set of application scenarios. This comprehensive approach required quite some modeling effort: there are more than 40 DMOP classes made subclass of dolce:abstract-region, and Characteristic (with its 94 subclasses) and Parameter (with 42 subclasses) are subclasses of dolce:abstract-quality, and most are used in class expressions.

A few other choices are briefly mentioned in the paper.

Eventually, these and future improvements to DMOP are expected to pay off in the quality of the meta-miner so that it will compute better optimal workflows.

References

[1] Hilario, M., Nguyen, P., Do, H., Woznica, A., Kalousis, A. Ontology-based meta-mining of knowledge discovery workflows. In: Meta-Learning in Computational Intelligence. Volume 358 of Studies in Computational Intelligence. Springer (2011) 273–315.

[2] Keet, C.M., Lawrynowicz, A., d’Amato, C., Hilario, M. Modeling issues and choices in the Data Mining OPtimisation Ontology. 8th Workshop on OWL: Experiences and Directions (OWLED’13), 26-27 May 2013, Montpellier, France. CEUR-WS vol xx (to appear).

[3] Keet, C.M.. Detecting and Revising Flaws in OWL Object Property Expressions. Proc. of EKAW’12. Springer LNAI vol 7603, pp2 52-266.

Logical and ontological reasoning services?

The SubProS and ProChainS compatibility services for OWL ontologies to check for good and ‘safe’ OWL object property expression [5] may be considered ontological reasoning services by some, but according others, they are/ought to be plain logical reasoning services. I discussed this issue with Alessandro Artale back in 2007 when we came up with the RBox Compatibility service [1]—which, in the end, we called an ontological reasoning service—and it came up again during EKAW’12 and the Ontologies and Conceptual Modelling Workshop (OCM) in Pretoria in November. Moreover, in all three settings, the conversation was generalized to the following questions:

1. Is there a difference between a logical and an ontological reasoning service (be that ‘onto’-logical or ‘extra’-logical)? If so,
   1. Why, and what, then, is an ontological reasoning service?
   2. Are there any that can serve at least as prototypical example of an ontological reasoning service?

There’s still no conclusive answer on either of the questions. So, I present here some data and arguments I had and that I’ve heard so far, and I invite you to have your say on the matter. I will first introduce a few notions, terms, tools, and implicit assumptions informally, then list the three positions and their arguments I am aware of.

Some aspects about standard, non-standard, and ontological reasoning services

Let me first introduce a few ideas informally. Within Description Logics and the Semantic Web, a distinction is made between so-called ‘standard’ and ‘non-standard’ reasoning services. The standard reasoning services—which most of the DL-based reasoners support—are subsumption reasoning, satisfiability, consistency of the knowledge base, instance checking, and instance retrieval (see, e.g., [2,3] for explanations). Non-standard reasoning services include, e.g., glass-box reasoning and computing the least common subsumer, they are typically designed with the aim to facilitate ontology development, and tend to have their own plugin or extension to an existing reasoner. What these standard and non-standard reasoners have in common, is that they all focus on the (subset of first order predicate logic) logical theory only.

Take, on the other hand, OntoClean [4], which assigns meta-properties (such as rigidity and unity) to classes, and then, according to some rules involving those meta-properties, computes the class taxonomy. Those meta-properties are borrowed from Ontology in philosophy and the rules do not use the standard way of computing subsumption (where every instance of the subclass is also an instance of its super class and, thus, practically, the subclass has more or features or has the same features but with more constrained values/ranges). Moreover, OntoClean helps to distinguish between alternative logical formalisations of some piece of knowledge so as to choose the one that is better with respect to the reality we want to represent; e.g., why it is better to have the class Apple that has as quality a color green, versus the option of a class GreenObject that has shape apple-shaped. This being the case, OntoClean may be considered an ontological reasoning service. My SubProS and ProChainS [5] put constraints on OWL object property expressions so as to have safe and good hierarchies of object properties and property chains, based on the same notion of class subsumption, but then applied to role inclusion axioms: the OWL object sub-property (relationship, DL role) must be more constrained than its super-property and the two reasoning services check if that holds. But some of the flawed object property expressions do not cause a logical inconsistency (merely an undesirable deduction), so one might argue that the compatibility services are ontological.

The arguments so far

The descriptions in the previous paragraph contain implicit assumptions about the logical vs ontological reasoning, which I will spell out here. They are a synthesis from mine as well as other people’s voiced opinions about it (the other people being, among others and in alphabetical order, Alessandro Artale, Arina Britz, Giovanni Casini, Enrico Franconi, Aldo Gangemi, Chiara Ghidini, Tommie Meyer, Valentina Presutti, and Michael Uschold). It goes without saying they are my renderings of the arguments, and sometimes I state the things a little more bluntly to make the point.

1. If it is not entailed by the (standard, DL/other logic) reasoning service, then it is something ontological.

Logic is not about the study of the truth, but about the relationship of the truth of one statement and that of another. Effectively, it doesn’t matter what terms you have in the theory’s vocabulary—be this simply A, B, C, etc. or an attempt to represent Apple, Banana, Citrus, etc. conformant to what those entities are in reality—as it uses truth assignments and the usual rules of inference. If you want some reasoning that helps making a distinction between a good and a bad formalisation of what you aim to represent (where both theories are consistent), then that’s not the logician’s business but instead is relegated to the domain of whatever it is that ontologists get excited about. A counter-argument raised to that was that the early logicians were, in fact, concerned with finding a way to formalize reality in the best way; hence, not only syntax and semantics of the logic language, but also the semantics/meaning of the subject domain. A practical counter-example is that both Glimm et al [6] and Welty [7] managed to ‘hack’ OntoClean into OWL and use standard DL reasoners for it to obtain de desired inferences, so, presumably, then even OntoClean cannot be considered an ontological reasoning service after all?

2. Something ‘meta’ like OntoClean can/might be considered really ontological, but SubProS and ProChainS are ‘extra-logical’ and can be embedded like the extra-logical understanding of class subsumption, so they are logical reasoning services (for it is the analogue to class subsumption but then for role inclusion axioms).

This argument has to do with the notion of ‘standard way’ versus ‘alternative approach’ to compute something and the idea of having borrowed something from Ontology recently versus from mathematics and Aristotle somewhat longer ago. (note: the notion of subsumption in computing was still discussed in the 1980s, where the debate got settled in what is now considered the established understanding of class subsumption.) We simply can apply the underlying principles for class-subclass to one for relationships (/object properties/roles). DL/OWL reasoners and the standard view assume that the role box/object property expressions are correct and merely used to compute the class taxonomy only. But why should I assume the role box is fine, even when I know this is not always the case? And why do I have to put up with a classification of some class elsewhere in the taxonomy (or be inconsistent) when the real mistake is in the role box, not the class expression? Differently, some distinction seems to have been drawn between ‘meta’ (second order?), ‘extra’ to indicate the assumptions built into the algorithms/procedures, and ‘other, regular’ like satisfiability checking that we have for all logical theories. Another argument raised was that the ‘meta’ stuff has to do with second order logics, for which there are no good (read: sound and complete) reasoners.

3. Essentially, everything is logical, and services like OntoClean, SubProS, ProChainS can be represented formally with some clearly, precisely, formally, defined inferencing rules, so then there is no ontological reasoning, but there are only logical reasoning services.

This argument made me think of the “logic is everywhere” mug I still have (a goodie from the ICCL 2005 summer school in Dresden). More seriously, though, this argument raises some old philosophical debates whether everything can indeed be formalized, and provided any logic is fine and computation doesn’t matter. Further, it conflates the distinction, if any, between plain logical entailment, the notion of undesirable deductions (e.g., that a CarChassis is-a Perdurant [some kind of a process]), and the modeling choices and preferences (recall the apple with a colour vs. green object that has an apple-shape). But maybe that conflation is fine and there is no real distinction (if so: why?).

In my paper [5] and in the two presentations of it, I had stressed that SubProS and ProChainS were ontological reasoning services, because before that, I had tried but failed to convince logicians of the Type-I position that there’s something useful to those compatibility services and that they ought to be computed (currently, they are mostly not computed by the standard reasoners). Type-II adherents were plentiful at EKAW’12 and some at the OCM workshop. I encountered the most vocal Type-III adherent (mathematician) at the OCM workshop. Then there were the indecisive ones and people who switched and/or became indecisive. At the moment of writing this, I still lean toward Type-II, but I’m open to better arguments.

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] F. Baader, D. Calvanese, D. L. McGuinness, D. Nardi, and P. F. Patel-Schneider (Eds). The Description Logics Handbook. Cambridge University Press, 2009.

[3] Pascal Hitzler, Markus Kroetzsch, Sebastian Rudolph. Foundations of Semantic Web Technologies. Chapman & Hall/CRC, 2009,

[4] Guarino, N. and Welty, C. An Overview of OntoClean. In S. Staab, R. Studer (eds.), Handbook on Ontologies, Springer Verlag 2009, pp. 201-220.

[5] Keet, C.M. Detecting and Revising Flaws in OWL Object Property Expressions. Proc. of EKAW’12. Springer LNAI vol 7603, pp2 52-266.

[6] Birte Glimm, Sebastian Rudolph, and Johanna Volker. Integrated metamodeling and diagnosis in OWL 2. In Peter F. Patel-Schneider, Yue Pan, Pascal Hitzler, Peter Mika, Lei Zhang, Jeff Z. Pan, Ian Horrocks, and Birte Glimm, editors, Proceedings of the 9th International Semantic Web Conference, volume 6496 of LNCS, pages 257-272. Springer, November 2010.

[7] Chris Welty. OntOWLclean: cleaning OWL ontologies with OWL. In B. Bennet and C. Fellbaum, editors, Proceedings of Formal Ontologies in Information Systems (FOIS’06), pages 347-359. IOS Press, 2006.

A couple of OWL requirements for using ontologies in Indigenous Knowledge Management Systems

Knowledge about, say, long established agricultural practices, culinary customs and typical dishes (and its ingredient evolution over the centuries), medicinal plants and so on falls under the term indigenous knowledge in South Africa, cultural heritage in Europe (that I wrote about earlier), and traditional knowledge in other countries. Whichever term you prefer, it’s that kind of knowledge that is on the way of being lost due to changes in society. There is consensus to preserve it somehow (and possibly make some money from it along the way). Given that there’s lots of it—hence, lots of data, information, and knowledge, that has to be managed—computing and IT enter the picture.

For South Africa, this is managed through the large-scale project from the Department of Science & Technology’s NIKSO office that aims at building a “national recordal system” and an IT infrastructure (IKMS) to both store and access the indigenous knowledge. Setting up such a system consists of some typical software development themes (following consultation with stakeholders), such as the need for handling varied data formats (documents, images, audio), integration of the existing disparate databases and other IT resources in SA into the IKMS, availability of the information in all 11 official languages, the need for a citizen portal, and so on.

Some of the requirements smelled very much like a possible nice use case for Semantic Web Technologies so as to implement a really state of the art infrastructure with enhanced capabilities compared to standard applications. Ronell Alberts, Thomas Fogwill and I assessed that when I was visiting CSIR-Meraka in August and September 2010 as one of the secondments from the EU FP7 Net2 Project. The assessment of possibilities of using semantic web technologies, including the assessment of maturity for off-the-shelf usage, was accepted at IST-Africa recently [1]. We focused on enhanced querying, semantic browsing, questions answering, multilingual information access, knowledge generation, classification of information, formalisation of scientific knowledge & discovery, and knowledge-based data integration.

This we took a step further by zooming in on the ontologies-part of semantic web technologies for four of the usage scenarios, the selection of which was based on their potential for impact and maturity and inclusion into the IKMS. These are: ontology based querying and browsing; a natural language independent ontology for multilingual data access; support for collaborative knowledge generation; and the formalisation of IK for scientific discovery. More precisely, we investigated the requirements for ontology languages to meet the IKMS needs and how well they are met, if at all. A paper describing the details was just accepted for OWLED’12 [2].

In short: some of the required OWL features include representation of vagueness, mereotopology, modularisation, and extended support for internationalization (i.e., multilingualism) and annotation for collaborative ontology development. Thus, the first three put new requirements on the expressiveness of the OWL language itself, and the latter two formulate requirements akin to ‘usability’ extension for OWL. To motivate it all, we first describe each topic, provide real examples, and a few references to current research and tools, which is then followed by the OWL requirements taking into account the examples and generalizing from them; details can be found in the paper.

Hopefully there will an extensive and useful response at OWLED’12, like the feedback we received at OWLED’07 and DL’07 on the requirements on automated reasoning for bio-ontologies [3]. Obviously, if you have a solution to one or more of the gaps that we had overlooked, please leave a comment or send me an email.

References

[1] Fogwill, T., Alberts, R., Keet, C.M. The potential for use of semantic web technologies in IK management systems. IST-Africa Conference 2012. May 9-11, Dar es Salaam, Tanzania.

[2] Alberts, R., Fogwill, T., Keet, C.M. Several Required OWL Features for Indigenous Knowledge Management Systems. 7th Workshop on OWL: Experiences and Directions (OWLED 2012). 27-28 May, Heraklion, Crete, Greece. CEUR-WS Vol-xxx. 12p.

[3] Keet, C.M., Roos, M., Marshall, M.S. A survey of requirements for automated reasoning services for bio-ontologies in OWL. Third international Workshop OWL: Experiences and Directions (OWLED 2007), 6-7 June 2007, Innsbruck, Austria. CEUR-WS Vol-258. 10p. This was described informally in an earlier post.

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 , with the following instances in our knowledge base , , and , then it deduces correctly that , 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!

The DiDOn method to develop bio-ontologies from semi-structured life science diagrams

It is well-known among (bio-)ontology developers that ontology development is a resource-consuming task (see [1] for data backing up this claim). Several approaches and tools do exists that speed up the time-consuming efforts of bottom-up ontology development, most notably natural language processing and database reverse engineering. They are generic and the technologies have been proposed from a computing angle, and are therefore noisy and/or contain many heuristics to make them fit for bio-ontology development. Yet, the most obvious one from a domain expert perspective is unexplored: the abundant diagrams in the sciences that function as existing/’legacy’ knowledge representation of the subject domain. So, how can one use them to develop domain ontologies?

The new DiDOn procedure—from Diagram to Domain Ontology—can speed up and simplify bio-ontology development by exploiting the knowledge represented in such semi-structured bio-diagrams. It does this by means of extracting explicit and implicit knowledge, preserving most of the subject domain semantics, and making formalisation decisions explicit, so that the process is done in a clear, traceable, and reproducible way.

DiDOn is a detailed, micro-level, procedure to formalise those diagrams in a logic of choice; it provides migration paths into OBO, SKOS, OWL and some arbitrary FOL, and guidelines which axioms, and how, have to be added to the bio-ontology. It also uses a foundational ontology so as to obtain more precise and interoperable subject domain semantics than otherwise would have been possible with syntactic transformations alone. (Choosing an appropriate foundational ontology is a separate topic and can be done wit, e.g., ONSET.)

The paper describing the rationale and details, Transforming semi-structured life science diagrams into meaningful domain ontologies with DiDOn [2], has just been accepted at the Journal of Biomedical Informatics. They require a graphical abstract, so here it goes:

DiDOn consists of two principal steps: (1) formalising the ‘icon vocabulary’ of a bio-drawing tool, which then functions as a seed ontology, and (2) populating the seed ontology by processing the actual diagrams. The algorithm in the second step is informed by the formalisation decisions taken in the first step. Such decisions include, among others, the representation language and how to represent the diagram’s n-aries (with n≥2, such as choosing between n-aries as relationship or reified as classes).

In addition to the presentation of DiDOn, the paper contains a detailed application of it with Pathway Studio as case study.

The neatly formatted paper is behind a paywall for those with no or limited access to Elsevier’s journals, but the accepted manuscript is openly accessible from my home page.

References

[1] Simperl, E., Mochol, M., Bürger, T. Achieving maturity: the state of practice in ontology engineering in 2009. International Journal of Computer Science and Applications, 2010, 7(1):45-65.

[2] Keet, C.M. Transforming semi-structured life science diagrams into meaningful domain ontologies with DiDOn. Journal of Biomedical Informatics. In print. DOI: http://dx.doi.org/10.1016/j.jbi.2012.01.004

The rough ontology language rOWL and basic rough subsumption reasoning

Following the feasibility assessments on marrying Rough Sets with Description Logic languages last year [1,2], which I blogged about before, I looked into ‘squeezing’ into OWL 2 DL the very basic aspects of rough sets. The resulting language is called, rOWL, which is described in a paper [3] accepted at SAICSIT’11—the South African CS and IT conference (which thus also gives me the opportunity to meet the SA research community in CS and IT).

DLs are not just about investigating decidable languages, but, perhaps more importantly, also about reasoning over the logical theories.  The obvious addition to the basic crisp automated reasoning services is to add the roughness component, somehow. There are various ways to do that. Crisp subsumption (and definite and possible satisfiability) of rough concepts have been defined by Jiang and co-authors [4], and there was a presentation at DL 2011 about paraconsistent rough DL [5]. I have added the notion of rough subsumption.

There are two principal cases to consider (the “” before the OWL class name denotes it is a rough class):

• If is asserted in the ontology, what can be said about the subsumption relations among their respective approximations?
• Given a subsumption between any of the lower and upper approximations of C and D, then can one deduce ?

Addressing this raises questions: because being rough or not depends entirely on the chosen properties for C together with the available data, should these two cases be solved only at the TBox level or necessarily include the ABox for it to make sense? And should that be under the assumption of standard instantiation and instance checking, or in the presence of a novel DL notion of rough instantiation and rough instance checking?

These questions are answered in the second part of the paper Rough Subsumption Reasoning with rOWL [3]. In an attempt to make the proofs more readable and because the presence of instances is intuitively tied to the matter, the proofs are done by counterexample, which is relatively ‘easy’ to grasp. But maybe I should have obfuscated it with another proof technique to make the results look more profound.

Last, but not least: just in case you thought there is little motivation to bother with rough ontologies: the hypothesis testing and experimentation described in [2] still holds, and a small example is added to [3].

The succinct paper abstract is as follows:

There are various recent efforts to broaden applications of ontologies with vague knowledge, motivated in particular by applications of bio(medical)-ontologies, as well as to enhance rough set information systems with a knowledge representation layer by giving more attention to the intension of a rough set. This requires not only representation of vague knowledge but, moreover, reasoning over it to make it interesting for both ontology engineering and rough set information systems. We propose a minor extension to OWL 2 DL, called rOWL, and define the novel notions of rough subsumption reasoning and classification for rough concepts and their approximations.

I’ll continue looking into the topic, and more is in the pipeline w.r.t. the logic aspects of rough ontologies (in collaboration with Arina Britz).

References

[1] C. M. Keet. On the feasibility of description logic knowledge bases with rough concepts and vague instances. Proceedings of the 23rd International Workshop on Description Logics (DL’10), CEUR-WS, pages 314-324, 2010. 4-7 May 2010, Waterloo, Canada.

[2] C. M. Keet. Ontology engineering with rough concepts and instances. P. Cimiano and H. Pinto, editors, 17th International Conference on Knowledge Engineering and Knowledge Management (EKAW’10), volume 6317 of LNCS, pages 507-517. Springer, 2010. 11-15 October 2010, Lisbon, Portugal.

[3] C.M. Keet. Rough Subsumption Reasoning with rOWL. SAICSIT Annual Research Conference 2011 (SAICSIT’11), Cape Town, South Africa, October 3-5, 2011. ACM Conference Proceedings. (accepted).

[4] Y. Jiang, J. Wang, S. Tang, and B. Xiao. Reasoning with rough description logics: An approximate concepts approach. Information Sciences, 179:600-612, 2009.

[5] H. Viana, J. Alcantara, and A.T. Martins. Paraconsistent rough description logic. Proceedings of the 24th International Workshop on Description Logics (DL’11), 2011. Barcelona, Spain, July 13-16, 2011.

A few notes on ESWC2011 in Heraklion

It’s the end of a interesting and enjoyable ESWC’11 conference in Heraklion, Crete. Compared to other conferences, there were many keynote speeches (and not all of them that much on the Semantic Web, but interesting nevertheless), and, as usual, there were parallel sessions with (unfortunately) many co-scheduled presentations I would have liked to attend. Here follows a few notes on them (which I might update once travelled back to SA, as this is written rather hastily before departure).

Keynotes

Jim Hendler’s talk was entitled “Why the Semantic Web will never work”—with the quotation marks. There have been quite a few people uttering that sentence, but, in Hendler’s review of the past 10 years, we actually have achieved more in some areas than initially anticipated and more than pessimists thought was feasible. For instance, “the semantic web will never scale”: it does, according to Hendler, as demonstrated, e.g., by participants in the billion triple challenge and the growing LOD data cloud. Or the “folksonomies will win” (as opposed to, at least, structured vocabularies): wrong again, mainly because it does not achieve its goal without “social context” and it lacks the crucial aspect of links between entities. However, these achievements are principally in the bottom part of the Semantic Web layer cake and Hendler claims that the “ontology story is still confused”, although OWL is to a large degree “succeeding as a KR standard”. Key challenges for Hendler include: relating linked data to ontologies, the equivalent of a database calculus for linked data, and the need for providing a means for evaluating reasoning with incomplete and possibly inconsistent data. UPDATE (13-6): Hendler’s slides are on slideshare.

Lars Backstrom, data scientist at Facebook, gave a keynote about analyzing FB data and working toward ranking and filtering news feeds by turning it into a classification problem using a set of properties (localization, relation to actor, and others). Interestingly, Backstrom emphasized that FB is moving toward more structured data, which makes it easier to manage and analyse with the algorithms they are developing. If that is a good thing or not is a separate discussion, especially regarding privacy issues, which was the talk of Abe Hsuan about (clearly, this does not hold only for FB but the web in general). According to Hsuan, “Privacy cannot exist on a lawless Semantic Web”. It was good for several after-talk discussions among the attendees, and the last word on how to deal with all this has not been said and done yet. In this context, someone may want to have a look at episode 3 of The virtual revolution documentary about non-free services on the Web, the TED-talk on The filter bubble, or the less recent Database nation book.

Andraz Tori, CTO of Zemanta, gave a keynote describing some background of the ‘writing help’, as offered by WordPress since recently, whilst trying to avoid wrong usage of it and cleaning up the data. As you may have guessed, I have not used that feature yet when writing my blog posts (and do not see the need for it from my perspective). Prasad Kantamneni from Yahoo! Gave an interactive keynote on HCI applied to the effects of different web interfaces for their search engines—and the consequences on revenue, which was lively and interesting. Seemingly ‘silly little things’ like putting the keyword in boldface in the search results makes a big difference on how a user scans through the results (more efficient), likewise auto-completion that in the end make you read more of the results page.

Last, but most certainly not least, Chris Welty gave the conference dinner keynote, which was entertaining. He described some hurdles they had overcome in building ‘Watson’, a sophisticated question answering engine that finds answers to trivia/general knowledge quizzes for the Jeopardy! game that, in the end, did consistently outperform the national human experts on it. The talk was filled with entertaining mistakes they encountered during the development of Watson, and what it required to fix them. The key message was that one cannot go in a linear fashion from natural language to knowledge management, but one has to use a integration of various technologies to make a successful ‘intelligent’ tool.

Sessions and other things

Normally I have a dense section on the papers presented in the session here, but due to the very busy conference schedule and shortage of free online papers before the conference, I did not get around reading all the papers that I would have liked (and I don’t cite papers I have not read, still roughly following my approach to conference blogging). The one on removing redundancy in ontologies presented by Jens Wissmann [1] was quite interesting, in particular for its creative reuse of computing justifications to remove ‘redundant’ axioms, i.e., those which can be derived from other knowledge represented in the ontology anyway. This was computationally costly, so they also developed another algorithm with better performance; details and experimental results can be found in the paper. My own paper [2] on the experiment of the use of foundational ontologies in ontology engineering was well-received, and generated quite some interest, such as on the quality of the foundational ontologies themselves and how the results presented could translate to their particular domain ontology scenario. I may add something on epistemic queries, computing generalizations, matching 4K ontologies in one year, and cross-lingual ontology mappings (provided I find the time to do so in the upcoming days).

The panel session about e- and open- Government was a bit meager and can be summarized as: Linked Open Data (LOD) is good and catching on well but the integration problems still exist, and we need (at least) structured controlled vocabularies to fix it.

I will close with an announcement that Alexander Garcia-Castro brought under my attention: there will be an “Ontologies come of Age in the Semantic Web” workshop co-located with ISWC’11.

References

[1] Stephan Grimm and Jens Wissmann. Elimination of redundancy in ontologies. In: Proceedings of the 8th Extended Semantic Web Conference (ESWC’11). Heraklion, Crete, Greece, 29 May – 2 June 2011. Springer LNCS 6643, 260-274.

[2] Keet, C.M. The use of foundational ontologies in ontology development: an empirical assessment. In: Proceedings of the 8th Extended Semantic Web Conference (ESWC’11). Heraklion, Crete, Greece, 29 May – 2 June 2011. Springer LNCS 6643, 321-335.

Every American is a NamedPizza

Or: verbalizing OWL ontologies still doesn’t really work well.

Ever since we got the multi-lingual verbalization of ORM conceptual data models (restricted FOL theories) working in late 2005 [1]—well: the implementation worked in the DOGMA tool, but the understandability of the output depended on the natural language—I have been following on and off the progress on solutions to the problem. It would be really nice if it all had worked by now, because it is a way for non-logician domain experts to validate the knowledge represented in the ontology and verbalization has been shown to be very useful for domain experts (mainly enterprise) validating (business) knowledge represented in the ORM conceptual data modeling language. (Check out the NORMA tool for the latest fancy implementation, well ahead of OWL verbalization in English Controlled Natural Language).

Some of my students worked on it as an elective ‘mini-project’ topic of the ontology engineering courses I have taught [SWT at FUB, UH, UCI, UKZN]. They have tried to implement it for OWL into Italian and Spanish natural language using a template-based approach with some additional mini-grammar-engine to improve the output, or in English as a competitor to the Manchester syntax. All of them invariable run, to a greater or lesser extent, into the problems discussed in [1], especially when it comes to non-English languages, as English is grammatically challenged. Now, I do not intend to offend people who have English as first language, but English does not have features like gendered articles (just ‘the’ instead of ‘el’ and ‘la’, in Spanish), declensions (still ‘the’ instead of ‘der’ ‘des’, ‘dem’, ‘den’ depending on the proposition, in German), conjunction depending on the nouns (just ‘and’ instead of ‘na’, ‘ne’, ‘no’ that is glued onto the second noun depending on the first letter of that noun, in isiZulu), or subclauses where the verb tense changes by virtue of being in a subclause (in Italian). To sort out such basic matters to generate an understandable pseudo-natural language sentence, a considerable amount of grammar rules and a dictionary have to be added to a template-based approach to make it work.

But let us limit ourselves to English for the moment. Then it is still not trivial. There is a paper comparing the different OWL verbalizers [2], such as Rabbit (ROO) and ACE, which considers issues like how to map, e.g., an AllValuesFrom to “Each…”, “Every…” etc. This is an orthogonal issue to the multi-lingual aspects, and I don’t know how that affects the user’s understanding of the sentences.

I had another look at ACE, as ACE also has a web-interface that accepts OWL/XML files (i.e., OWL 2). I tried it out with the Pizza tutorial ontology, and it generated many intelligible sentences. However, there were also phrases like (i) “Everything that is hasTopping by a Mushroom is something that is a MozzarellaTopping or that is a MushroomTopping or that is a TomatoTopping.”, the (ii) “Every American is a NamedPizza” mentioned in the title of this post, and then there are things like  (iii) “Every DomainConcept that is America or that is England or that is France or that is Germany or that is Italy is a Country”. Example (iii) is not a problem of the verbalizer, but merely an instance of GIGO and the ontology should be corrected.

Examples (i) and (ii) exhibit other problems, though. Regarding (ii), I have noticed that when (novice) ontologists use an ontology development tool, it is a not uncommon practice to not name the entity fully, probably because it is easy for a human reader to fill in the rest from the context; in casu, American is not an adjective to people, but relates to pizza. A more precise name could have avoided such issues (AmericanPizza), or a new solution to ‘context’ can be devised. The weird “is hasTopping by” is due, I think, to the lexicalization of OWL’s ObjectPropertyRange in ACE, which takes the object property, assumes that to be in the infinitive and then puts it in the past participle form (see the Web-ACE page, section 4). So, if the Pizza Ontology developers had chosen not hasTopping but, say, the verb ‘top’, ACE would have changed it into ‘is topped by’. In idea the rule makes sense, but it can be thwarted by the names used in the ontology.

Fliedl and co-authors [3] are trying to resolve just such issues. They propose a rigid naming convention to make it easier to verbalize the ontology. I do not think it is a good proposal, because it is ‘blaming’ the ontologists for failing natural language generation (NLG) systems, and syntactic sugar (verbalization) should not be the guiding principle when adding knowledge to the ontology. Besides, it is not that difficult to add another rule or two to cater for variations, which is probably what will be needed in the near future anyway once ontology reuse and partial imports become more commonplace in ontology engineering.

Power and Third [4] readily admit that verbalizing OWL is “dubious in theory”, but they provide data that it may be “feasible in practice”. The basis of their conclusion lies in the data analysis of about 200 ontologies, which show that the ‘problematic’ cases seldom arise. For instance, OWL’s SubClassOf takes two class expressions, but in praxis it is only used in the format of SubClassOf(C CE) or SubClassOf(C C), idem regarding EquivalentClasses—I think that is probably due to Protégé’s interface—which makes the verbalization easier. They did not actually build a verbalizer, though, but the tables on page 1011 can be of use what to focus on first; e.g., out of the 633,791 axioms, there were only 12 SubDataPropertyOf assertions, whereas SubClassOf(Class,Class) appeared 297,293 times (46.9% of the total) and SubClassOf(Class,ObjectSomeValuesFrom(ObjectProperty,Class)) 158,519 times (25.0%). Why this distribution is the way it is, is another topic.

Going back to the multi-lingual dimension, there is a general problem with OWL ontologies, which is, from a theoretical perspective, addressed more elegantly with OBO ontologies. In OBO, each class has an identifier and the name is just a label. So one could, in principle, amend this by adding labels for each natural language; e.g., have a class “PIZZA:12345″ in the ontology with associated labels “tomato @en”, “pomodoro @it”, “utamatisi @zulu” and so forth, and when verbalizing it in one of those languages, the system picks the right label, compared to the present cumbersome and error-prone way of developing and maintaining an OWL file for each language. Admitted, this has its limitations for terms and verbs that do not have a neat 1:1 translation, but a fully lexicalized ontology should be able to solve this (though does not do so yet).

It is very well possible that I have missed some recent paper that addresses the issues but that I have not come across. At some point in time, we’ll probably will (have to) develop an isiZulu verbalization system, so anyone who has/knows of references that point to (partial) solutions is most welcome to add them in the comments section of the post.

References

[1] M. Jarrar, C.M. Keet, and P. Dongilli. Multilingual verbalization of ORM conceptual models and axiomatized ontologies. STARLab Technical Report, Vrije Universiteit Brussels, Belgium. February 2006.

[2] R. Schwitter, K. Kaljurand, A. Cregan, C. Dolbear, G. Hart. A comparison of three controlled natural languages for OWL 1.1. Proc. of OWLED 2008 DC. Washington, DC, USA, 1-2 April 2008.

[3] Fliedl, G., Kop, C., Vöhringer, J. Guideline based evaluation and verbalization of OWL class and property labels. Data & Knowledge Engineering, 2010, 69: 331-342.

[4] Power, R., Third, A. Expressing OWL axioms by English sentences: dubious in theory, feasible in practice. Coling 2010: Poster Volume, pages 1006–1013,

Beijing, August 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 and an option to state this in a Description Logic is to use role chaining: .  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, . 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.