-Ontology engineers use a variety of software tools to design, manage and interrogate their ontologies. These tools often include visualisation features which provide a graphical depiction of parts of the ontology. In this paper we describe a new tool, ConceptViz, which uses a novel notation called concept diagrams, based on Euler diagrams. Although work is at an early stage, ConceptViz is highly expressive, allowing information to be expressed in a single diagram that would normally need to be gathered from several parts of an ontology management tool. To further motivate the use of concept diagrams we highlight their balance of iconic and symbolic notation and show how symbolic features can be used to reduce clutter in diagrams.
The secondary topic of this work is the problem of
devising effective formal visual languages. In order to justify its
existence, we believe that each such language should benefit
the user by exploiting the particular cognitive properties of
predominately iconic (as opposed to symbolic) languages.
A solution to this problem has been the explicit goal of
researchers in visual reasoning since the time of Peirce. A
number of logicians and computer scientists have addressed the
same problem since, such as Shin and Hammer [
II.
An ontology represents knowledge as a set of concepts
(sets, classes) within a particular domain, along with
individuals inhabiting the concepts and roles (relations) between
concepts and/or individuals. Thus, an ontology is a “formal,
explicit specification of a shared conceptualisation” [
Fig. 1. The ConceptViz plugin
OWL semantics are based on description logics (DLs), decidable fragments of FOL with efficient SAT solvers. These have been incorporated into ontology management tools, allowing users to reason about their ontology.
There are a diverse range of tasks involved in the creation, use and maintenance of ontologies. These include design, debugging, comprehension/discovery (bottom-up and top-down), maintenance, query and reasoning. However, although visualisation tools have long been recognised as an essential part of ontology workflows, most visualisations focus almost entirely on comprehension.
Shneiderman [20] identified a number of high-level tasks a
visualisation should support: overview, zoom, filter, details on
demand (e.g. right click a concept to see properties, roles etc),
and so on. There are a wide variety of ontology visualisations
available, many described in a useful survey by Katifori [
The next most common representations are tree-based, such as OntoGraf, which is a Prote´ge´ plugin. OntoGraf provides a powerful and intuitive visualisation of the hierarchy, but one which makes poor use of space and can quickly become cluttered. OntoGraf can be used to visualise concepts, roles and individuals, making it more expressive than most other visualisations. It offers the user a great deal of flexibility about which parts of the ontology are displayed and which are hidden. This flexibility comes at a cost, however, since it makes it easy to create diagrams which may be misleading. OntoGraf users can reduce clutter in their diagrams by choosing not to show certain relations: in figure 3 the is-a relation between Country and Thing is not shown, which may surprise or confuse novice users. In contrast, diagrams in ConceptViz are produced using an unambiguous visual logic (concept diagrams). Thus, the inferences a user may draw from a diagram are always valid, provided that they draw these inferences correctly.
One of the most important developments since Katifori’s
survey is the idea of key concepts [
While all visualisations have strengths and weaknesses and are more suitable for some tasks than others, it seems fair to say that they all leave something to be desired. Key problems identified by Katifori include clutter and other scalability issues. There are also crucial features we may want which go beyond visualisation. Reasoning is not supported to any significant degree by any of the tools (e.g. OWLViz can indicate inconsistent concepts but that is about as far as it goes).
Also, editing is not supported: several tools allow the user to add a new concept, but then resort to forms etc to specify the details. Finally, existing tools focus on taxonomy: support for individuals is unusual, and support for roles and other axiombased information more so.
In the previous section we described some existing approaches to ontology visualisation and identified important gaps in functionality. ConceptViz is our work-in-progress ontology visualisation based on concept diagrams. In this section we aim to motivate the use of concept diagrams (CDs) as the basis of an alternative visualisation.
Our first observation is that CDs are more expressive than most existing visualisations. CDs are expressive enough to represent entire ontologies diagrammatically. Figure 4 shows a concept diagram with syntactic features that we intend to incorporate into ConceptViz. These features allow the representation of individuals (using solid dots), roles (using arrows) and quantification (using extra-diagrammatic symbolic expressions).
The second observation is that, alone among the visualisations we have considered, CDs are formal and come equipped with a framework for developing proofs and carrying out reasoning. This property enables a visualisation based on CDs to cover all stages of the ontology workflow described in the previous section, providing the potential for purely diagrammatic ontology management. This expressiveness and inferential capability doesn’t imply, however, that CDs are fit for purpose. For that to be true, they must also be “easy” to understand relative to other approaches, for some measure of ease.
The question of the usability, or relative ease of comprehension, of a visualisation based on CDs can only be definitively answered by empirical studies. As well as “road testing” the usability of CDs, we can also attempt to show that their use is justified from a theoretical perspective. This requires an analysis of the affordances of CDs – the possible meanings of some piece of notation, and the ways in which an actor perceives and constructs that meaning. The starting point for . .
Fig. 4. A concept diagram
this analysis is the work of C.S. Peirce, who founded the
field of semiotics. Peirce categorised the modes by which we
construct the meaning of signs as iconic, symbolic and
indexical [
Although he stressed the interdependence of the modes, Peirce privileged the iconic mode as the most “natural” and in designing his systems of existential graphs, Peirce’s aim was to create a system which was as iconic as possible. Iconicity is related to Gurr’s notion of well-matchedness [5]. The Euler basis of CDs is well-matched to meaning, in that the syntax corresponds in a natural way to the semantics (e.g. topological separation means disjointness). Individuals are well-matched (relatively iconic) too. Placing a dot in a region asserts the existence of an individual in the concept modelled by that region and outside the others. Two separate dots assert the existence of two separate individuals.
Hammer and Shin [
We can think of the number of perceptual inferences
required by a given notation to convey a particular statement
as its relative efficiency [
Furthermore, Shin points out that several of the conditions
we might want to represent are incapable of depiction without
convention, particularly disjunctive information and certain
types of negative information. Thus, although advocates of
Euler-based notations have typically argued for their
effectiveness by an appeal to their well-matched features, an expressive
notation needs to make use of non-iconic features. In order
to understand the real nature of well-matchedness we need to
focus on the correspondence between topological and semantic
structure rather than any idea of physical resemblance. In
recent work, Legg [
To expand on Peirce’s dictum that symbolic notation
should be used to represent “general rules”, symbolic features
have the capacity for a very compact expression, freed of
the responsibility to depict structural correspondence. The
designers of CDs add several symbolic features, neither of
which adds to expressiveness, but which can both be used to
reduce clutter in diagrams: dashed arrows and nested bounding
boxes (also called nested universes). As well as inheriting the
benefits of Euler diagrams, CDs inherit some limitations: an
Euler diagram can quickly become cluttered [
Each arrow in a concept diagram has a source, a target and a label. The arrow tells us that when the domain of the role represented by the label is restricted to the concept represented by the source, then the image of that role is the concept represented by the target. Informally, 5 tells us that members of the concept A are related to members of the unlabelled concept under f . The semantics of the arrow assert that elements of A are not related to anything else under f .
Assume that the creators of figure 5 want to focus on the presence of B in the target of the arrow. One way of drawing attention to B is to remove other concepts from the diagram, resulting in figure 6. This is a limited solution; the creators cannot now reintroduce C or D to the diagram without reintroducing clutter and losing the focus on B in the target of the arrow.
In contrast to arrows drawn with a solid line, dashed arrows provide partial information. The dashed arrow in figure 7 tells us that elements of A are related to at least elements of B under f . The diagram creators could reintroduce C and D to figure 7 without needing to change the target of the arrow. Howse et al.[ISWC TUTORIAL] show several larger examples in which the “savings” (in terms of clutter reduction) are amplified further still.
In our next example we consider nested bounding boxes. The bounding box of each concept diagram represents the concept Thing or, in set-theoretic terms, the universe of discourse. Diagrams may include several bounding boxes, each of which represents Thing. Suppose that we want to add a fourth concept, D, to figure 8, so that D is disjoint from B. Also, D is the source of an arrow which has C as its target. This arrow is the main focus of what the diagram creator wants to convey.
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The result of adding D to figure 8 in this way is shown in figure 9. We can see that the resulting diagram is rather cluttered. The diagram creators goal of highlighting the information provided by the arrow depends partly on the way we lay out the diagram, but is hard to achieve.
When a concept diagram includes several bounding boxes, the spatial relations between elements in separate boxes has no meaning. Thus, nested universes allow us to add D without specifying its disjointness or otherwise from A, B and C. This results in the diagram in figure 10, which is less cluttered than figure 9, making the communicative goal of focusing on the arrow easier to achieve.
Dashed arrows and nested bounding boxes can reduce clutter because they allow us to convey partial information in an unambiguous way. As stated above, OntoGraf users can reduce clutter by choosing not to show some relations in the diagram, but this may lead to results that are difficult to understand out of their original context.
IV.
We have seen that concept diagrams contain both iconic and symbolic features and noted that, historically, the main claim for the usability of Euler-based notations has been the iconic nature of the underlying Euler circles. However, symbolic features have great expressive potential and we have shown examples of symbolic syntax in concept diagrams that allows the compact representation of ontologies. Given that clutter is recognised as a common problem in ontology visualisation and that a medium-sized ontology may contain thousands of concepts, we see this as a strong point of concept diagrams. Although the current version of ConceptViz contains only Euler diagrams, it provides an adequate basis for implementing more of the concept diagram notation.
We conclude by providing a few details of the implementation of ConceptViz and the goals for its future development. The plugin uses the Inductive Circles (iCircles) library by Jean Flower. iCircles uses ideas and algorithms developed by Stapleton, Flower, Rodgers and Howse (2012) [CITE] to draw Euler diagrams using circles. To ensure that the diagram can be drawn, it relaxes a topological property, normally desirable, which states that labels should be unique.
There is a growing number of ontology visualisation tools in existence, but none that support the entire ontology management workflow. A major goal for the plugin is to incorporate editing functionality, enabling ConceptViz to go beyond visualisation to ontology design and maintenance. Users will be able to generate and alter ontologies diagrammatically, observing the changes in other parts of the Prote´ge´ interface, and vice versa. This will result in “round-trip” diagrammatic ontology engineering. The interface for the tool will make a number of ontology design patterns available (such as applying a domain restriction to a role), giving users a toolkit for assembling ontologies from frequently used components.
One of the interesting problems is to ensure predictability when drawing the same or similar diagrams – when we reveal sub-concepts in one part of the diagram, we want the rest of the diagram to be as unchanged as possible. Unpredictability may cause serious usability problems (Herman, 1998) [CITE]. The layouts of diagrams produced by iCircles are currently rather unpredictable, since layout choices are based on heuristics. Work is underway to abstract these choices into reusable layout policies. [20] B. Shneiderman. The eyes have it: A task by data type taxonomy for information visualizations. In Proceedings of the IEEE Symposium on Visual Languages, VL’96, page 336. IEEE, 1996.