=Paper=
{{Paper
|id=Vol-1299/paper1
|storemode=property
|title=A Vision for Diagrammatic Ontology Engineering
|pdfUrl=https://ceur-ws.org/Vol-1299/paper1.pdf
|volume=Vol-1299
}}
==A Vision for Diagrammatic Ontology Engineering==
https://ceur-ws.org/Vol-1299/paper1.pdf
A Vision for Diagrammatic Ontology
Engineering
Gem Stapleton1 , John Howse1 , Adrienne Bonnington2 , and Jim Burton1
1
University of Brighton, UK,
{g.e.stapleton,john.howse,j.burton}@brighton.ac.uk,
2
Horizons Regional Council, NZ,
adrienne.bonnington@horizons.govt.nz
Abstract. Ontology engineering is becoming more important, given the
rapid rise of data in this information age. To better understand and rea-
son about this data, ontologies provide us with insight into its structure.
With this comes the involvement of a wide range of stakeholders, such as
information analysts, software engineers, lawyers, and domain experts,
alongside specialist ontology engineers. These specialists are likely to be
adept at using existing approaches to ontology development, typically
description logic or one of its various stylized forms. However, not all
stakeholders can readily access such notations, which often have a very
mathematical style. Many stakeholders, even including fluent ontology
engineers, could benefit from visual approaches to ontology engineering,
provided those approaches are accessible. This paper presents ongoing re-
search into a diagrammatic approach to ontology engineering, outlining
key research advances that are required.
Keywords: ontology engineering, diagrams, visualization
1 Introduction
Ontologies are used as structural frameworks for organizing information and
are a form of knowledge representation. Ontology engineering - the process of
producing ontologies - is becoming increasingly important and ubiquitous in
society as a way of understanding the vast deluge of data that now exists in this
information age. Notable examples include the semantic web, medicine (including
SAPPHIRE for public health, SNOMED-CT for healthcare) and bioinformatics
(e.g. the gene ontology GenNav). Indeed, there are various large repositories of
freely available ontologies such as the Manchester OWL Corpus which contains
over 4500 ontologies including, between them, over 3 million axioms [4], the
Swoogle repository contains over 10000 ontologies [7] and BioPortal contains
nearly 400 ontologies from the biomedical domain [3].
Ontology engineering requires the involvement of domain experts, who need
to be able to communicate domain knowledge to ontology engineers. In turn,
ontology engineers need to verify ontological choices with the domain experts
and amend or refine the ontology based on feedback. Thus, the process of pro-
ducing ontologies is very much bidirectional and depends on cross-disciplinary
1
A Vision for Diagrammatic Ontology Engineering
communication. Barriers to communication can lead to errors, compounding an
already difficult task.
Description logics and OWL are the commonly used (symbolic) notations
for ontology engineering, and the latter is often seen as a stylized form of the
former; the W3C’s most recent specification of the web ontology language, called
OWL 2.0 [5] is a decidable description logic [9]. Description logics promote a hi-
erarchical taxonomy of concepts (called classes in OWL) as a primary modelling
feature. Individuals can be members of concepts. Binary relations over concepts,
called roles in description logic and properties in OWL, are used to relate in-
dividuals and concepts. In particular, individuals, concepts and roles form the
vocabulary over which the axioms that form the ontology are defined. The term
description logic actually refers to a family of logics, with the simplest such logic
of significance being called ALC and perhaps the most practically used being
called SHOIN (D) . The latter description logic is supported in the prominent
ontology engineering tool called Protégé [6], which has a strong community of
users including academics, governments and corporations [6].
As well as Protégé, other software tools have been implemented to support
the creation of symbolically specified ontologies. However, when people meet
to develop conceptual structures, including models of knowledge intended to
become ontologies, they sometimes quickly move to sketching images to commu-
nicate their thoughts; see Howse et al. [16]. The inaccessibility of the DL family
of symbolic notations is recognised by Rector et al. [18]: “Understanding the
logical meaning of any description logic or similar formalism is difficult for most
people, and OWL-DL is no exception.”
Warren et al. back this insight up with an empirical study of the most
commonly used OWL constructs, including class subsumption, disjointness and
equivalence alongside All Values From and other role restrictions [24]. They
found that “despite training, users are prone to certain misconceptions” and
they observed that “one-third of [participants] commented on the value of draw-
ing a diagram ... In the context of [description logics], diagrams offer a strategy
to overcome misconceptions and generally support reasoning.” Warren et al.
further recognise that existing visualizations are “chiefly aimed at viewing the
structure of the overall ontology or parts of the ontology rather than the more
cognitively difficult features of Description Logics” and they identify that con-
cept diagrams [16] are the exception. A major aim of our research is to address
this identified shortcoming of symbolic notations by providing a diagrammatic
alternative based on concept diagrams.
This paper presents an overview of the challenges that must be addressed in
order to deliver a practical framework for using concept diagrams for ontology
engineering. Key challenges include
1. devising a novel pattern-driven diagrammatic method for ontology engineer-
ing,
2. producing a heterogeneous logic that allows diagrams and symbols to be
used in combination, and
3. developing techniques for automatically visualizing symbolically ontologies.
2
A Vision for Diagrammatic Ontology Engineering
Throughout this paper we discuss the advances necessary to address these
challenges. To begin, we present a brief overview of the state-of-the-art in on-
tology visualization research. We then discuss the design of concept diagrams,
showing how they reflect known theories of what constitutes a good diagram.
This motivates them as a suitable choice of notation for approaching the chal-
lenges set out above. We recognise the need for extensive empirical evaluations
to ensure that concept diagrams are an accessible alternative to notations such
as description logic, but for space reasons we do not discuss this further.
Our ambition is not only to visualize ontologies, but to enable them to be
engineered and maintained visually, placing diagrams on an equal footing with
traditional approaches. Throughout the paper, we illustrate key points using
a real world ontology concerning cemeteries and burials. Ontology engineers
interested in using concept diagrams are able to download a free practical user
guide from http://www.ontologyengineering.org, under downloads.
2 State-of-the-Art Ontology Visualization Research
Ontology visualization improves access to information by ontology engineers,
domain experts and other end-users. Benefits of visualization include reveal-
ing information that could be somewhat hidden, or unapparent, when using
traditional symbolic notations. Such benefits have long been recognised in the
related area of software engineering, as has the need to ensure that software
models (akin to ontologies) are accessible to as wide a range of stakeholders as
possible [8]. Katifori et al. survey the state-of-the-art in ontology visualization
techniques up to 2007 [17], with examples including OWLViz [2], OntoGraf [1],
and CMap Tools [14]. Like OWLViz, OntoGraf exploits node-link diagrams (also
called graphs) to visualize subsumption relationships between concepts, but does
not depict disjointness relationships. There is potential, therefore, for confusion
to arise because of the partial information given. CMap Tools also exploit node-
link diagrams and, as with OntoGraf, uses directed edges (arrows) to represent
both subsumption relationships and role restrictions. Consequently, the saliency
of these two different types of information is significantly reduced.
An example produced using CMAP Tools can be seen in figure 1. The fact
that each Deceased is also a Person is asserted by the arrow labelled is a between
Deceased and Person. The fact that each Deceased has a memorial of some sort is
asserted by the use of the same syntactic device: the arrow labelled hasMemorial
between Deceased and Memorial. CMaps are also capable of depicting disjointness
information via arrows, though none is shown in figure 1. Thus, node-link-based
visualizations such as CMaps and OntoGraf use arrows for role restrictions,
subsumption and (where these can be depicted) disjointness relationships.
Similarity theory tells us that saliency is an important visual factor and,
in particular, that different syntactic devices should represent different types of
information [11]. This is because when visually searching for particular types
of information, increasing degrees of similarity between the target syntax (rep-
3
A Vision for Diagrammatic Ontology Engineering
Fig. 1. A CMap visualization. Fig. 2. A concept diagram.
resenting the required information) and distracter syntax (representing other
information) leads to an increase in the time taken to perform tasks.
Concept diagrams aid information saliency by avoiding the use of identical
syntactic types for different informational types: dots (or, in general, node-link
diagrams), closed curves, and arrows represent individuals, concepts and roles
respectively. An example concept diagram, expressing similar information to the
CMap visualization, is in figure 2. The placement of (the curve labelled) Deceased
inside Person expresses that Deceased is subsumed by Person. Since Person and
Memorial do not overlap, the diagram also expresses that these two concepts
are disjoint (have no individuals in common). The arrow labelled firstName,
sourced on Person and targeting the unlabelled curve inside Name asserts that
people’s first names are all names (in DL, this is an All Values From restriction:
Person v ∀firstName.Name). Here, the unlabelled curve represents an anonymous
concept containing precisely the names that are people’s first names. The other
two arrows are interpreted in the same way.
One visualization technique which was developed specifically as a diagram-
matic logic equivalent to the simple description logic ALC is a variation on
existential graphs by Dau and Eklund [10]. An example of an existential graph
is given in figure 3 that expresses the All Values From restriction Person v
∀firstName.Name. The existential graph literally translates to ‘it is not the case
that there is a person who has a first name that is not a Name’; curves rep-
resent negation, lines represent anonymous individuals and the written words
correspond to concepts and roles. Existential graphs are not readily accessible
since their syntax is somewhat restrictive: they have the flavour of a minimal
first-order logic with only existential quantification, negation and conjunction.
Fig. 3. An existential graph. Fig. 4. Representing individuals.
4
A Vision for Diagrammatic Ontology Engineering
3 The Design of Concept Diagrams
The design of concept diagrams has been informed by theories as to what con-
stitutes an effective visualization. We have already seen that similarity theory
leads us to use different syntactic items for different kinds of constructions. This
is consistent with the Gestalt principle of good form, which tells us that there
is a tendency for people to group together graphical objects that share some
property, such as colour or shape. In concept diagrams, individuals are visual-
ized using nodes, concepts by closed curves and role restrictions by arrows. We
have already seen the use of curves and arrows; figure 4 shows how individuals
are represented. This diagram asserts that Clifton is a Cemetery but not a Plot,
with the same being true of the other seven individuals. Using different types of
graphical objects ensures the same type of syntax is used to represent the same
type of semantic property. Further, we use shape to partition the curves into two
distinct sets: those which represent named concepts and, respectively, unnamed
concepts are represented using rounded rectangles and, respectively, circles.
Similarly, graphical objects that have different properties will typically be
considered as being in different groups by people. This suggests that different
semantic constructs should be represented by different graphical objects, consis-
tent with similarity theory. Colour could also be used to good effect, if we want
to give visual clues about some semantic commonality or distinctness. We have
adopted the convention, when colouring concept diagrams, that nodes, curves,
and arrows are assigned different colours (in this paper, red, blue and green
respectively). Rectangles, which identify diagram boundaries, are all black.
The way in which concept diagrams use this syntax to make statements has
been carefully considered. In particular, the spatial relationship between curves
reflects the semantic relationships that they convey: concept subsumption, dis-
jointness and intersection are represented by enclosure, disjointness and overlap
of curves respectively. Likewise, the location of nodes either inside or outside of
curves corresponds to the individuals represented being either members of, or not
members of respectively, the corresponding concepts. Properties are directional
relationships which are captured by arrows, indicating direction. These types of
features, embodied in concept diagrams’ design, are known as well-matched [13].
An important feature of concept diagrams is that they are fully formal-
ized [22]. As is standard with visual languages [12, 15], concept diagrams are
formalized using an abstract syntax (sometimes called type syntax). Their se-
mantics are defined using a standard model-theoretic approach, akin to that
used for description logics. Due to space reasons, we refer the reader to [22] for
the full details on the formalization of concept diagrams.
4 Patterns
We believe that concept diagrams are able to readily express commonly occur-
ring symbolic axioms, for which we have devised a set of simple diagrammatic
patterns [23]. Such an approach is thought to aid building ontologies (i.e. defining
5
A Vision for Diagrammatic Ontology Engineering
the axioms), since the patterns will, essentially, be standard templates for com-
monly occurring constraints. However, using a separate diagram for each piece
of information does not allow the exploitation of many important diagrammatic
features. In particular, single diagrams that express rich information can do so
in an accessible way and such diagrams can correspond to many symbolic ax-
ioms (discussed further in section 5). To this end, we demonstrate how simple
diagrammatic patterns can be merged to produce informationally rich diagrams.
4.1 Simple Patterns
A series of simple patterns was presented in [23], expressing concept subsump-
tion and disjointness as well as All Values From and Some Values From role
restrictions. Here, we illustrate eight of these simple patterns.
Figures 5 and 6 show instances of patterns for asserting that individuals are
and, respectively, are not members of concepts. In particular, figure 5 asserts
that M (short for ‘male’) is a Gender whereas figure 6 asserts that M is not an
Occupation. Figures 7 and 8 are instances of the concept subsumption and con-
cept disjointness patterns. The former figure tells us that Deceased is subsumed
by Person whereas the latter expresses that Person and Gender are disjoint.
Fig. 5. Inclusion. Fig. 6. Exclusion.
Fig. 7. Subsumption. Fig. 8. Disjointness.
Turning our attention to roles, figure 9 diagrammatically expresses an All
Values From restriction. In particular, it tells us that under the role gender, Per-
son has all values from the concept Gender. This concept diagram illustrates the
use of multiple boundary rectangles. The spatial relationships between syntactic
items are only of semantic importance within innermost boundary rectangles. In
this case, the two innermost rectangles mean that the diagram does not tell us
that Person and Gender are disjoint (even though this happens to be true, given
the information in figure 8).
6
A Vision for Diagrammatic Ontology Engineering
Fig. 9. All Values From. Fig. 10. Some Values From.
Fig. 11. Role subsumption. Fig. 12. Role disjointness.
The Some Values From pattern used in figure 10 (which is different from the
Some Values From pattern in [23]) illustrates two further features of concept
diagrams: dashed arrows and the use of quantifiers to talk about anonymous
individuals. This concept diagram makes an assertion about all individuals that
are people, using the quantification expression For all Person, p. The dashed
arrow targets an anonymous individual that is a Gender. This dashed arrow tells
us that the individual, p, is related to at least the individual at the target. That
is, the person p has at least one gender.
Patterns for role subsumption and role disjointness are instantiated in fig-
ures 11 and 12 respectively. As with concept subsumption and disjointness, they
also exploit the topological properties of containment and disjointness to express
the required information. For example, figure 11 tells us that, for each thing t,
the set of t’s headstones in subsumed by the set of t’s memorials.
4.2 Merging Patterns
Using one diagram to express a small amount of information may be helpful
when developing ontologies, but sometimes having diagrams containing rich in-
formation can give a better overview of how concepts and roles interact. We
plan to develop methods of merging simple patterns together in order to pro-
duce richer diagrams. Such a merging process is illustrated in figures 13 to 15.
Firstly, figure 8 tells us that Person and Gender are disjoint, meaning that we
can delete the two innermost rectangles from figure 9. The result is in figure 13,
which expresses the same information as the two original patterns. The other
diagrams in figures 14 and 15 are similarly obtained; here the graph labelled M
indicates that M is a Gender where the edge represents disjunction.
Using merging techniques, semantically rich diagrams that display significant
proportions of ontologies can be produced. An example is given in figure 16,
7
A Vision for Diagrammatic Ontology Engineering
Fig. 13. Merging figures 8 and 9.
Fig. 14. Merging figures 13 and 7
Fig. 15. Merging figures 14 and 5
which depicts a large fragment of a cemetery ontology. This diagram depicts 13
inclusion axioms, four subsumption axioms, 709 (binary) disjointness axioms
and 46 all values from axioms. It is an interesting avenue of future work to
determine which patterns can be merged, and how. For example, in figure 16
only axioms whose patterns do not include explicit quantification have been
merged. A key aspect of this work will be to devise heuristics that identify
diagrams that can be merged to produce effective visualizations. The fact that
figure 16 depicts 772 axioms in a single readable diagram indicates that the
notation scales to some reasonable extent; of course, screen real estate presents
a scalability problem for both visual and symbolic notations.
5 Heterogeneous Ontology Engineering
Unlike many stakeholders, expert ontology engineers are fluent in the use of
symbolic logics. The framework for diagrammatic ontology engineering that we
envisage will allow ontologies to be engineered symbolically and diagrammati-
cally and, as a by-product, allow the visualization of already developed symbolic
ontologies. A major challenge is to allow diagrams and symbols to be used in
tandem by providing a seamless integration of the two paradigms. This requires
the two ‘views’ (diagrammatic and symbolic) of the ontology to be kept in sync,
so any update made to the symbolic axioms is reflected diagrammatically and
8
A Vision for Diagrammatic Ontology Engineering
Fig. 16. A large fragment of the cemetery ontology.
9
A Vision for Diagrammatic Ontology Engineering
vice versa; this idea of two views is illustrated using figure 15 and the DL ax-
ioms: Person v ∀gender.Gender, Person u Gender v ⊥, Deceased v Person, and
Gender(M).
Core to solving this challenge is the derivation of effective translations be-
tween diagrammatic axioms and symbolic axioms. It is expected that the pat-
terns described above, with the merging results, will form a basis for translat-
ing symbolically-specified ontologies into concept diagrams. However, significant
advances are required, using patterns as a starting point. Requirements of the
translation methods are likely to include, but not be limited to: visualize the
entire ontology; visualize all concepts; visualize all axioms involving a particular
concept or set of concepts; and visualize all axioms involving a particular role
or set of roles.
Further, we expect to devise translations that permit multiple levels of visu-
alization: top-level overviews, some means of exploring the overview including
zooming and filtering, and drilling down to low-level detail as required. Lastly,
when symbolic axioms are altered, as will often happen during the refinement
and debugging phases of ontology development, the corresponding diagrammatic
axioms must be updated. Translations from concept diagrams to description logic
will also be devised but, again, finding an optimal symbolic set of axioms will
be difficult; as a trivial example, one must choose between the axioms C1 v C2
and C1 v C3 and the single axiom C1 t C2 v C3 .
6 Automated Layout
When devising heterogeneous approaches to ontology engineering, it is impor-
tant that one is able to automatically draw – or lay out – concept diagrams.
When automatically drawing diagrams, one starts with the abstract syntax of
the required diagram or diagrams. The problem is to draw effective diagrams,
with the given abstract syntax. There is considerable choice of layout, where
figure 17 shows what we consider to be a bad layout of the diagram shown in
figure 2.
Fig. 17. A bad layout.
Indeed, the problem of drawing multiple diagrams, where common parts of
two or more diagrams should – for effective use – look identical substantially in-
creases the difficulty. This is illustrated in figures 18 and 19. Figure 18 presents, in
10
A Vision for Diagrammatic Ontology Engineering
separate diagrams, some relationships involving the classes Memorial and Head-
stone. The two diagrams have been drawn so that they have a layout that reflects
the structurally similar information represented. However, we expect that the di-
agrams in figure 19 are a more effective pair of visualizations than those figure 18,
since their common parts have the same relative positioning in the plane.
Fig. 18. Some Deceased relationships and some Memorial relationships.
Fig. 19. Memorial relationships redrawn to align with layout of Deceased relationships
The problem of drawing multiple-diagrams when translating between nota-
tions, where many diagrams can arise from symbolic axioms. Whilst the drawing
problem is inherently computationally complex, it is necessary to seek drawing
and layout algorithms that have acceptable run times for most cases that arise
in practice and that produce usable results. Empirical evaluations will be neces-
sary to determine what constitutes an effective layout, informing choices about
diagram topology and geometry.
As a staring point for a general drawing algorithm for concept diagrams, ex-
isting Euler diagram drawing methods such as [19–21] can be extended to simply
add the extra syntax required (giving primacy to the Euler diagram). However,
11
A Vision for Diagrammatic Ontology Engineering
this approach will require extensive modifications to existing algorithms, since
the initially drawn Euler diagram may compromise the layout of the subsequently
drawn syntax. Ideally, the drawing algorithms will consider the entirety of the
to-be-drawn diagram when making layout choices, not assigning primacy to any
one syntactic part. Moreover, general drawing algorithms are computationally
expensive and may not always produce effective layouts. For this reason, we plan
to devise, first, a layout algorithm for classes of concept diagrams that commonly
arise in practice.
Lastly, drawing algorithms are required that incrementally update diagrams
when edits are made to a symbolically specified ontology, to keep the two views in
sync. These edits can include: deleting axioms, adding new axioms or amending
existing axioms (which can be considered as a deletion followed by an addi-
tion). When an axiom is deleted, this can have profound effects on the layout of
diagrams. For instance, deleting a disjointness axiom may require some of the
(non-overlapping) curves in a diagram to be re-routed (so they overlap, thus not
asserting disjointness). Similarly, adding an axiom can also require significant
changes to parts of the diagrams, such as removing an overlap between curves.
When diagrams include a lot of syntax, making such changes to curves is not
necessarily straightforward.
7 Conclusion
Our vision is to produce a fully supported diagrammatic logic for ontology engi-
neering, which includes implementing software to support its use. If successful,
this diagrammatic logic will provide more accessible ways to develop, update and
maintain ontologies. Since the diagrammatic framework that we envisage will be
fully integrated with existing symbolic approaches, expert ontology engineers
will be able to effectively collaborate with stakeholders who prefer a diagram-
matic approach. We view this integration as necessary for the take-up of concept
diagrams generally.
Acknowledgements We are indebted to Rangitikei District Council for pro-
viding us with access to the cemetery data on which the examples in this paper
are based.
References
1. OntoGraf. http://protegewiki.stanford.edu/wiki/OntoGraf (2014), accessed Aug
2014
2. OWLViz. http://protegewiki.stanford.edu/wiki/OWLViz (2014), accessed Aug
2014
3. The BioPortal ontology repository. http://bioportal.bioontology.org/ (2014), ac-
cessed Aug 2014
4. The Manchester OWL Corpus. http://owl.cs.manchester.ac.uk/publications/
(2014), accessed Aug 2014
12
A Vision for Diagrammatic Ontology Engineering
5. The OWL 2 Web Ontology Language. http://www.w3.org/TR/owl2-overview/
(2014), accessed Aug 2014
6. The Protégé web site. http://protege.stanford.edu/ (2014), accessed Aug 2014
7. The Swoogle ontology repository. http://swoogle.umbc.edu/ (2014), accessed Aug
2014
8. Atkinson, C., Kühne, T.: Model-Driven Development: A Metamodeling Founda-
tion. IEEE Softw. 20, 36–41 (Sep 2003)
9. Baader, F., Calvanese, D., McGuinness, D., Nadi, D., (eds), P.P.S.: The Description
Logic Handbook. CUP (2003)
10. Dau, F., Eklund, P.: A diagrammatic reasoning system for the description logic
ACL. Journal of Visual Languages and Computing 19(5), 539–573 (2008)
11. Duncan, J., Humphreys, G.W.: Visual search and stimulus similarity. Psychological
review 96(3), 433 (1989)
12. Erwig, M.: Abstract syntax and semantics of visual languages. Journal of Visual
Languages and Computing 9, 461–483 (1998)
13. Gurr, C.: Effective diagrammatic communication: Syntactic, semantic and prag-
matic issues. Journal of Visual Languages and Computing 10(4), 317–342 (1999)
14. Hayes, P., Eskridge, T.C., Mehrotra, M., Bobrovnikoff, D., Reichherzer, T., Saave-
dra, R.: Coe: Tools for collaborative ontology development and reuse. In: Knowl-
edge Capture Conference (K-CAP). vol. 2005 (2005)
15. Howse, J., Molina, F., Shin, S.J., Taylor, J.: Type-syntax and token-syntax in
diagrammatic systems. In: Proceedings FOIS-2001. pp. 174–185. ACM Press (2001)
16. Howse, J., Stapleton, G., Taylor, K., Chapman, P.: Visualizing ontologies: A case
study. In: International Semantic Web Conference. pp. 257–272. Springer (2011)
17. Katifori, A., Halatsis, C., Lepouras, G., Vassilakis, C., Giannopoulou, E.: Ontology
visualization methods a survey. ACM Comput. Surv. 39(4), 10+ (Nov 2007)
18. Rector, A., Drummond, N., Horridge, M., Rogers, J., Knublauch, H., Stevens, R.,
Wang, H., Wroe, C.: OWL Pizzas: Practical Experience of Teaching OWL-DL. In:
Motta, E., Shadbolt, N., Stutt, A., Gibbins, N. (eds.) Engineering Knowledge in
the Age of the Semantic Web, LNCS, vol. 3257, chap. 5, pp. 63–81. Springer (2004)
19. Riche, N., Dwyer, T.: Untangling Euler diagrams. IEEE Transactions on Visual-
ization and Computer Graphics 16(6), 1090–1099 (2010)
20. Simonetto, P.: Visualisation of Overlapping Sets and Clusters with Euler Diagrams.
Ph.D. thesis, Université Bordeaux (2012)
21. Stapleton, G., Flower, J., Rodgers, P., Howse, J.: Automatically drawing Euler
diagrams with circles. Journal of Visual Languages and Computing 23(3), 163–193
(2012)
22. Stapleton, G., Howse, J., Chapman, P., Delaney, A., Burton, J., Oliver, I.: For-
malizing Concept Diagrams. In: Visual Languages and Computing. pp. 182–187.
Knowledge Systems Institute (2013)
23. Stapleton, G., Howse, J., Taylor, K., Delaney, A., Burton, J., Chapman, P.: To-
wards Diagrammatic Ontology Patterns. In: 4th Workshop on Ontology and Se-
mantic Web Patterns. CEUR, Sydney, Australia (Oct 2013)
24. Warren, P., Mulholland, P., Collins, T., Motta, E.: The Usability of Description
Logics. In: Presutti, V., d’Amato, C., Gandon, F., d’Aquin, M., Staab, S., Tordai,
A. (eds.) The Semantic Web: Trends and Challenges, LNCS, vol. 8465, pp. 550–564.
Springer (2014)
13