Garcia, Jhonatan

Jekjantuk, Nophadol

Pan, Jeff Z.

Ren, Yuan

Information Technology and Nanotechnology

English

Research Archive

Reasoning the FMA Ontologies with TrOWLJeff Z. Pan, Yuan Ren, Nophadol Jekjantuk, and Jhonatan GarciaDepartment of Computing Science, University of Aberdeen,Aberdeen, AB23 3UE, United KingdomAbstract. In this paper, we briefly introduce the TrOWL ontology rea-soning infrastructure and share our experience of using TrOWL to reasonwith various versions of the Foundational Model of Anatomy Ontology(FMA), which are among the most challenging ontologies for DescriptionLogic reasoners.1 TrOWLTrOWL1 is a tractable reasoning infrastructure for the second version of the WebOntology Language, or simply OWL22, which comes with a family of ontologylanguages, including:– OWL2-DL, the most expressive decidable language in the OWL2 family, and– three tractable sub-languages of OWL2-DL, i.e. OWL2-EL, OWL2-QL andOWL2-RL.There are at least three approaches to reasoning in OWL2:1. Sound and complete reasoning in OWL2-DL. Until recently, no OWL2-DLreasoners could classify the FMA ontology, due to the high worst case com-plexity of OWL2-DL (2NEXP-TIME-complete). In 2010, Glimm et. al. [2]proposed the core blocking optimisation, enabling HermiT3 to classify theTBox of the FMA-Constitutional ontology in about 30 minutes [4].2. Sound and complete reasoning in OWL2-EL, OWL2-QL and OWL2-RL.Although these sub-languages are tractable, none of them are sufficientlyexpressive to cover FMA.3. Approximate reasoning for OWL2-DL. The idea here is to approximateOWL2-DL ontologies to those in its tractable sub-languages, so as to ex-ploit the efficient and scalable reasoner. In Sections 3 and 4 of the paper, wewill provide more details on the performance of our approximate reasoner inTrOWL for the FMA ontologies.TrOWL supports OWL2 by using the approaches 2 and 3 mentioned above.On the tractable language level, TrOWL contains an OWL2-EL reasoner (REL)1 http://trowl.eu/2 http://www.w3.org/TR/owl2-overview/3 http://www.hermit-reasoner.com/2 Jeff Z. Pan, Yuan Ren, Nophadol Jekjantuk, Jhonatan Garciaand an OWL2-QL reasoner (Quill). The approach of TrOWL is to offer tractablesupport for all the expressive power of OWL2 by using quality guaranteed (interms of soundness and/or completeness) approximate reasoning. TrOWL con-tains an OWL2 profile checker to detect which profile an ontology may fit into.The semantic approximation from OWL2 to OWL-QL is based on the workdescribed in Pan and Thomas [11]. Semantic approximation applies the knowl-edge compilation [18] to precompute the entailment of an arbitrary ontology intoa DL-Lite ontology. In general, this approach is soundness preserving and couldbe incomplete. Furthermore, a conditional completeness condition is identified:if input queries are database style queries, i.e. the variables only bound to namedindividuals, the approach is also complete. In other words, database style queriesare not expressive enough to tell the difference between the original OWL2-DLontology and its approximation. A drawback for this approach is that reasonersare required to compute the semantic approximation; therefore, the constructionof the approximation is usually done off-line.The syntactic approximation from OWL2 to OWL2-EL is based on thesoundness preserving approximate reasoning approach presented in Ren et al.[14]. The construction of the approximation is on the syntax and hence can bedone efficiently just before applying approximate reasoning. The idea is not tothrow away the axioms that are beyond OWL2-EL; otherwise, we might sufferfrom low recall — for example, if we naively remove from the Cyc ontology allthe axioms that are beyond OWL2-EL, the recall is only 1% for classification.Therefore, in this approach, we introduce some fresh named classes to representnon-OWL2-EL class expressions. In order to recover the hidden semantics withinthese fresh named classes, some relation between such named classes and exist-ing classes are maintained and some extra completion rules (beyond those inOWL2-EL) are introduced, with the extended set of completion rules still beingtractable. In [14], we reported that the recall of such approximate reasoning isvery high for TBox classification, 100% for most existing benchmark ontologiesexcept the Wine Ontology (99.4%). A further investigation indicates that it isdue to the syntax sensitivity nature of our approach. After adding a furthernormalisation step into TrOWL, the recall for the Wine Ontology is also 100%.TrOWL supports both OWL and Jena APIs. It has a plug-in for the Prote´ge´ontology editor v4.3.2 FMA OntologiesThe Foundational Model of Anatomy Ontology (FMA) [16] is an evolving comput-er-based knowledge source for biomedical informatics, mainly developed by theUniversity of Washington since 1994. The importance of this ontology residesin the fundamental underlining of anatomy in all fields of medicine. Proper in-terpretation of these data relies on an implicit understanding of anatomy. Theinferences entailed in such reasoning call upon cognitive or computational pro-cessing of abstractions about physical entities of the body, making use of rela-tionships that exist among anatomical concepts. Relevance and impact of theReasoning the FMA Ontologies with TrOWL 3File Source File size Cls Props Inds ExpressivityFMA-DLR4 bioontology.org 147.6 Mb 78989 110 139374 ALUIN (D)FMA-FullR4 bioontology.org 37.7 Mb 23597 77 82935 ALCOF(D)FMA-Constitutional [5] 42.1 Mb 41647 148 85 ALCOIF(D)FMA-OWL2G noMTC [4] 261.7 Mb 85005 140 74698 SROIQ(D)FMA-DLR M15 this paper 140Kb 26 133 26 ALCOIF(D)FMA-DLR M26 this paper 225Kb 56 133 56 ALCOIF(D)Table 1. List of FMA ontologiesFMA ontology on its field can now be compared to other well-known medicalontologies such as SNOMED [12] or GALEN [6].Nowadays, the FMA can be viewed as a complex, highly connected networkin which nearly 70,000 anatomical concepts, from over 170,000 frames, are in-terrelated by over 570,000 relationship instances. There have been a numberof approaches [5, 10, 4] to translating the knowledge encapsulated by the FMAontology into the OWL ontology language. Golbreich et al. [4] developed theFMA-OWLizer tool, which can be applied to automatically obtain a translationof the FMA ontology into OWL 2.Given the size and complexity of the FMA ontology, reasoning under OWLhas proven to be a real challenge. Table 1 provides a list of FMA ontologieswritten in OWL that we used in our evaluation.3 FMA with MetamodelingThe FMA features a complex structure of superclasses and subclasses that re-quires the support of metamodeling. For example, “Physical anatomical entity”is an instance of “Anatomical entity template”, and a subclass of both “Anatom-ical entity template” and “Anatomical entity” [1]. In OWL, a class is interpretedas a set of objects. Similarly, a metaclass is interpreted as a set of sets in meta-modeling extensions of OWL, such as OWL-FA [7]. For example, the metaclassVertebra can be interpreted as a set of different types of vertebrae, such as cer-vical, thoracic, lumbar, which in turn can be interpreted as subsets of other sets,e.g., first, ..., fifth lumbar vertebra.There have been several attempts in dealing with metamodeling in FMA.Dameron et al. [1] converted the frame-based FMA ontology into an OWL1-DL version and an OWL1-Full version, with metaclasses included in the latterone. Golbreich et al. [5] tried to capture (some of) the knowledge encoded atmetaclasses differently in OWL1-DL directly (cf. the FMA-Constitutional on-tology in Table 1). The idea is to replace instance-of links between a class andits metaclasses with subClassOf links. The structure of their instances, property4 http://www.bioontology.org/wiki/index.php/FMAInOwl5 http://homepages.abdn.ac.uk/jeff.z.pan/pages/onto/fma-dlr-m1.owl6 http://homepages.abdn.ac.uk/jeff.z.pan/pages/onto/fma-dlr-m2.owl4 Jeff Z. Pan, Yuan Ren, Nophadol Jekjantuk, Jhonatan Garciarestrictions of metaclasses are interpreted as closure axioms and approximatedby universal restrictions while restrictions of classes are translated into existen-tial restriction. Later on, Golbreich et al. further encoded the FMA ontologyin OWL2-DL, producing two ontologies, one with metaclasses and one withoutthem. The idea is to use the OWL 2 metamodeling capability, i.e., punning,to represent metaclasses, using the same URI to refer to a class and an indi-vidual at the same time in FMA-OWL2G MT. For example, the name Heartcan be used both for the metaclass Heart and for the class Heart, instance ofOrgan with cavitated organ parts.The drawback of the punning approach is that, although a class and anindividual can share the same name, say C, they are treated as different entities.For example, even if the class C is entailed to be equivalent to a class D, theindividuals C and D can still be different. This has been regarded as non-intuitivedue to the lack of expected entailments (e.g., the individuals C and D should bethe same). To deal with this problem, we apply the class-based approach fromGlimm et al. [3] to enrich some small (but already challenging for DL reasoners)subsets of FMA-DLR ontology and accommodate metaclasses (cf. the last twoontologies in Table 1) with the Typing and MatSubClass functions proposedin [3].Ontology RT FaCT++ HermiT TrOWL MORe RecallFMA-DLR C 32.425 s 46.94 s 32.596 s 47.794 s 100%FMA-FullR C 121.041 s 1064.947 s 4.45 s 4.571 s 100%FMA-Constitutional C t/o 3043.61 s 155.808 s t/o 100%FMA-OWL2G noMTC C o/m t/o 967.59 s t/o N/AFMA-DLR M1 M 932.5 s 26.39 s 0.819 s N/A 100%FMA-DLR M2 M t/o 737.43 s 2.863 s N/A 100%Table 2. Reasoning with FMA ontologies via OWL API (‘RT’ for Reasoning Task,‘C’ for Classification, ‘M’ for Materialisation, ‘s’ for second, ‘t/o’ for time out after onehour, ‘o/m’ for out of memory)Table 2 lists the classification (for the first four ontologies) and materialisa-tion (for the last two ontologies) time (reasoning time + retrieving time) fromsome of the state of the art DL reasoners (including FaCT++ v1.6.2, HermiTv1.3.8, TrOWL v1.3 and MORe v0.1.3 [15]) over the FMA ontologies in Table1. The machine used for the experiment is a MacBook, with CPU 2.26 core 2duo, Ram 8 GB and 6 GB allocated to JVM. The last column of Table 2 reportsthe recall (on the number of subsumptions among named classes) of TrOWLwith respect to results of HermiT. Note that FaCT++ had a datatype error forthe FMA-DLR ontology, so we did not import the FMA-DLR ontology into theFMA-FullR ontology when testing FMA-FullR. Moreover, as MORe does notsupport ABox reasoning, its time with the FMA-DLR M1 and FMA-DLR M2ontologies is not reported.Reasoning the FMA Ontologies with TrOWL 54 Dealing with Unsatisfiable Concepts in FMAConstitutionalAn ontology is called incoherent [17] if it contains unsatisfiable concepts, whichare equivalent to the bottom concept ⊥ and can not have any instance. Unsatis-fiable named concepts (except the bottom concept ⊥) in a constructed ontologyusually indicates possible design flaws. For example, 33,433 out of 41,648 con-cepts are unsatisfiable in the FMA-Constitutional ontology. This was apparentlynot intended since the current version of FMA has already eliminated all theseunsatisfiabilities.Understanding ontology incoherence is not trivial. Incoherence can usually beexplained and resolved by computing justifications [8], i.e., minimal entailment-preserving sub-ontologies. However, computing justifications with a black-boxalgorithm requires a large number of entailment checking, which can be expensivegiven the complexity of reasoning and size of the ontology. Also, looking into33,433 justifications to debug the ontology will be very time consuming.We notice that some of the concepts are unsatisfiable due to other unsatis-fiable concepts. For example in FMA-Constitutional we can infer Neuron v ⊥and Central neuron v Neuron, hence we also have Central neuron v ⊥. Inthis case, Central neuron is unsatisfiable due to the unsatisfiability of Neuron.Such a phenomena has been formally characterised by Kalyanpur et al. [9] asroot and derived unsatisfiable concepts. Particularly, A is a derived unsatisfiableconcept if there is a justification for A v ⊥ that contains a justification forB v ⊥, where B is another unsatisfiable concept, and B is called the parent ofA. Otherwise, A is a root unsatisfiable concept.The REL reasoner in TrOWL is using a forward-chaining completion-basedalgorithm, in which each rule infers a set of consequence axioms from a setof antecedence axioms. Such an algorithm can be easily extended to computejustifications on the fly by incorporating a truth-maintenance system (TMS) [13].However naively applying such a solution has the following limitations:1. For big and complex ontologies, maintaining the entire in TMS is a bigoverhead on reasoning. In fact, we are only interested in justifications forunsatisfiability but not the others so a fully-fledged TMS is unnecessary.2. Repairing all the root unsatisfiabilities cannot always repair all the derivedunsatisfiabilities because a derived unsatisfiability may have another justi-fication that depends on no other unsatisfiability. In this case, one need toiteratively reclassify, debug and repair. For difficult ontologies such as FMAConstitutional, we would like to minimise the number of such iterations.In order to improve efficiency, we introduce Type I and Type II unsatisfiableconcepts as approximations to the root and derived unsatisfiable concepts withthe following procedure in REL:1. When a rule infers A v ⊥, if the antecedences contain B v ⊥, where bothA and B are named concepts in the original ontology, we label A as a TypeII unsatisfiable concept. Otherwise, we label A as a Type I unsatisfiableconcept.6 Jeff Z. Pan, Yuan Ren, Nophadol Jekjantuk, Jhonatan Garcia2. We continue reasoning on Type II concepts regardless their unsatisfiability,and label them with Type I if possible. They will not be treated immediatelyas sub-concept of all concepts.The above point 2 is important to explore alternative derivation of unsatisfiabil-ity for Type II concepts. If such a derivation does not depend on other unsatis-fiability, the concept will be labeled Type I as well. It is possible for a derivedunsatisfiable concept to be labeled earlier than its parent, making it mistakenlylabeled as a Type I. For example, considering the following axiom:A v B, (1)B v C, (2)B v ¬C, (3)if we infer A v C from (1) and (2), then A v ¬C from (1) and (3), andthen A v ⊥, then we have A as a Type I unsatisfiable concept. To avoid suchsituations as much as possible, we apply a depth-first classification strategy,always classifying super-concepts before classifying sub-concepts.Using the above mechanism we are able to distinguish the different types ofunsatisfiable concepts in the FMA-Constitutional. Results show that only 145concepts belong to Type I, which is only 0.43% of all the unsatisfiable concepts.By examining their justifications, we realise that they are due to similar reasons.Particularly, there is a boolean-valued functional datatype property has massin the ontology. With the axioms in FMA Constitutional, it is possible to in-fer both A v ∃has mass.{true} and A v ∃has mass.{false} for concept A,making A unsatisfiable. Another boolean-valued functional datatype propertyhas inherent 3-D shape has a similar problem. There are in total only 6 con-cept axioms with these two properties. Debugging these 6 axioms is apparentlymuch easier than debugging all the 122,136 logical axioms, or the justificationsof all the 33,433 unsatisfiable concepts.5 Conclusion and OutlookThis paper briefly introduces the TrOWL ontology reasoning infrastructure. Ourevaluations with the FMA ontologies indicate that approximate reasoners canbe useful for reasoning and debugging complex ontologies. The tested FMAontologies are only some of the existing ones. We will further test more FMAontologies, in particular those related to metamodeling.References1. O. Dameron, D. L. Rubin, and M. A. Musen. Challenges in converting frame-basedontology into OWL: the Foundational Model of Anatomy case-study. In the Proc.of the AMIA Annual Symposium, 2005.2. Birte Glimm, Ian Horrocks, and Boris Motik. Optimized description logic reasoningvia core blocking. In IJCAR, pages 457–471, 2010.Reasoning the FMA Ontologies with TrOWL 73. Birte Glimm, Sebastian Rudolph, and Johanna Vo¨lker. Integrated metamodelingand diagnosis in owl 2. In Proceedings of the 9th International Semantic WebConference, volume 6496 of LNCS, pages 257–272. Springer, November 2010.4. C. Golbreich, J. Grosjean, and S. J. Darmoni. The fma in owl 2. In Proceedings ofthe 13th conference on Artificial intelligence in medicine, AIME’11, pages 204–214,Berlin, Heidelberg, 2011. Springer-Verlag.5. Christine Golbreich, Songmao Zhang, and Olivier Bodenreider. The foundationalmodel of anatomy in owl: Experience and perspectives. J. Web Sem., 4(3):181–195,2006.6. 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In theProc. of the 22nd National Conference on Artificial Intelligence (AAAI-07), pages1434–1439, 2007.12. Stearns M. Q., Price C., Spackman K. A., and Wang A. Y. Snomed clinicalterms: overview of the development process and project status. In Proceedingsof the AMIA Symposium, American Medical Informatics Association, pages 662–666, 2001.13. Yuan Ren and Jeff Z Pan. Optimising ontology stream reasoning with truth main-tenance system. In Proceedings of the 20th ACM international conference on In-formation and knowledge management, pages 831–836. ACM, 2011.14. Yuan Ren, Jeff Z. Pan, and Yuting Zhao. Soundness Preserving Approxima-tion for TBox Reasoning. In the Proc. of the 25th AAAI Conference Conference(AAAI2010), 2010.15. Ana Armas Romero, Bernardo Cuenca Grau, and Ian Horrocks. More: Modularcombination of owl reasoners for ontology classification. In Proceedings of the 11thInternational Semantic Web Conference (ISWC 2012), LNCS. Springer, 2012.16. Cornelius Rosse and Jose´ L. V. Mejino Jr. A reference ontology for biomedical in-formatics: the foundational model of anatomy. Journal of Biomedical Informatics,36(6):478–500, 2003.17. Stefan Schlobach and Ronald Cornet. Non-standard reasoning services for thedebugging of description logic terminologies. In IJCAI, pages 355–362. MorganKaufmann, 2003.18. Bart Selman and Henry Kautz. Knowledge compilation and theory approximation.J. ACM, 43(2):193–224, March 1996.

Reasoning the FMA ontologies with TrOWL

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Reasoning the FMA ontologies with TrOWL

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