=Paper=
{{Paper
|id=Vol-1912/paper6
|storemode=property
|title=Applying Description Logics Extended with Meta-modelling to SNOMED-CT
|pdfUrl=https://ceur-ws.org/Vol-1912/paper6.pdf
|volume=Vol-1912
|authors=Regina Motz,Edelweis Rohrer,Paula Severi
|dblpUrl=https://dblp.org/rec/conf/amw/MotzRS17
}}
==Applying Description Logics Extended with Meta-modelling to SNOMED-CT==
https://ceur-ws.org/Vol-1912/paper6.pdf
Applying description logics extended with
meta-modelling to SNOMED-CT
Regina Motz1 , Edelweis Rohrer1 , and Paula Severi2
1
Instituto de Computación, Facultad de Ingenierı́a,
Universidad de la República, Uruguay
{rmotz, erohrer}@fing.edu.uy
2
Department of Computer Science, University of Leicester, England
pgs11@leicester.ac.uk
Abstract. SNOMED-CT is a clinical and medical ontology that covers a wide
range of concepts in the health domain. It is mostly used as a standard vocabulary
to be referenced in electronic health records of patients. The SNOMED-CT on-
tology has been formalized with a description logic, the Web Ontology language
OWL 2 profile OWL-EL. To integrate electronic health records to SNOMED-
CT in an OWL-EL ontology, references to SNOMED-CT concepts in these
records are modelled as instances of the referenced concepts. In this paper, the
ontological model of this integration is analyzed. As our main contribution, we
propose to give solution to some problems of this integration by defining a meta-
model layer of SNOMED-CT with its concepts represented also as individuals,
using an approach of description logics extended with meta-modelling.
1 Introduction
SNOMED-CT is a clinical and medical ontology that covers a wide range of concepts
in the health domain, such as diseases, diagnotics and treatments [10, 23]. It has been
formalized with the Web Ontology language OWL 2 profile OWL-EL, which is a
lightweight description logic with some modelling restrictions that improve reasoning
efficiency and scalability [13, 24, 25]. The building blocks of all description logics are
concepts, roles and individuals [2, 7]. The OWL-EL SNOMED-CT ontology has con-
cepts, such as Disease that subsumes HeartDisease and Endocarditis, and roles,
such as f indingSite that represents where diseases are located. However, it has not
individuals.
SNOMED-CT is mostly used as a standard vocabulary to be referenced in electronic
health records of patients [4, 12, 19, 21]. In most case studies, an ontology of electronic
health records of patients referencing SNOMED-CT terms is modelled with individuals,
that represent such references and instantiate the SNOMED-CT concepts [3, 4, 19]. Fig-
ure 1 illustrates the electronic health records of two patients Juan and P edro, who suf-
fer endocarditis. Ovals represent concepts, bullets represent individuals and arrows rep-
resent roles. The individuals juanEHRendocarditis, juanEHRendocardium and
juanEHRinf lammation, instances of the concepts Endocarditis, Endocardium
and Inf lammation, are just the references to these concepts in the electronic health
Fig. 1: Integration of Electronic Health Records with SNOMED-CT
records of Juan. Moreover, the individuals are linked through instances of roles, such as
f indingSite and associatedM orphology.
In the present work, the ontological model of SNOMED-CT is analyzed. In particular,
we study the integration of SNOMED-CT to electronic health records, as sketched in
Figure 1. There exist several works which criticize the logical structure of SNOMED-
CT and its integration to electronic health records, and propose some changes to the
model of SNOMED-CT [20–22]. However, we argue that a more realistic approach is
to keep SNOMED-CT unchanged and add an upper view by representing its concepts
also as individuals. As a result, we conceptualize the health domain at a higher level of
abstraction and introduce a different approach to solve some of the identified problems.
To formalize our proposal, we need a logic which allows us to represent the same real
object as an individual and as a concept, for example, the term Endocarditis as a con-
cept (as in SNOMED-CT) and also as an individual. Standard description logics, and
in particular OWL-EL, are not expressive enough to model this scenario. Hence, we
use our approach of description logics extended with meta-modelling [14, 16, 17], that
allows to express that an individual corresponds to a concept through meta-modelling.
We adjust this extension to allow that concept names to be treated also as individuals.
The main contribution of the present work is to enrich the logical model of the SNOMED-
CT ontology with meta-modelling, to enhance its the integration with electronic health
records. Our solution prevents from possible mistakes in the population of the SNOMED-
CT concepts with references of electronic health records.
The remainder of this paper is organized as follows. Section 2 presents some related
work about SNOMED-CT. Section 3 outlines the meta-modelling extension to descrip-
tion logics. In Section 4 we explain our proposal of integration of SNOMED-CT to
electronic health records using the meta-modelling extension presented in Section 3.
Finally, Section 5 presents some conclusions and future work.
2 Related work
In this section, we present some related work about SNOMED-CT.
Despite nowadays SNOMED-CT is broadly used in several health applications, the
correctness of its logical structure is questioned in several works. Schulz et al. [22]
describe several structural problems. Among others, since SNOMED-CT concepts were
thought as a node hierarchy, and not as ontological concepts, they say that nodes could
be concepts, meta-concepts, individuals or roles. They found that the role-group relation
hides roles such as has-part, and that the concept hierarchy subsumption is overloaded,
instead of defining roles. They propose to represent SNOMED-CT using the description
logic EL++ , to add the part-of role, symmetric and reflexive roles, and domain and
range axioms.
Schulz et al. [21] distinguish three ways to instantiate SNOMED-CT concepts: (i) with
real instances in patients (standard interpretation) (ii) with references to SNOMED-CT
concepts in electronic health records (EHR interpretation) or (iii) with patients affected
by a disease (epidemiological interpretation). They consider as correct the standard
interpretation, but the EHR interpretation, that we take in the present work, is the more
feasible to be implemented.
Rector et. al. [19] analyze a mechanism for using generic information models, such us
HL7 RIM or OpenEHR [3], with different code systems, as SNOMED-CT or ICD [1].
They identify three elements, (i) electronic healthcare records messages, implemented
according to an information model (ii) an ontology or “model of meaning”, such as
SNOMED-CT, where instances of its concepts are the references in health records,
for example “John Smith’s diabetes” and (iii) the coding system of the ontology, that
“should be a meta model of the model of meaning”, where each code (referenced in
records messages) is associated to a concept. They propose that the three elements to
be separated, with interfaces between the application and each code system.
Schulz et al. [20] analyze SNOMED-CT complex concepts such as the following:
ExtrOf F oreignBodyF romStomachByExcision ≡
∃hasP art(∃procedureSite.StomachStructureu
∃method.IncisionAction)u
(1)
∃hasP art(∃procedureSite.StomachStructureu
∃directM orphology.F oreignBodyu
∃method.RemovalAction)
They observe that instances of the concept StomachStructure in the first existential
can be different from instances of StomachStructure in the second existential, and
that these “stomachs” could belong to different patients, but they do not give solution,
by using OWL-EL, to this kind of misinterpretations.
The above overview shows that SNOMED-CT have several structural problems, that
nowadays have not been fixed. The definition (1) shows that SNOMED-CT also has
problems to be integrated into electronic health records, in the scenario where refer-
ences to SNOMED-CT terms are instances of the SNOMED-CT concepts. The exam-
ple shows that its concepts does not properly describe such references. In Section 4
we introduce an approach for giving a solution to this problem, among others we have
detected.
3 A meta-modelling extension to description logics
In this section we introduce a meta-modelling extension to description logics which
allows to treat a given concept A as an individual.
Example 1. Consider the ontology
DiseaseObject(Endocarditis) Endocarditis v Disease
In the first axiom, the name Endocarditis plays the role of an individual whereas in the
second axiom it plays the role of a concept. This is possible by dropping the syntactic
requirement of description logics that the sets of atomic concepts and individuals should
be disjoint. From the semantical point of view, the interpretation domain cannot consist
of only basic objects, but it can contain sets, sets of sets, etc. The key point of our
semantics is that the interpretation of a given name is the same either as concept or as
individual.
Example 2. Consider the following ontology with meta-modelling:
DiseaseObject(Endocarditis) DiseaseObject v Endocarditis
By the defined semantics, EndocarditisI ∈ DiseaseObjectI ⊆ EndocarditisI
Here the interpretation of Endocarditis belongs to itself, which is nonsense for real
applications. To formalize the intuition of Example 2, some definitions are recalled [16,
17] before defining the notion of model of an ontology with meta-modelling.
Definition 1 (Sn for n ∈ N). Given a non empty set S0 of atomic objects, we define Sn
by induction on N as follows: Sn+1 = Sn ∪ P(Sn )
Definition 2 (Well-founded set). A set X is well-founded if X does not have infinite
3-decreasing sequences, i.e. there is no {xi | i ∈ N} ⊆ X such that xi 3 xi+1 for all
i ∈ N.
It is important to see that the sets Sn are well-founded [17]. In Example 2, the inter-
pretation of Endocarditis is not a well-founded set.
Given a logic L without meta-modelling, with the restriction that the sets of concept,
individual and role names are pairwise disjoint, we denote LM the same logic but
dropping the requirement that the sets of atomic concepts and individuals be disjoint.
We next define the notion of model for the description logic LM, which is L with
meta-modelling.
Definition 3 (Model of an Ontology with meta-modelling). Let an ontology O =
(T , R, A) in the logic LM, with T a TBox, R an RBox and A an ABox. An interpre-
tation I is a model of O (denoted as I |= O) if the following holds:
1. the domain ∆I of the interpretation is a subset of some Sn for some n ∈ N.
2. I satisfies all axioms in O = (T , R, A), i.e. C I ⊆ DI for each C v D in T ,
RI ⊆ S I for each R v S in R, aI ∈ C I for each C(a) in A and (aI , bI ) ∈ RI
for each R(a, b) in A.
The first part of Definition 3 restricts the domain of an interpretation to be a subset of
Sn , so ∆I is well-founded and can now contain sets of objects. The second part of
Definition 3 refers to the semantics for the description logic LM, which is the same as
for L, except that for LM a given symbol can be treated as individual and as concept,
and in both cases it has the same interpretation.
In our previous work, we required that the sets of concepts and individuals should be
disjoint and added new axioms of the form a =m A where a is an individual and A is an
atomic concept [16, 17], to express that a and A have the same interpretation. These two
approaches are equivalent in the sense that it is easy to transform one ontology where
the same name N is used as an individual and as a concept by introducing two new
names: aN for each individual occurrence of N and AN for each concept occurrence
of N , and the axiom aN =m AN . The approach of [16, 17] is suitable for integrating
ontologies where the same real object is represented as an individual in one ontology
and as a concept in the other one (the URI’s will be necessarily different). But it is not
the scenario of our case study, because what we do is to add a new level of abstraction
to the SNOMED ontology, allowing the concept names to be treated as individuals.
A tableau algorithm for checking consistency of an ontology with meta-modelling is
defined in [16, 17], by adding new rules and a new condition to ensure the well-
foundedness of the interpretation domain. This algorithm can be used for an ontology
with meta-modelling for the approach presented here, by applying the transformation
described above.
An exhaustive analysis and comparison of different meta-modelling extensions of de-
scription logics is done in [17]. We now give an overview of that analysis by addressing
two aspects of the language: syntax and semantics.
Fixed layers vs flexible syntax. There exist some approaches which force the user to ex-
plicitly write the information of the meta-modelling layer (or level) in the concept [6,
8, 9, 11, 18]. For example, for the axiom DiseaseObject(Endocarditis) the concept
Endocarditis belongs to the level 1, whereas the concept DiseaseObject has level 2.
A Fixed layer approach has the drawback that it cannot mix levels, i.e., we cannot have
a TBox axiom C v D if C and D belong to different layers. In our meta-modelling
approach the user does not have to write or know the layer of the concept because the
reasoner will infer it for him. Moreover we can mix different meta-modelling levels
in axioms because our reasoner (tableau extended with rules and well-foundess valida-
tion) checks for posible inconsistencies such as non well-founded models. This is more
realistic because in a scenario of evolving ontologies, that need to be integrated, not all
objects of a given class need to have meta-modelling and hence, they do not have to
belong to the same level.
Henkin vs Hilog semantics. The semantics of our meta-modelling approach follows
the style of the Henkin semantics, in which higher order objects have a direct set-
theoretical interpretation via a hierarchy of power sets. In Example 1, the interpretation
of Endocarditis is the same both as individual and as concept. This is also the style of
semantics followed by Pan et al [11, 18]. Conversely, the semantics for meta-modelling
given by Motik, De Giacomo et al. and Homola et al. follows a Hilog style semantics
[5, 8, 9, 15]. In this style of semantics, the same syntactic object can have different in-
terpretations depending on the position or role it plays in a sentence. In Example 1,
the first Endocarditis playing the role of an individual does not always have the same
interpretation as the second Endocarditis which plays the role of a concept. a concept.
The main drawback of Hilog semantics is that it cannot really express that the interpre-
tation of a given symbol taken as individual is the same as the interpretation of another
(or the same) symbol taken as concept. The Hilog style semantics for meta-modelling
is weaker than the Henkin semantics, which allows us to check for inconsistencies such
as that of Example 2, not detected with the Hilog semantics.
The main advantage of our meta-modelling approach is to combine a flexible syntax,
without fixed layers, with a strong semantics, the Henkin semantics. As far as we know,
none of the existing meta-modelling approaches has this characteristic. As a drawback
of our approach we do not consider meta-modelling for roles, as other works do [5, 11,
15, 18].
4 SNOMED-CT with meta-modelling in electronic health records
In this section, we present a different approach for the integration of electronic health
records of patients to SNOMED-CT.
Taking as example the simplified description (2) of the concept Endocarditis, first
of all, we describe some problems we found in the model illustrated in Figure 1, in
which references to SNOMED-CT concepts in electronic health records are visualized
as individuals that are instances of these concepts.
Endocarditis v∃f indingSite.Endocardiumu
(2)
∃associatedM orphology.Inf lammation
General knowledge of the health domain is not represented at the proper level. In
Figure 1, the patients Juan and Pedro have references to the concept Endocarditis,
represented by the instances juanEHRendocarditis and pedroEHRendocarditis.
The TBox axiom (2) is consistent with the following ABox axioms:
f indingSite(juanEHRendocarditis, juanEHRendocardium)
(3)
f indingSite(pedroEHRendocarditis, pedroEHRendocardium)
Since the disease endocarditis will always be located in the endocardium, having these
assertions at the level of each patient does not add any value, since it is general knowl-
edge of the health domain, which does not differ for each patient.
Definitions of SNOMED-CT concepts does not give a real description of references in
electronic health records. The TBox axiom (2) also admits extensions, as illustrated in
Figure 2, for the assertions given below.
f indingSite(juanEHRendocarditis, juanEHRendocardium)
f indingSite(pedroEHRendocarditis, pedroEHRendocardium) (4)
f indingSite(pedroEHRendocarditis, juanEHRendocardium)
Even though the knowledge base is consistent, it does not represent a real situation,
because Pedro suffers endocarditis located in the endocardium of Juan!! In order to
restrict that references to SNOMED-CT concepts to be linked for the same patients,
a more expressive description logic with inverse roles and cardinality restrictions is
needed. Considering that SNOMED-CT is already a large knowledge base and that of
electronic health records is even larger, a more expressive description logic increase the
complexity to exponential, becoming no longer tractable.
Fig. 2: An extension for the definition of the concept Endiocarditis
Some frequent queries about records of patients can return invalid results. Suppose
we want to obtain a chronological report about all clinical situations that affected the
Pedro’s endocardium, for the scenario of Figure 2. If we formulate the query below, we
obtain the instances juanEHRendocardium and pedroEHRendocardium.
q(z) =∃x, y.hasEHRdetail(pedroEHR, x) ∧ hasRef erenceT o(x, y)
(5)
∧ f indingSite(y, z) ∧ Endocardium(z)
From the analysis of the above problems we start elaborating a solution to solve the
identified drawbacks. Several works criticize the logical structure of SNOMED-CT, as
well as the interpretation given to its concepts. In particular, Schulz et al. [20] admit
that SNOMED-CT concepts does not give a real description of references in electronic
health records. However, even though they propose some solutions such as to modify
the structure of SNOMED-CT, or to represent SNOMED-CT in a logic more expressive
than OWL-EL, nowadays SNOMED-CT have the same problems.
As SNOMED-CT is broadly used, we think it is not a realistic approach to change
its structure. In the present paper, we introduce a solution that, instead of changing
SNOMED-CT, adds a layer that represents the same knowledge at an upper level. Our
proposal consists in to treat SNOMED-CT concepts also as individuals, and for the se-
mantics, a given concept name has the same interpretation either as a concept or as an
individual, representing the same real object. Moreover, instead of having references to
diseases as instances of SNOMED-CT concepts, we propose to link instances of elec-
tronic health records directly to the SNOMED-CT terms treated as individuals.
We use the meta-modelling approach described in Section 3, in which the same concept
name plays the role of individual or concept depending on its position in the OWL-EL
axiom. Then, our proposal is to add to SNOMED-CT a layer of ABox axioms that rep-
resent the general health domain knowledge independent from the records of patients.
For each TBox axiom containing an existential restriction, such as the description (2),
we add an ABox axiom to represent the existential connecting SNOMED-CT concept
names treated as individuals through the SNOMED-CT roles. Moreover, records of
patients are linked to the SNOMED-CT individuals. Our solution for the scenario of
Figure 1, illustrated in Figure 3, is given by the following ABox axioms:
hasEHRdetail(juanEHR, juanEHRdet1)
hasRef erenceT o(juanEHRdet1, Endocarditis)
(6)
f indingSite(Endocarditis, Endocardium)
associatedM orphology(Endocarditis, Inf lammation)
With our proposal, to have instances of SNOMED-CT concepts such as
juanEHRendocarditis and juanEHRendocardium, connected by SNOMED-CT
roles becomes unnecessary because now we have this kind of information at the level
of the meta-model layer. The SNOMED-CT terms represented as individuals are now
connected through the SNOMED-CT roles. We argue that the SNOMED-CT meta-
model has some advantages that are explained below.
Facilitates a modular design and reuse. As SNOMED-CT is now broadly used, we
propose a solution that keeps SNOMED-CT as a hierarchy of concepts, favoring the
reuse of existing ontologies. We think the integration of SNOMED-CT in medical ap-
plications can be enhanced by adding a meta-model of the hierarchy of concepts.
Connects patients to medical terms at the proper level. We represent the health do-
main through two different layers with different purposes. In the lower level, we have
the SNOMED-CT ontology that represent the hierarchy of medical terms, distinguish-
ing more general from more specialized concepts. The upper level is defined to link
electronic health records of patients to medical terms. As illustrated in Figure 3, for
the patient Juan there is a record represented by the individual juanEHRdet1 that is
linked to the name Endocarditis treated as individual. To connect the upper with the
lower layer we apply the meta-modelling approach described in Section 3, that maps
a given name to a unique interpretation, either as individual or as concept. In Figure
Fig. 3: SNOMED CT with the meta-model layer
3, the individual Endocarditis and the concept Endocarditis represent the same real
object.
Avoids redundancy of SNOMED-CT role instances. The representation of references to
SNOMED-CT concepts as instances of them has the drawback that roles of SNOMED-
CT link individuals in a redundant way, as showed in (3). It is more intuitive to represent
this kind of knowledge at a more general level, independently of the electronic health
records of patients. So, by representing medical terms as individuals, we avoid to having
SNOMED-CT role instances at the level of each patient. Hence, we have just ABox
axioms such that f indingSite(Endocarditis, Endocardium), illustrated in Figure 3
through an arrow representing the role f indingSite, that connects the medical terms
Endocarditis and Endocardium in the meta-model, but not at the level of patients.
Prevents from invalid extensions of SNOMED-CT concepts. The TBox axiom (2) ad-
mits extensions such that the assertions (4). It is avoided in our approach because
records of patients are directly connected to SNOMED-CT terms as individuals. These
individuals are in a meta-model layer that describe how the medical terms are concep-
tually related, whereas the lower layer describes the hierarchy of the vocabulary.
Provides a more direct mechanism to query records of patients, avoiding unexpected
results. Let’s come back to the example of obtaining a report about all situations that
affected the Pedro’s endocardium. With our solution, it is sufficient to obtain the records
of Pedro that point to SNOMED-CT individuals related to the individual Endocardium.
Then, this kind of queries can be solved at the upper level going through the SNOMED-
CT individuals. The query for the new approach is:
q(x) =∃y.hasEHRdetail(pedroEHR, x) ∧ hasRef erenceT o(x, y)∧
(7)
f indingSite(y, Endocardium)
Links upper and lower levels to infer useful information and detect inconsistencies.
Finally, we argue why it is important that SNOMED-CT terms both as individuals and
concepts to be interpreted as the same real objects. Suppose we have the patient Juan
who suffers endocarditis. In order to exploit the SNOMED-CT hierarchy, it is useful to
get inferences like “if Juan has endocarditis then Juan has a heart disease”, and in this
case to obtain all patients that suffer a heart disease. We can formulate the query:
q(x) =∃y, z.hasEHRdetail(x, y) ∧ hasRef erenceT o(y, z)∧
(8)
z v HeartDisease
Here we exploit the fact that SNOMED-CT terms can be treated either as individuals
or concepts. The set of solutions is the set of electronic health records of patients that
reference SNOMED-CT individuals which, treated as concepts are subsumed by the
concept HeartDisease. Moreover, giving the same interpretation to SNOMED-CT
terms as individuals and concepts we also prevent from inconsistencies, such as those
of Example 2, where the interpretation domain becomes a non-well founded set.
5 Conclusions and future work
In this paper, we have analyzed the logical model of the ontology SNOMED-CT, in
a case study of electronic health records of patients referencing SNOMED-CT terms.
Several works have proposed to modify the logical structure of SNOMED-CT. How-
ever, we propose an approach that, on the one hand, keeps the SNOMED-CT ontology
unchanged, extending it with a meta-model layer, and on the other hand, gives a solution
to the problem of the population of SNOMED-CT presented by Schulz et al. [20] for the
“stomachs” example. Moreover, general knowledge about the health domain is repre-
sented at an upper level. In this layer SNOMED-CT concepts are treated as individuals,
and the key point is that they are semantically equal in both layers. To formalize our
approach, we slightly adapt an existing meta-modelling extension of description logics.
As future work we aim to implement our approach in a concrete case study of a med-
ical institution, to integrate electronic health records of patients with SNOMED-CT
concepts, as well as for other medical applications.
References
1. Icd. http://www.who.int/classifications/icd/en/, Last date accessed December 2016.
2. F. Baader, D. Calvanese, D. L. McGuinness, D. Nardi, and P. F. Patel-Schneider, editors.
The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge
University Press, 2003.
3. T. Benson and G. Grieve. Principles of Health Interoperability. SNOMED CT, HL7 and
FHIR. Springer-Verlag, 2016.
4. S. El-Sappagh, M. E. Mogy, and A. M. Riad. A standard fragment of EHR relational data
model for diabetes mellitus diagnosis. In Proceedings of Informatics and Systems, pages
235–243, 2014.
5. G. De Giacomo, M. Lenzerini, and R. Rosati. Higher-order description logics for domain
metamodeling. In Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelli-
gence, AAAI 2011, pages 183–188. AAAI Press, 2011.
6. B. Glimm, S. Rudolph, and J. Völker. Integrated metamodeling and diagnosis in OWL 2. In
International Semantic Web Conference, ISWC 2010, pages 257–272, 2010.
7. P. Hitzler, M. Krötzsch, and S. Rudolph. Foundations of Semantic Web Technologies. Chap-
man & Hall/CRC, 2009.
8. M. Homola, J. Kluka, V. Svátek, and M. Vacura. Towards typed higher-order description
logics. In Proceedings of DL Workshop, pages 221–233, 2013.
9. M. Homola, J. Kluka, V. Svátek, and M. Vacura. Typed higher-order variant of SROIQ - why
not? In Proceedings of DL Workshop, pages 567–578, 2014.
10. IHTSDO. SNOMED CT Starter Guide, 2014.
11. N. Jekjantuk, G. Gröner, and J. Z. Pan. Modelling and reasoning in metamodelling enabled
ontologies. I. J. Soft. Informatics, 4(3):277–290, 2010.
12. Bevan Koopman, Guido Zuccon, Anthony Nguyen, Deanne Vickers, Luke Butt, and Peter D.
Bruza. Exploiting snomed ct concepts and relationships for clinical information retrieval :
Australian e-health research centre and queensland university of technology at the trec 2012
medical track. In 21st Text REtrieval Conference (TREC 2012), pages 1–8, 2012.
13. M. Krötzsch. OWL 2 profiles: An introduction to lightweight ontology languages. In Rea-
soning Web. Tutorial, pages 112–183, 2012.
14. M. Martinez, E. Rohrer, and P. Severi. Complexity of the description logic ALCM. In
Proceedings of KR 2016, pages 585–588, 2016.
15. B. Motik. On the properties of metamodeling in OWL. J. Logic and Computation,
17(4):617–637, 2007.
16. R. Motz, E. Rohrer, and P. Severi. Reasoning for ALCQ extended with a flexible meta-
modelling hierarchy. In Proceedings of JIST, Lecture Notes in Computer Science, pages
47–62, 2014.
17. R. Motz, E. Rohrer, and P. Severi. The description logic SHIQ with a flexible meta-modelling
hierarchy. J. Web Sem., 35(4):214–234, 2015.
18. J. Z. Pan, I. Horrocks, and G. Schreiber. OWL FA: A metamodeling extension of OWL DL.
In OWLED, CEUR Workshop Proceedings, 2005.
19. A. L. Rector, R. Qamar, and T. Marley. Binding ontologies and coding systems to electronic
health records and messages. Applied Ontology, 4:51–69, 2009.
20. Schulz S., Markó K., and Suntisrivaraporn B. Formal representation of complex SNOMED
CT expressions. BMC Med. Inf. & Decision Making, 8(S-1):S9, 2008.
21. S. Schulz, R. Cornet, and K. A. Spackman. Consolidating snomed ct’s ontological commit-
ment. Applied Ontology, 6(1):1–11, 2011.
22. S. Schulz, B. Suntisrivaraporn, F. Baader, and M. Boeker. SNOMED reaching its adoles-
cence: Ontologists’ and logicians’ health check. I. J. Medical Informatics, 78:S86–S94,
2009.
23. M. Q. Stearns, C. Price, K. A. Spackman, and A. Y. Wang. SNOMED clinical terms:
overview of the development process and project status. Proceedings of the AMIA Sym-
posium, pages 662–666, 2001.
24. B. Suntisrivaraporn, F. Baader, S. Schulz, and K. A. Spackman. Replacing SEP-triplets in
SNOMED CT using tractable description logic operators. In Proceedings of AIME 2007,
pages 287–291, 2007.
25. W3C. OWL 2 Web Ontology Language Profiles (Second Edition), Last date accessed May
2016.