Toward principles for the representation of hierarchical
knowledge in formal ontologies
Dean M. Jones, Ray C. Paton
Department of Computer Science, University of Liverpool, Liverpool, UK, L69 7ZF
Abstract
Early ontological engineering methodologies have necessarily focussed on the management of the whole
ontology development process. There is a corresponding need to provide advice to the ontological engineer
on the finer details of ontology construction. Here, we specifically address the representation of hierarchical
relationships in an ontology. We identify five types of problem that may be encountered in moving from an
informal description of a domain to a formal representation of hierarchical knowledge. Each problem type
is discussed from the perspective of knowledge sharing and examples from biological ontologies are used
to illustrate each type.
Keywords: Ontological engineering; Hierarchical relationships; Knowledge sharing
1. Introduction
It is largely accepted that one of the most important aspects of a domain ontology is the organisation of
class definitions into inheritance hierarchies. Methodologies that describe processes for developing domain
ontologies commonly include recommendations to define hierarchical relationships. For example, in the
METHONTOLOGY approach to ontology development described in [5], it is suggested that the
representation of concepts as ‘classification trees’ is one of the main steps in ontology development.
Taxonomic analysis, during which hierarchical relationships in a domain should be identified and
represented, is defined as a distinct stage in the latest version of the ONIONS approach to ontology
development [19]. These methodologies are mainly concerned with the organisation of the various activities
that an ontological engineer engages in and providing a means of managing the many products of the
ontology development process. There has been a necessary focus on what must be done in the development
of the formal ontologies. However, there is a parallel need to provide advice to the ontological engineer on
how to achieve each stage in the development of a formal ontology. Here, we focus on the development of
hierarchical representations.
Although the representation of hierarchical knowledge is widely seen as an important aspect in the
design of a formal ontology, very little advice is available on the problems that may be encountered and how
these problems might be addressed. Furthermore, the advice that is available (e.g. [4]) is often based on the
classical model of category membership. The classical model states that an object is an instance of a category
if and only if it exhibits certain necessary features. It has long been recognised that this is an inadequate
model of the way in which category membership is decided (see [11] for a good summary of the arguments).
As the frame-based paradigm was developed largely in response to non-classical theories of category
membership and concept definition [12], the problems involved in adopting the classical model of
categorisation have been recognised for almost as long by the knowledge representation community. There
has, however, been little work on how the complexity of category structure can be addressed in practice. The
aim of this article is to describe some common problems that are encountered in the formal representation
of hierarchical knowledge and discuss ways in which these problems can be addressed.
The problems described are illustrated with examples taken from cellular and molecular biology. This
domain was selected because:
(a) hierarchical conceptual structures have traditionally been important in the organisation of knowledge
in the biological sciences. This is exemplified by the most familiar representation of biological
knowledge, the classification of living entities into kingdoms, phyla, classes, orders, families, genera,
species, etc.
(b) biological systems are generally very complex, especially at the cellular and molecular levels [15,10].
The hierarchical relations in these domains are correspondingly complex and are therefore likely to
exhibit any problems.
(c) scientific domains are generally more formal than non-technical domains. It is hoped that in analysing
biological theories, it will be seen that a fortiori the same problems will exist in non-technical, less
formal domains.
In the following sections, we analyse some hierarchical relationships in biological domains and discuss some
of the issues that are relevant to the representation of this knowledge in a formal ontology. The source for
this analysis was [2], a standard text used in the domain.
2. Classification Problems
Firstly, as there is often confusion regarding the terms that are used to discuss hierarchical
representations of knowledge, definitions of some terms will be useful.
entity: a member of the Universe of Discourse.
class: a class c is a subset of the Universe of Discourse to which some predicate applies. The set of
classes c1 to cn form a partial order. If c1>c2 then c2 is a subclass of c1.
instance: a member of a class.
We now describe five types of classification problem. A classification problem is informally defined as a
situation in which there might be some confusion about the hierarchical relationships that should be included
in a formal ontology. Each type of problem will be defined more fully in the following subsections. The types
that we have so far identified are:
(i) atypical instances: an instance is not a typical example of a class to which it belongs. This may lead to
difficulties with identification of the instance as a member of the class and with inheritance of properties
from the class to the instance.
(ii) overlapping siblings: a member of a class is also a member of a sibling of that class.
(iii) context-sensitive subclasses: whether a hierarchical relationship is said to exist between two classes or
not varies between contexts.
(iv) excluded instances: an instance of a class cannot be included as an instance of any of the immediate
subclasses of that class.
(v) non-instance similarity: an entity satisfies the criteria for membership of a class which it is not a member
of.
Instances of classification problems can hinder the development of a formal ontology from an informal
description of a domain. They may also hinder the sharing of knowledge across resources where different
decisions have been made in the resolution of these problems. It is hoped that a classification of these
problems will aid the identification of the issues involved in developing a formal representation.
It is commonly the case that a formal ontology is intended to be reusable. It has been suggested that in
such situations, the definitions which comprise a formal ontology should be objective [7]. Although
desirable, this is a difficult ideal to satisfy and evaluate in practice. We prefer to use the term verisimilitude
to describe the purpose of this goal. Verisimilitude is as a property of scientific theories that “have stood up
to severe criticism, including tests” ([17], p.57). Ontologies should be assessed in relation to the requirements
of the ontology. Thus verisimilitude can only be evaluated with respect to the intended use of the ontology.
We will introduce some tests that can be applied during the ontology design phase in order that the
verisimilitude of an ontology can be maximised prior to a final assessment. Each of the five types outlined
above will now be described in more detail and illustrated with examples. Some of the issues raised for their
formal representation will be discussed in relation to these examples.
2.1 Atypical Instances
We begin the discussion of the various kinds of classification problems with one that will be familiar
to knowledge engineers. The existence of atypical instances has long been recognised. One of the most
important analyses was that of Rosch and her colleagues (e.g. [18]), which focussed on two implications of
the classical view of categories:
(a) that no members of a category can be better examples than others.
(b) that category membership is independent of the person doing the categorisation.
Experimental evidence showed the existence of typicality ratings, where some members of a class are judged
to be more typical examples of that class than other members. The explanation that was given for this effect
was that categories exhibit gradience i.e. that some instances are more ‘central’ to the categories than others.
Membership of a class is therefore a matter of degree, based on the similarity of an entity to the prototype
of the category. Typicality ratings are explained as resulting from differing degrees of similarity to this
prototype. Although the prototype view is no longer widely held as an explanation for human categorisation,
the existence of typicality ratings is not disputed.
As an example, consider one of the most basic distinctions made in cell biology, the classification of
cells into one of two kinds, procaryotic or eucaryotic. The distinguishing features of these cells are given in
Table 1 (reproduced from [2]). This table is introduced by the sentence: “the major existing eucaryotes have
in common both mitochondria and a whole constellation of other features that distinguish them from
procaryotes (Table 1-1)” ([2], p.19). Table 1 is taken to describe the distinguishing features of the two child
classes of the class ‘cell’ and constitutes an informal representation of the classes ‘eucaryotic cell’ and
‘procaryotic cell’. According to the classical theory, the properties described here could be taken to be
necessary and sufficient features of these classes. However, many of the listed properties are generalisations
that do not apply to every member of each class. For example, it is clear that the property ‘contains a nucleus’
is one of the defining characteristics of eucaryotic cells. This view is reinforced by the statement “Eucaryotic
cells, by definition and in contrast to procaryotic cells, have a nucleus” ([2], p.15). Although this is presented
as a defining feature of eucaryotic cells, there are exceptions, as shown by the eucaryotic red blood cells:
“erythrocytes (or red blood cells) are very small cells, usually with no nucleus” ([2], p.25).
Another example is that the location of genetic material and associated processes is presented as a means
of distinguishing between the two subclasses of ‘cell’. In procaryotic cells, the two stages of gene expression,
Table 1: Comparison of Procaryotic and Eucaryotic Organisms
([2], Table 1-1, p.19)
transcription and translation, occur in the same location: “in procaryotic cells, there is no
compartmentalization - the translation of RNA sequences into protein begins as soon as they are transcribed”
([2], p.26). In eucaryotic cells, these processes are generally located in physically distinct regions of the cell:
“in eucaryotes, however (except in mitochondria and chloroplasts, which in this respect as in others are closer
to bacteria), the two steps in the path from gene to protein are kept strictly separate” ([2], p.26). Indeed,
exceptions have been identified for most of the ‘defining’ characteristics listed in Table 1.
For classes that have many atypical instances, we would typically give multiple partial definitions of the
class rather than a single complete definition. A complete definition should only be given where we can
identify a set of necessary and sufficient features that define a class. For many concepts this is not possible
as no such set of properties exists. A generalised example is given below for a class c defined in terms of the
properties p1,…, p6:
(~x) p1(x) Y p2(x) Y p4(x) c(x)
(~x) p1(x) Y p3(x) Y p5(x) c(x)
(~x) p2(x) Y p5(x) Y p6(x) c(x)
Note this is only a partial definition as we have only defined the sufficient cases. Adequate definitions in
terms of necessary features cannot always be given for categories exhibiting gradience. The purpose of each
sufficient case is to cover a set of instances of c and with all of the partial definitions we hope to cover all
possible instances of the class. Although it is usually straightforward to give some partial definitions that
cover a set of instances, it is more difficult to coordinate these definitions in order that they collectively cover
all possible instances. For example, we may have the instance i about which we know the following:
c(i) Y p1(i) Y p2(i) Y p3(i) Y p6(i)
Although i is a member of the class c it would not, according to our definition of c, be included as such
(although this additional information does not contradict the earlier definition since no necessary definition
was given). The problem here of course lies with the definition but this is not always the case. If the
generalised example seems to be an unrealistic strawman, consider giving a definition for the class
‘eurcaryotic cell’. Having a nucleus gives us the basis for one partial definition but as we know, this does
not completely cover the instances of the class. It is unlikely that we would be able to give a set of
meaningful partial definitions for the class that completely covered the instances of the class. For purely
practical reasons, we would probably never have access to a full set of instances formally specified with their
known properties. It is impossible to know a priori whether we have managed to exhaustively define the
class. It seems that this uncertainty is something we must live with.
We can identify two distinct issues involved in the representation of classes with many atypical
instances:
1) there is no set of necessary properties that will enable us to determine that entities are definitely not
members of a class e.g. knowing that a cell has a nucleus implies that the cell is eucaryotic. However,
many eucaryotic cells do not have a nucleus. The property of not having a nucleus does not allow us to
say that the cell is not eucaryotic.
2) many of the properties are generalisations and are therefore difficult to formalise, e.g. knowing that a
cell have size between 10 and 100 )m gives a reason for believing that the cell is eucaryotic but does
imply that the cell is eucaryotic.
Cases of type (1) require the use of partial rather than complete definitions. Type (2) situations restrict the
properties that we can include in the partial definitions. We cannot use the size of a cell as an implication of
eucaryotic-hood since this only implies a probability of a cell being eucaryotic. Unless our chosen
representation is expressive enough to allow us to represent probabilities (and most languages chosen to
represent ontologies do not permit this), such properties can only be utilised when conjoined with other
properties. For example, it if were the case the all cells that have a size between 10 and 100 )m and which
exist naturally in a multicellular organisation are eucaryotic, we can utilise these two generalisations to give
another¸partial definition.
How then, should we represent such classes with due regard to the maximisation of verisimilitude? If
there is no set of properties that are necessary features that all instances of the class exhibit, we must use one
or more sufficient definitions. Given such a representation of a class, we then need to assess whether or not
the set of the partial definitions covers all instances of the class. Since we may not have access to all
instances of the class, domain knowledge must be used, in the form of a domain expert, to provide us with
atypical instances to test against our definitions.
2.2 Overlapping Siblings
It is a common problem in knowledge representation for an instance of a class to also be an instance of
two or more of the immediate children of that class. In the classical view of category membership, this
situation should not be possible as sibling classes are distinguished from their immediate parent and each
other by some differentia and therefore will not overlap in this way. Here, it is not always possible to identify
the differentia that distinguish the sibling classes. An entity that is an instance of two or more overlapping
sibling classes will commonly be judged atypical of at least one of those classes. Descriptions of sibling
classes that overlap commonly occur in biological literature. The problem for the ontology developer is to
identify those subclasses to include and those to exclude.
This kind of problem can perhaps be explained more clearly using an example. In [2], the subclasses of
the class ‘remote signalling cell’ are described as follows:
Three Strategies of Chemical Signaling: Endocrine, Paracrine, and Synaptic
Figure 1: Possible Classifications of ‘neuroendocrine cell’
Chemical signaling mechanisms vary in the distances over which they operate: (1) In endocrine
signaling, specialized endocrine cells secrete hormones, which travel through the bloodstream to
influence target cells that are distributed widely throughout the body. (2) In paracrine signaling,
cells secrete local chemical mediators, which are so rapidly taken up, destroyed, or immobilized
that the mediators act only on cells in the immediate environment, perhaps within a millimeter or
so. (3) In synaptic signaling, which is confined to the nervous system, cells secrete
neurotransmitters at specialized junctions called chemical synapses; the neurotransmitter diffuses
across the synaptic cleft, typically a distance of about 50 nm, and acts only on the adjacent
postsynaptic target cell.
[2], p.682)
Suppose that on the basis of this description we make the (seemingly reasonable) decision to distinguish three
subclasses of the class ‘remote signalling cell’ - i.e. ‘endocrine cell’, ‘paracrine cell’ and ‘nerve cell’.
Subsequently, another type of remote signalling cell is identified:
The linking function of the hypothalamus is mediated by cells that have properties of both nerve
cells and endocrine cells; for this reason they are called neuroendocrine cells. ([2], p.683)
The class ‘neuroendocrine cell’ can, according to the existing hierarchy, be included as both a subclass
of‘endocrine cell’ and a subclass of ‘nerve cell’. Neuroendocrine cells secrete hormones into the bloodstream
like endocrine cells and respond to synaptic stimulation like nerve cells, although they are typical of neither
of the superclasses. On the surface, it is not at all clear how we should represent the further subclass of
‘neuroendocrine cell’. For the above example, four possible representations of the class ‘neuroendocrine cell’
can be identified, as shown in Fig. 1. In more detail, these are:
(i) as a subclass of the class ‘endocrine cell’ i.e. as an atypical instance of an endocrine cell.
(ii) as a subclass of the class ‘nerve cell’ i.e. as an atypical instance of a nerve cell.
(iii) as a subclass of both the ‘endocrine cell’ and ‘nerve cell’ classes.
(iv) as a new subclass of the ‘remote signalling cell’ class.
Solutions (i) to (iii) share the notion that ‘neuroendocrine cell’ is a subclass of one or more of the three
existing classes, whereas solution (iv) suggests that the relationship of ‘neuroendocrine cell’ to the existing
classes is at most one of similarity. More generally, if we have the following definitions of the class c and
its subclasses c1 and c2 in terms of properties p1,…, p4:
(~x) c(x) c1(x) Z c2(x) Z … cn(x)
(~x) c(x) Y p1(x) Y p2(x) c1(x)
(~x) c(x) Y p3(x) Y p4(x) c2(x)
It can be seen that we have given partial definitions for the classes c1 and c2. Now suppose that we have
another subclass cn+1:
c(x) Y p1(x) Y p2(x) Y p3(x) Y p4(x) cn+1(x)¸
That is, instances of the class cn+1 are also instances of both c1 and c2 and cn+1 can unproblematically be
included as a subclass of both c1 and c2. This is the same situation that we encountered in the signalling cell
example above and suggests that solution (iii) is the most accurate representation in that situation. However,
such a representation would give us more problems than it solved. For example, there are various different
kinds of neuroendocrine cell, some of which are more similar to endocrine cells than nerve cells and others
for which the opposite applies. In such circumstances, solution (iii) will involve much overwriting of
inherited properties. There is a fundamental problem with our initial representation of the three subclasses
of ‘remote signalling cell’. Two of the subclasses (‘endocrine’ and ‘paracrine’) are functional descriptions
in that they describe the way in which some cells act. These are therefore more properly represented as roles
that certain cells play rather than classes of cell. Tests in these situations that help maximise verisimilitude
would include the use of principles that help us to identify those predicates that are sortal i.e. that identify
an entity as a kind of thing (examples of such principles can be found [8] and [20]). The use of such
principles would help to avoid the development of ontologies in which concepts such as ‘endocrine cell’ that
represent functional roles are defined as classes. Not all classificatory knowledge is ontological knowledge.
2.3 Context-sensitive Subclasses
To some degree all classifications are dependent on the context in which they are made. In [3] it is suggested
that categories are often formed on the basis of temporary goals. It is often difficult to know which concepts
such be defined as classes in an ontology and how to define those classes that we choose to include in our
ontology. The context-sensitivity of an ontology is discussed in [19], where it is suggested that the meaning
of terms depends on the context in which a term appears and the context in which the term is used. They
suggest that an ontology should only be specified as far as the context of use requires.
As an example of context-sensitive membership from the biological domain, consider the classification
of the kinds of chemical bonds that exist between biological molecules. There are two classes of chemical
bond, covalent and non-covalent. The subclasses of the non-covalent bond class are described in the
sentence: “The non-covalent bonds encountered in biological molecules are usually classified into three
types: ionic bonds, hydrogen bonds, and van der Waals attractions” ([2], p.88). Sometimes, however,
hydrophobic forces are included as another kind of non-covalent bond: “Another important weak force is
created by the three-dimensional structure of water, which tends to force hydrophobic groups together” ([2],
p.88). Although this force has features in common with the non-covalent bonds, it is not strictly a member
of this category: “This expulsion from the aqueous solution generates what is sometimes thought of as a
fourth kind of weak non-covalent bond.” ([2], p.88). This is a somewhat weaker assertion than stating that
hydrophobic forces are atypical instances of non-covalent bonds as it is suggested that only under certain
conditions are hydrophobic forces considered to be non-covalent bonds.
Although it is impossible to exhaustively specify all relevant contexts, it is usually possible to identify
those subclasses that should or should not be included as part of the definition of the superclass. Where the
existence of a hierarchical relationship is dependent on the context, it is unlikely that it should be included
in an ontology. It is more likely that a similarity is being drawn between two different ontological kinds as
a didactic aid rather than as a description of the meaning of terms. It is important to be clearly distinguish
between these two different kinds of explanation. The phrase “biological molecules are usually classified into
three types” ([2], p.88) suggests that in the majority of contexts, hydrophobic forces are not members of the
class ‘non-covalent bond’ and that the hierarchical relationship between non-covalent bond and hydrophobic
force should not be included in a formal description of the domain. The description of hydrophobic forces
as a kind of non-covalent bond seems to clearly be a didactic explanation, where an analogy is being drawn
between hydrophobic groups and non-covalent bonds in order to highlight the similarities between the ways
in which the different forces act. This distinction forms the basis of a test for maximising verisimilitude here:
the context of the description of the subclasses is assessed in order to determine the purpose of the
description. If it seems that the description is made in the context of a didactic explanation, we cannot assume
that any statements made in the description will be relevant to an ontological representation of the domain.
Generally, verisimilitude will be maximised by including those relationships that go towards defining
the meaning of terms across the majority of contexts in which the ontology will be used. Although it is
impossible to exhaustively specify all potential contexts, it is often possible to determine from a knowledge
source which representation will maximise verisimilitude (and thereby also maximise the potential for reuse
of the ontology). One caveat is that not all examples of context-sensitive subclasses will be as clear as the
above description. This will be especially evident when considering non-scientific domains and each case
needs to be judged individually.
2.4 Excluded Instances
We have a case of an excluded instance when an instance of a class is not an instance of any of the subclasses
of that class. For example, consider the class of small organic molecules, the subdivision of which is
described in [2] as follows: “cells contain just four major families of small organic molecules: the simple
sugars, the fatty acids, the amino acids, and the nucleotides” (p.43). It appears that the class ‘small organic
molecule’ has four immediate¸ subclasses. However, this is not strictly the case as “some cellular compounds
do not fit into these categories” ([2], p.43). In an ontology that includes only the above four subclasses of
‘small organic molecule’, any of these cellular compounds will be an excluded instance.
As a generalised example of this problem, consider the following definitions of the classes c, c1 and c2
and the instance i in terms of the properties p1, …, p6:
(~x) c(x) c1(x) Z c2(x)
(~x) p1(x) Y p2(x) c1(x)
(~x) p3(x) Y p4(x) c2(x)
c(i) Y p5(i) Y p6(i)
The instance i is excluded from the definitions of the subclasses. A simple solution to this problem is to
define an additional class c3 along the lines of the following:
(~x) p5(x) Y p6(x) c3(x)
However, we have to question how general this solution is. It is not always feasible to extend the number of
subclasses to cover for each instance of the superclass. For example, although their number is small
compared to the four subclasses outlined above, there are very many other kinds of small organic molecule.
Should the number of subclasses of ‘small organic molecule’ be extended to include each type or should we
only include the four subclasses already identified? The solution that has been adopted for the above case
is to specify a miscellaneous subclass of small organic molecule called ‘other small organic molecules’ and
state in the ontology that the five subclasses exhaustively cover the instances of the class ‘small organic
molecule’. This seems to be acceptable solution in this situation since it reflects how the domain is
conceptualised by biologists. The class ‘other small organic molecules’ can straightforwardly be defined as
those molecules that are an instance of the superclass ‘small organic molecule’ but are not an instance of any
of the other four subclasses. The use of such ‘miscellaneous others’ subclasses is common in biological
resources, e.g. the PDB [1] and SCOP [13] databases.
Here it seems that there is no single general approach that will always produce an optimal solution. We
can assess the description of the domain to determine whether the use of a ‘miscellaneous others’ subclass
is appropriate or not. The test for verisimilitude here is whether the domain supports this notion or not. If not,
then we cannot always expect to exhaustively specify the subclasses. Practical considerations may require
that such a subclass is included -¸this is subject to the requirements of the ontology. If we consider that
extensibility of our ontology is an important requirement, we may want to include a ‘miscellaneous other’
subclass in such situations as this will allow the representation of molecules that could not be included
otherwise. This may facilitate the identification of further subclasses as more instances are represented in this
way and it becomes possible to identify commonalities among them that may be generalised to classes.
It is perhaps also worth noting that the ability to express the fact that a set of subclasses completely cover
a common superclass depends upon the language that is used to represent the ontology.
2.5 Non-instance Similarity
There is no completely objective way of deciding the relative importance of the infinitely many properties
exhibited by any entity [11]. Two entities may be judged to be more or less similar to each other, depending
on which properties are taken to be relevant to the comparison, the relative weighting given to the selected
properties, and so forth. For example, following on from the information given in §2.1 regarding the way in
which mitochondria and chloroplasts are similar to bacteria, it is clear that the former pair exhibit many
features that are similar to procaryotic cells. Table 2 details the similarities between procaryotic¸cells and
the organelles mitochondria and chloroplasts, based on some of the distinguishing features of procaryotic
cells outlined in Table 1. These are the features that would, according to the prototype theory of
categorisation, be the most important in deciding on membership of the category ‘procaryotic cells’. Although
“mitochondria and chloroplasts show important differences from … present day aerobic bacteria and
cyanobacteria” ([2], p.18) and would probably not be judged to be typical instances of the class ‘procaryotic
cell’, based on the similarities described in Table 2 it is possible they would be included as atypical instances.
However, mitochondria and chloroplasts are organelles and as such do not belong to the class ‘cell’. They
should not be considered even as atypical members of the class of procaryotic cells.
The similarities outlined in Table 2 can be explained in terms of biological theory, as “chloroplasts share
a common ancestry with cyanobacteria and evolved from procaryotes that made their home inside eucaryotic
cells” ([2], p.18). Mitochondria and chloroplasts are descended from procaryotes but are not classified as
such: “Although they seem to have originated as symbiotic bacteria, they have undergone large evolutionary
changes” ([2], p.18-19). This explanation of the classification of chloroplasts and mitochondria as organelles
also explains the degree of similarity between these organelles and procaryotic cells. The identification of
such cases will help prevent the inclusion of erroneous instances of classes in the definition of formal
ontologies. We do not consider this to be a theoretical problem as the situation described may only arise as
a result of mistakes made in the development of an ontology. It would be useful, however, to include
solutions to common kinds of mistakes in a methodology for ontological engineering.
3. Knowledge Sharing Example
We have stated that the solution to some of the problems will often be based on the requirements we
have of the ontology. We now consider an example of the development of a fragment of an ontology where
Table 2: Comparison of Procaryotic Cells with Mitochondria and Chloroplasts
(after [2], Table 1-1, p.19)
the requirement is to facilitate knowledge sharing between various data and knowledge sources. Given this,
we would like to design our ontology such we can maximise the potential for accurate communication and
minimise the communication of erroneous messages, regardless of the representation at the individual
resources. The options available in the representation of the problem cases in the shared ontology are
identified and assessed.
The example we describe is based on the domain of remote cellular signalling, a brief introduction to
which was given in §2.2, where the representation of the concept ‘neuroendocrine cell’ was discussed. The
discussion in this section is based on solution (ii), where ‘neuroendocrine cell’ was defined as a subclass
‘nerve cell’. As described in the extract from [2] given in §2.2, there are three kinds of signalling molecules:
hormones, neurotransmitters and local chemical mediators. Each of these molecules is associated with a
particular type of remote signalling cell. Based on this, the following Ontolingua-style definitions can be
given (we assume an existing definition of ‘signalling-molecule’):
(Define-Class Remote-Signalling-Molecule (?RSM)
“A molecule that is emitted by a remote signalling cell and acts at a distance on some other cell”
:Def
(Signalling-Molecule ?RSM)
:Template-Slots
(Emitted-By ?RSM ?RSC)
:Template-Facets
(Value-Type Emitted-By Remote-Signalling-Cell))
(Define-Class Hormone (?H)
“A remote signalling molecule that is emitted by an endocrine cell”
:Def
(Remote-Signalling-Molecule ?H)
:Axioms
(<=> (Emitted-By ?H ?RSC)
¸
(Endocrine-Cell ?RSC)))
(Define-Class Local-Chemical-Mediator (?LCM)
“A remote signalling molecule that is emitted by a cell acting in the paracrine mode”
:Def
(Remote-Signalling-Molecule ?LCM)
:Axioms
(<=> (Emitted-By ?LCM ?RSC)
¸
(Paracrine-Cell ?RSC)))
(Define-Class Neurotransmitter (?NT)
“A remote signalling molecule that is emitted by a nerve cell”
:Def
(Remote-Signalling-Molecule ?NT)
:Axioms
(<=> (Emitted-By ?NT ?RSC)
¸
(Nerve-Cell ?RSC)))
The class ‘neurotransmitter’ describes the signalling molecules released by nerve cells during synaptic
signalling. However, nerve cells can also act in paracrine signalling mode: “In the paracrine mode the
neurotransmitter functions as a local chemical mediator” ([2], p.682). Here we appear to have overlapping
siblings, as there are molecules which are classified as both a kind of neurotransmitter and a kind of local
chemical mediator. Although it is possible that local resources might share this representation (which makes
it easier to define mappings between the shared ontology and the local ontologies), it is generally problematic
to include such representations in the shared ontology. At the most basic level, some resources may have
defined nerve cells as acting in neurotransmitter mode only (since this is the functionality most associated
with nerve cells). Where local resources have different kinds of representation, we encounter problems in
mapping between the shared ontology and some local resources. We need a shared ontology that allows us
to define mapping functions to both kinds of representation.
Testing the verisimilitude of our representation, we see that the definitions of subclasses of ‘remote
signalling molecule’ are based on functional descriptions of molecules. We should therefore describe these
as subclasses of a class such as ‘molecular signalling function’ which describes how such a signalling
molecule might act and define this as a role of the class ‘molecule’ (we assume existing definitions of the
classes ‘molecular function’ and ‘chemical-thing’):
(Define-Class Molecule (?M)
“A molecule is a set of atoms that are chemically bonded to each other; typically, by means of covalent
bonds.”
:Def
(Chemical-thing ?M)
:Template-Slots
(Has-Function ?M ?F)
:Template-Facets
(Value-Type Has-Function Molecular-Signalling-Function))
(Define-Class Molecular-Signalling-Function (?MF)
“A molecular signalling function describes one way in which a molecule can act as a signal to a cell.”
:Def
(Molecule-Function ?M))
(Define-Class Hormone (?H)
“A remote signalling molecule that is emitted by an endocrine cell”
:Def
(Molecular-Signalling-Function ?H))
(Define-Class Local-Chemical-Mediator (?LCM)
“A remote signalling molecule that is emitted by a cell acting in the paracrine mode”
:Def
(Molecular-Signalling-Function ?NT))
(Define-Class Neurotransmitter (?NT)
“A remote signalling molecule that is emitted by a nerve cell”
:Def
(Molecular-Signalling-Function ?NT))
Here we include mainly the subclass relations. A fuller representation would involve defining classes for each
method of cellular signalling and defining axioms for the subclasses of ‘molecular signalling function’ based
on these. We can now map any representation of signalling molecule based on the original definition to our
shared ontology by defining a mapping function from the local ontology classes ‘hormone’,
‘neurotransmitter’ and ‘local chemical mediator’ to the shared ontology class ‘molecule’ and giving the ‘HasFunction’ slot of the class ‘molecule’ the required value.
A further complication is described in the sentence: “Many peptide hormones, for example, also act as
neurotransmitters (in the paracrine mode) in the vertebrate brain” ([2], p.684). The obvious temptation here
is to classify ‘peptide hormone’ as a subclass of ‘hormone’. However, since ‘hormone’ is a functional
description, we instead choose to classify ‘peptide hormone’ as a subclass of ‘molecule’ and constrain the
allowable values of ‘Has-Function’ to ‘hormone’ and ‘paracrine’. This does not however, express the notion
that the molecule is acting as a neurotransmitter. Therefore we need to further elaborate our description of
the domain to include
(i) an attribute of the ‘molecular function’ class to indicate the locations where the molecule functions can
occur (e.g. in nerve cells).
(ii) add an axiom the defines a neurotransmitter as any molecule that has a functionality that can occur nerve
cells.
We now begin to see how careful consideration of the kinds of classes we can define allows us to develop
more shareable ontologies. The problems that we encounter are caused by the temptation to give simplistic
definitions of complex situations. Some of these complications are:
(A) a metonymic relationship between the biological concepts ‘nerve-cell’ and ‘synaptic signalling cell’
which leads to the assumption that these are synonymous terms. Nerve cells can signal in both the
synaptic and paracrine modes.
(b) molecules having dual roles acting as, for example, hormones in some situations and as neurotransmitter.
This knowledge is not supported by a definition of these two types of signalling molecules as disjoint
classes.
Complications such as these are usually evident in any reasonably complex domain.
4. Conclusions
In this paper, we have shown that the formal representation of complex biological concepts is far from
straightforward as they can rarely be specified in terms of necessary and sufficient features. Careful
consideration of various alternative representations is required. We have identified several types of problem
that can arise in the formal representation of hierarchical representations and have analysed the issues
involved in selecting one representation above another. We believe that this analysis may prove to be of
practical use in the definition of formal ontologies across different domains. We should note that some of
the problem types identified (such as atypical instances) are familiar and have been the focus of substantial
research. Other types (such as context-sensitive classification) are not so well documented, perhaps because
they are less common. It is also worth pointing out that we do not believe that this list of problems and
potential solutions is by any means exhaustive and also that they will be subject to further refinement and
additional problem types and examples.
The acquisition and representation of ontological knowledge need to take into account the complexity
that is often present in domains. Principled techniques that allow the ontological engineer to deal with the
problems caused by such complexity need to be developed. Fortunately, there has recently been much interest
in the principled development of formal ontologies (summarised in [9]). However, the initial emphasis has
necessarily been on the management of the overall process rather than the fine grain details. As more
ontologies are developed, we will become aware of more of the general problems that lie in the details and
we have argued elsewhere a detailed analysis of the domain is necessary in order to overcome these [16].
It is also worth remembering that knowledge in scientific domains is continually evolving. Under such
circumstances, it is impossible to define standard ‘objective’ representations of a domain as there does not
exist a consensus opinion amongst the practitioners in the domain. It has been argued [14] that the lack of
ontology stationarity is an impediment in the use of formal ontologies for knowledge sharing. If this practice
is to become widespread in evolving domains, it will be necessary to develop methods of evaluating different
representations of the same domain [6, 21]. This will allow user of an ontology to select the most suitable
for their needs from those available.
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