=Paper=
{{Paper
|id=Vol-1552/paper6
|storemode=property
|title=Collaborative Conceptual Exploration as a Tool for Crowdsourcing Domain Ontologies
|pdfUrl=https://ceur-ws.org/Vol-1552/paper6.pdf
|volume=Vol-1552
|authors=Sergei Obiedkov,Nikita Romashkin
}}
==Collaborative Conceptual Exploration as a Tool for Crowdsourcing Domain Ontologies
==
https://ceur-ws.org/Vol-1552/paper6.pdf
Collaborative Conceptual Exploration as a Tool
for Crowdsourcing Domain Ontologies
Sergei Obiedkov and Nikita Romashkin
National Research University Higher School of Economics, Moscow, Russia
sergei.obj@gmail.com, romashkin.nikita@gmail.com
Abstract. Domain ontologies are essential in disciplines as diverse as
software engineering, medicine, or political science to name just a few.
This paper describes an ongoing effort to develop a methodology for
collaborative ontology construction by geographically spread communi-
ties of experts and implement a web-based prototype supporting this
methodology. A distinctive feature of the proposed approach is the use
of conceptual exploration techniques, which make it possible to organize
the process of ontology construction by automatically identifying and
explicitly highlighting issues that remain to be addressed. Given a set
of objects (facts, situations, etc.) of a subject domain, which is known
to have considerably more such objects, and their unified descriptions in
terms of presence or absence of certain attributes, a conceptual explo-
ration system maintains a compact representation of implications behind
the currently built ontology and offers them for experts to accept or fal-
sify by entering new objects or extending the description language with
new attributes. Upon termination, exploration results in identification of
a (relatively small) representative part of the domain from which a con-
ceptual hierarchy of the entire domain can be automatically constructed.
We consider theoretic, algorithmic, representational, and pragmatic is-
sues of transforming the exploration methods into a toolset useful for
domain experts.
1 Introduction
Domain ontologies provide common interfaces to knowledge accumulated in their
respective fields through achieving consensus on terminology used therein and
its meaning. Their construction is thus an important topic in knowledge engi-
neering. In this paper, we describe a project aimed at developing a platform for
online collaborative ontology construction by geographically distributed groups
of users that would not simply support sharing and common editing of formalized
knowledge, but would also include means for on-the-fly validation of the ontology
being constructed and automatic generation of guidelines for its completion.
The proposed approach is based on formal concept analysis, a mathematical
theory oriented at applications in knowledge representation, knowledge acqui-
sition, data analysis and visualization [5]. It provides tools for understanding
the structure of data given as a set of objects with certain descriptions, e.g., in
terms of their attributes, which is done by representing the data as a hierarchy
of concepts, or more exactly, a concept lattice (in the sense of lattice theory).
The objects, attributes, and relation between them constitute a formal context;
hence, the definition of a concept is necessarily contextual. Every concept has
extent (the set of objects that fall under the concept) and intent (the set of
attributes or features that together are necessary and sufficient for an object to
be an instance of the concept). Concepts are ordered in terms of being more
general or less general (i.e., covering more objects or fewer objects).
The concept lattice, being a rather universal structure, provides a wealth
of information about the relations among objects and attributes, which made
possible applications in areas ranging from sociology [8] to ontology construction
[14]. Indeed, it can help in processing a wide class of data types providing a
framework in which various data analysis and knowledge acquisition techniques
can be formulated.
One such technique is attribute exploration [4], which, in its basic version,
can be summarized as follows. Given a set of objects of a domain, which is known
to have many more such objects, and their descriptions in terms of presence or
absence of certain attributes, attribute exploration builds an implicational theory
of the entire domain and a representative set of its objects. The implicational
theory is the set of sentences of the form “if an object has all attributes from
set A, then it also has all attributes from set B” that are believed to hold for
all objects of the domain. It is always possible to find a minimal representation
of such a set, the Duquenne–Guigues or canonical basis of implications, from
which all valid implications can be inferred [6]. The representative set of objects
must respect all implications from the generated canonical basis and provide
a counterexample for every implication that cannot be inferred from the basis
(in this case, the concept lattice of the domain is isomorphic, i.e., structurally
identical, to the concept lattice of this relatively small set of objects).
The process of attribute exploration is interactive: it consists in computer
suggesting implications and the user accepting them or providing counterexam-
ples. Attribute exploration is designed to be efficient, i.e., to suggest as few impli-
cations as possible without loss in completeness of the result. It can work even if
the initial set of objects is empty. Attribute exploration is domain-independent:
although its application is more straightforward in precise domains such as math-
ematics [11], [12], it can certainly be used in other fields [10].
Advanced versions of attribute exploration can take into account background
information, such as relations among attribute values (not necessarily given as
implications), thus, avoiding suggesting trivial implications [4]. There are also
methods of concept exploration, relational exploration, and rule exploration that,
each in its own way, generalize attribute exploration, making it possible to work
with a broader class of dependencies [15, 13, 16]. We refer to all such methods
collectively as conceptual exploration.
Our aim is to extend these methods so as to make them suitable for collabora-
tive ontology construction over the web by a geographically spread community
of researchers working in the same domain. The idea is to provide tools that
59
would allow them to use attribute exploration and related techniques to re-
fine the language in which their domain is described and boost their knowledge
about it. Being suggested, an implication will be accepted only if no expert has
a counterexample for it. In the end, there will be a list of implications correctly
describing objects under study and a representative context. If, at a later stage,
a counterexample becomes known, it is added to the context and the implication
basis is modified accordingly. Thus, an up-to-date list of open problems of the
domain can be maintained.
We start with a short introduction into the relevant aspects of formal concept
analysis and then define attribute exploration. After that, we discuss possible
ways to make this procedure collaborative. Finally, we describe the current state
of our web-based exploration system and the work still to be done.
2 Concept Lattices
We briefly introduce necessary mathematical definitions [5] and then explain
them less formally. Given a (formal) context K = (G, M, I), where G is called a
set of objects, M is called a set of attributes, and the binary relation I ⊆ G × M
specifies which objects have which attributes, the derivation operators (·)I are
defined for A ⊆ G and B ⊆ M as follows:
AI = {m ∈ M | ∀g ∈ A : gIm}
B I = {g ∈ G | ∀m ∈ B : gIm}
In words, AI is the set of attributes common to all objects of A and B I is the
set of objects sharing all attributes of B.
If this does not result in ambiguity, (·)0 is used instead of (·)I . The double
application of (·)0 is a closure operator, i.e., (·)00 is extensive, idempotent, and
monotonous. Therefore, sets A00 and B 00 are said to be closed.
A (formal) concept of the context (G, M, I) is a pair (A, B), where A ⊆ G,
B ⊆ M , A = B 0 , and B = A0 . In this case, we also have A = A00 and B = B 00 .
The set A is called the extent and B is called the intent of the concept (A, B).
A concept (A, B) is a subconcept of (C, D) if A ⊆ C (equivalently, D ⊆ B).
The concept (C, D) is then called a superconcept of (A, B). We write (A, B) ≤
(C, D). The set of all concepts ordered by ≤ forms a lattice, which is called the
concept lattice of the context K.
The formal context makes precise the scope of the discussion by specifying
the domain to which it applies (listing all the objects of this domain) and defining
the terms in which it is going to be discussed (listing the attributes to be used
in object descriptions).
To flesh this out a bit, we give a small example based on the data from
the O*NET Resource Center (http://www.onetcenter.org/), which essentially
provides an interface to a taxonomy of occupations, organizing occupations in
various groups and describing the knowledge, skills, and abilities required by
60
Administration and Management
Computers and Electronics
Education and Training
Mathematics
Physics
Computer and Information
× × × ×
Research Scientists
Computer Programmers × × ×
Mathematicians × × ×
Fig. 1. A formal concept of some computer and mathematical occupations.
each occupation. Here, we focus on the knowledge required by occupations from
the Computer and Mathematical job family.
A formal context encompassing three occupations is shown in Fig. 1. Here,
rows correspond to objects (occupations) and columns correspond to attributes
(areas of knowledge). A cross indicates that the corresponding object has the
corresponding attribute; in our case, it means that an occupation requires knowl-
edge in a certain area.
A line diagram of the concept lattice of this context is shown in Fig. 2.
Nodes correspond to formal concepts, with more general concepts placed above
less general ones. Two concepts are connected with a line if one is more general
than the other and there is no concept between the two. Every concept in the
diagram is described extensionally, by a group of objects, and intensionally, by
attributes shared by all the objects in the extent of this node. The names of the
objects in the extent of a node can be read off from the diagram by looking at
the labels immediately below this node and below all nodes that can be reached
from this node by downward arcs. Conversely, the set of attributes forming the
intent of a node consists of labels immediately above this node and those above
nodes that can be reached from this node by upward arcs. For example, the
bottom-right node corresponds to the concept whose extent consists of a single
occupation, Computer and Information Research Scientists, whereas its intent
includes all attributes but Physics. The top concept is labelled by Computers
and Electronics and by Mathematics, which means that all the three occupations
require knowledge in these two areas.
It can be seen from this diagram that all occupations in our context requiring
knowledge in Education and Training also require knowledge in Administration
and Management. This is formally captured by the notion of an implication,
61
Computers and Electronics
Mathematics
Administration and
Management
Computer Programmers
Physics
Mathematicians
Education and Training
Computer and Information
Research Scientists
Fig. 2. The concept lattice of the context in Fig. 1.
which is, formally, an expression A → B, where A, B ⊆ M are attribute subsets.
It holds or is valid in the context if A0 ⊆ B 0 , i.e., every object of the context
that has all attributes from A also has all attributes from B.
An attribute subset X ⊆ M respects or is a model of an implication A → B
if A 6⊆ X or B ⊆ X. Obviously, an implication holds in a context (G, M, I) if
and only if {g}0 respects the implication for all g ∈ G. If an object g ∈ G is
such that {g}0 is not a model of A → B, we will call g a counterexample to this
implication.
If A0 = ∅ for A ⊆ M , then the implication A → M necessarily holds in the
context. We will sometimes write such an implication as A → ⊥, with ⊥ standing
for “contradiction”, meaning that attributes of A never occur all together.
All valid implications of the context can be summarized by means of the
Duquenne–Guigues basis:
{P → P 00 \ P | P ⊆ M is pseudo-closed},
where a set P ⊆ M is recursively defined to be pseudo-closed if P 6= P 00 and
Q00 ⊂ P for every pseudo-closed Q ⊂ P . The models of these implications are
precisely the models of all implications valid in the context, and the Duquenne–
Guigues basis has the smallest number of implications among all implication sets
with this property [6]. Any valid implication can be inferred from the basis using
Armstrong rules [2].
The Duquenne–Guigues basis of the context in Fig. 1 consists of three im-
plications shown in Fig. 3. Although they look similar, it may be more intuitive
to read them differently:
– The first implication says that all occupations require knowledge both in
Computers and Electronics and in Mathematics.
– The second implication says that, if an occupation requires knowledge in
Computers and Electronics, Mathematics, and Education and Training, then
it also requires knowledge in Administration and Management.
62
∅ → {Computers and Electronics, Mathematics} 3
{Computers and Electronics, Mathematics, Education and Training} →
{Administration and Management} 1
{Computers and Electronics, Mathematics, Administration and Management, Physics}
→ {Education and Training} 0
Fig. 3. The Duquenne–Guigues basis of the context in Fig. 1. The number in the end
of each line is the number of objects that “support” the implication, i.e., contain all
attributes from its premise.
– The third implication means that there are no occupations requiring at the
same time knowledge in Computers and Electronics, Mathematics, Admin-
istration and Management, and Physics.
These implications are valid in our context, but the context contains only three
occupations. How do we know if the three implications are valid for all computer
and mathematical occupations out there? This is where attribute exploration
becomes useful.
3 Attribute Exploration
The idea of attribute exploration is simple: consider every implication in the
Duquenne–Guigues basis of the context and add a counterexample if the impli-
cation is not valid generally. To be more precise, we are dealing with two contexts
here: one corresponds to the entire subject domain (computer and mathematical
occupations, in our case) and may not be immediately observable in its entirety,
while the other contains only a selection of objects. This smaller context is the
one that we can put into a cross-table such as one in Fig. 1 and for which we can
compute the implication basis. The goal is to make the smaller context repre-
sentative of the larger context in a very precise sense: the two contexts must be
models of exactly the same implications. Implications valid in the larger context
are always valid in the smaller context; we can force the converse to become true
as well by adding counterexamples to implications valid in the smaller context,
but not in the larger one. When we are done, the two contexts will share the
same implication basis and, furthermore, have isomorphic concept lattices: in
other words, the concept intents will be the same in the two contexts.
As an example, consider again the lattice in Fig. 2 and the corresponding
implication basis in Fig. 3. The implication
∅ → {Computers and Electronics, Mathematics}
is valid in our current context in Fig. 1, but according to the O*NET data,
knowledge of Mathematics is not really essential for Clinical Data Managers,
whose role is to “apply knowledge of health care and database management to
63
analyze clinical data, and to identify and report trends”. Out of the five areas
we consider, they must have knowledge of Computers and Electronics and of
Administration and Management. Therefore, we add Clinical Data Managers to
our context as a counterexample to the above implication:
Clinical Data Managers × ×
Note that Clinical Data Managers still must have knowledge of Computers
and Electronics; therefore, we still have to consider the implication
∅ → {Computers and Electronics}.
It seems that knowledge of Computers and Electronics is a requirement for all
computer and mathematical occupations; so, we accept the implication.
Since we changed the context by adding a new object, the implication basis
has also changed. Now, it includes the implication
{Computers and Electronics, Physics} → {Mathematics}
suggesting that, for an occupation within the job family under consideration,
knowledge of physics is useless without knowledge of mathematics. If we are to
believe the O*NET data, the knowledge of Physics is not required for anyone
within this job family but Mathematicians, for whom the knowledge of mathe-
matics is obviously a must. Thus, we accept the implication.
For the same reason, we accept the third implication in Fig. 2: the only
occupation category requiring knowledge of Physics is Mathematicians, but it
does not require knowledge in Administration and Management; hence, there
is no occupation satisfying the premise of the implication and the implication
trivially holds.
In our modified context, there remains only one implication to consider: Is it
true that, if an occupation requires knowledge both in Computers and Electronics
and in Education and Training, then it also requires knowledge in Mathematics
and in Administration and Management (as it is the case with Computer and
Information Research Scientists)? The answer is negative, because this does not
hold for Informatics Nurse Specialists, who are there to “apply knowledge of
nursing and informatics to assist in the design, development, and ongoing mod-
ification of computerized health care systems”. They “may educate staff [. . . ]
to promote the implementation of the health care system”, and, therefore, need
knowledge in Education and Training, but knowledge of Mathematics is not a
requirement for them. We add a new object to our context:
Informatics Nurse Specialists × × ×
Proceeding likewise, we add
Statisticians ×× ×
64
to give an example of those who, according to O*NET, typically need knowledge
of Education and Training, but not of Administration and Management; accept
the implication indicating that no occupation in this job family typically requires
the simultaneous knowledge of Physics and of Education and Training; and we
are done. The resulting concept lattice is shown in Fig. 4. Below, we present the
resulting implication basis:1
– ∅ → {Computers and Electronics}
– {Physics} → {Mathematics}
– {Administration and Management, Physics} → ⊥
– {Education and Training, Physics} → ⊥
Computers and Electronics
Administration
Mathematics Education and Training and Management
Clinical Data
Managers
Physics
Mathematicians Computer Programmers
Statisticians Informatics Nurse
Specialists
Computer and Information
Research Scientists
Fig. 4. The concept lattice resulting from attribute exploration on the context in Fig.
1.
Although we have considered only a small fraction of computer and mathe-
matical occupations, these four implications completely characterize the impli-
cational theory of all such occupations (at least, as long as we trust the O*NET
1
Here, implication premises are given in an abbreviated form using their so-called
minimal generating sets: instead of a pseudo-closed set P , we use its minimal subset
Q satisfying Q00 = P 00 . The resulting implication set is equivalent to the Duquenne–
Guigues basis.
65
data) and the six occupations covered by the concept lattice in Fig. 4 are repre-
sentative of the job family in this sense. The concept lattice contains all relevant
combinations of knowledge areas that may be required for computer and mathe-
matical occupations, and each such occupation can be placed into one of the ten
concepts of this lattice. For example, Web Administrators must have knowledge
of Computers and Electronics and of Administration and Management, but not
of any of the other three areas; therefore, they are covered by the same concept
as Clinical Data Managers.
But this is counterintuitive: surely, Web Administrators might need knowl-
edge in areas foreign to Clinical Data Managers. The problem is that the six
occupations we identified during attribute exploration and the concept lattice
generated from them are representative only with respect to the five knowledge
areas we have chosen before. However, the choice of knowledge areas might not
be representative itself. To correct this, we may use object exploration, a process
dual to attribute exploration, which involves working with object implications,
such as
{Informatics Nurse Specialists} → {Computer and Information Research
Scientists}.
In our case, this implication is interpreted as follows: “Every knowledge area
essential for Informatics Nurse Specialists is also important for Computer and
Information Research Scientists.” This is not so, since Informatics Nurse Spe-
cialists are typically required to have knowledge also in Medicine and Dentistry,
which forces us to introduce a new attribute into the context. Thus, object ex-
ploration ensures that the language we use to describe the domain is sufficiently
rich to differentiate between what must be differentiated.
Alternating between object and attribute exploration in this way, we can
arrive at a complete conceptual hierarchy (in the form of a concept lattice) of
the domain under consideration. Such a hierarchy modeling the subconcept–
superconcept relationship is an essential part of any domain ontology. Advanced
versions of attribute exploration, such as rule exploration [16], may be used to
identify other types of relations between objects or classes of objects.
4 Making Exploration Collaborative
The construction of the concept lattice is automatic, but the data needed for that
is gathered through exploration in an interactive fashion: the exploration system
asks the user questions and the user replies positively by accepting an implication
or negatively by providing a counterexample. Extending this approach to the case
of many users will make it possible to apply it in construction of ontologies for
large domains of which experts have only partial and mutually complementary
knowledge.
It is important to note that users of such a system must not be knowledge
engineers: they never have to explicitly describe the ontology of the domain
66
under consideration using a specialized knowledge representation formalism. In-
stead, they only supply data sufficient for building such ontology automatically,
while the exploration system directs them through questions/implications. If ex-
ploration is used within a scientific project, the users will typically be domain
experts. In other cases, it is possible that they even come from the “general
public”. For example, if we were to collect data about occupations, we would
welcome input not only from job market research analysts, but also from people
working in HR departments, who know their companies’ requirements, as well as
from job seekers, who know about such requirements from their own experience.
Thus, conceptual exploration provides a foundation for a toolset for crowdsourc-
ing data based on which a domain ontology (or its part) can be automatically
constructed.
One of the first experiments of collaborative exploration was conducted within
lattice theory already twenty years ago. The aim was to study relations between
various properties of lattices: algebraic, atomistic, finite, etc., and, indeed, inter-
esting non-trivial dependencies have been discovered [11]. In that setting, valid
implications corresponded to theorems, which had to be formally proven. The
resulting concept lattice (of lattice properties) was found valuable by lattice
theorists.
Obviously, the Internet together with appropriate software can make the pro-
cess much better organized and more realizable in practice. We experimented
with building a web system supporting attribute exploration within a joint
project with political scientists at Higher School of Economics in Moscow. The
project had as one of its goals developing a hierarchy of concepts of democracy
defined in literature and implemented in practice. The focus was on so-called “de-
fective democracies”, such as “delegative democracy” or “exclusive democracy”.
To make the construction of this concept hierarchy easier and more transparent,
a website was set up in order to allow political scientists to collectively build a
corresponding formal context using attribute exploration and related tools. Ob-
jects of this context were countries and/or regimes described in political science
literature, and attributes were their various properties. During exploration, users
consider implications of the form:
“If a regime is characterized by all attributes from set A, it is also char-
acterized by all attributes from set B,”
which they can accept or reject. In the latter case, the user must describe a
regime characterized by all attributes from A, but not by all attributes from B.
Similarly, object implications of the form
“Every attribute characterizing all regimes in A is shared by all regimes
in B”
propose the user to differentiate between regimes from sets A and B by adding
a new attribute shared by all regimes in A but missing from some regimes in B.
It turned out however that there are a number of issues that must be re-
solved before exploration techniques become a truly useful tool for people not
67
experienced in knowledge representation and formal concept analysis. Therefore,
we settled down to developing a general paradigmatic model of collaborative
conceptual exploration and its prototype implementation. A website is under
development that currently supports only the basic version of attribute explo-
ration, at the same time, providing some standard facilities of a collaborative
environment such as user profiles, separate projects, etc.
Upon signing up, the user can start a new exploration project or join an
existing project by contacting its owner. Of course, one user may participate
in several projects. A typical workflow is as follows: project members start at-
tribute exploration by defining an initial list of attributes (which can afterwards
be altered in any way) and continue by reviewing the dynamically updated im-
plication basis as described above, i.e., by accepting implications they deem valid
and providing counterexamples to other implications. The formal context main-
tained in the process can be modified directly, as long as the modifications do
not conflict with the accepted implications.
There are many issues that need to be addressed to allow for exploration of
complex domains:
– Object exploration was discussed earlier; it is essential for identifying features
differentiating objects from each other.
– Incomplete specification of examples. Users must still be able to add a coun-
terexample for an implication to the system even if they are unsure about
its status with respect to attributes not occurring in this implication. Its
description will be completed at later stages, either manually or automat-
ically (if accepting an implication forces certain values for some attributes
that have been left unspecified). This requires a modified definition of the
implication basis allowing for incompletely specified objects.
– Background knowledge. There must be a way to explicitly add known facts
about the domain to speed up exploration and concentrate on new knowl-
edge. The implication basis must be built relative to these facts summarizing
the part of knowledge behind the context not covered by them.
– Algorithmic issues. Since, for large ontologies, the canonical basis may also
be large, algorithms allowing for incremental update [9] of and navigation
through the basis must be developed.
– The policy of collaboration. It is essential to develop methods for resolution
of conflicts arising when different users have different views on the status
of an implication or when new information becomes available providing a
counterexample for an already accepted implication.
– Supporting tools. There must be a way for the user initiating any modifi-
cation to annotate it: provide a proof for an accepted implication, describe
the meaning of the new attribute, upload a document with evidence for the
new object, etc. In some domains, it may be possible to automatically prove
implications or search the Internet for potential counterexamples.
– More complex languages for object description. Attribute exploration can
easily be extended to the case of many-valued contexts (non-binary object–
attribute tables) by means of conceptual scaling [5]. However, which scales
68
to use for a many-valued attribute should be a matter of collective decision;
support for organizing the process of decision making must be envisioned.
Another possible extension is to the case when objects are described by
arbitrary formulas rather than only by conjunctions of attributes.
– Integration with state-of-the-art tools for ontology development, especially
those based on description logics. Attribute exploration has been used for
completing description logic knowledge bases, see, e.g., [3], although in a
slightly different context. Another relevant line of research to be taken into
account is learning ontologies in the framework of exact learning with queries
[1], which has a lot in common with attribute exploration; see, e.g., [7].
– Non-implicational knowledge. In some cases, it may be desirable to use a
richer subset of propositional logic to summarize the theory of the domain.
– Relational exploration. Attribute/object exploration is, for the most part,
concerned with the subsumption hierarchy of domain concepts. It may be
desirable to extract knowledge about other relations between concepts; rela-
tional or rule [16] exploration may be adapted for this purpose.
– Merging results of several explorations. It may be more appropriate for users
to work with subcontexts corresponding to their field of expertise rather
than with a larger context. Methods for combining the results of several
explorations must be devised.
5 Conclusion
We believe that conceptual exploration techniques provide a powerful frame-
work for collaborative development of domain ontologies. Recent developments
in Web applications open new prospects for tools based on exploration. A proper
implementation may result in a platform effectively supporting online social
networks of experts exchanging knowledge in a structured way and working
together towards constructing an ontology of their field. Nevertheless, a consid-
erable amount of research, development, and testing is still needed to unleash
the full potential of conceptual exploration in a distributive environment.
Acknowledgment
The first author was supported by the Russian Foundation for Basic Research
grant no. 14-01-93960.
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