In 'What Is an Ontology?' Guarino, Oberle and Staab offer a widely cited analysis of the term 'ontology' [5]. According to them an ontology is, roughly speaking, a logical theory, which models approximate, as best as possible, the intended models according to a given ontological commitment (which is based on a conceptualization). In this paper we offer six arguments against their proposed analysis of 'ontology'. It has technical flaws that lead to absurd consequences. Further, the analysis is based on implausible assumptions about the nature of conceptualizations.
In 2009 Nicola Guarino, Daniel Oberle and Steffen Staab published the paper ‘What Is
an Ontology?’ where the authors analyze the term ‘ontology’ [
The author of this paper has long considered [
Nevertheless, the purpose of this paper is simple: to convince the reader that the
answer to “What is an ontology?” that [
Since [
For this purpose we will first motivate why the question “What is an ontology?”
needs answering (section 2) and then summarize the analysis of “ontology” in [
Since most of this paper is going to be critical of [
specification of a shared conceptualisation.” [
Definition 1 is a variant from other definitions in the literature [
The answer is that all of these definitions are not helpful. Any definition is only useful if the meaning of its definiendum is less clear than the meaning of its definiens. It is quite easy to introduce the term “ontology” to a novice to the field by illustrating it with examples and use cases. Such an introduction leads to an operational understanding of the term ‘ontology’, which allows the novice to recognize typical examples of ontologies and to recognize typical situations where ontologies may be used to solve a problem. Thus, any definition of “ontology” is only helpful if our understanding of the definiens exceeds this kind of operational level of understanding.
However, the definiens of Definition 1 is at least as unclear as the term “ontology”,
in particular the term “conceptualization” is not well understood. Of course, the literature
contains attempts to clarify the terms in the definiens. For example, according to [
The major contribution of [
In [
logical language with the vocabulary V and an ontological commitment K. An ontology
ing of a set of formulas, designed so that the set of its models approximates as well as possible the set of intended models of L according to K.”
The authors assume that L is a given (variant of) first-order logic; the signature of L consists of constants and predicate symbols. (There are no function symbols.) The vocabulary V that is referred to in Definition 2 is defined as the signature of L, hence the vocabulary is not an independent parameter. Thus, in the rest of the paper we just use VL to denote the vocabulary of L and VcL and VpL to refer to the constants of L and predicate symbols of L, respectively. Further, we use WFFL to denote the set of all well-formed formulas of L.
A model of L is defined as a tuple hD; R; Ii, where the universe of discourse D is a
set1, R is a set of relations on D, and the interpretation function I maps VcL to elements
of D and VpL to elements of R. Let ModL be the set of all models of L. Further, [
Note that there is no reference to the conceptualization C in the body of Definition 2. Let’s further represent the ‘approximates as well as possible’-relationship with the symbol and ‘intended models of L according to K’ as Intended(L; K). This allows us to rewrite Definition 2 as follows:
fM 2 ModL j M j= Og
Definition 3 contains three elements that require clarification: (i) What is an
ontological commitment K? (ii) What is the meaning of the intended-models-function Intended?
(iii) What does the ‘approximates as well as possible’-relation mean? Unfortunately,
we cannot answer question (iii), since the nature of remains unclear in [
The intuition behind the formalization of ‘ontological commitment’ in [
1In contrast to usual classical first-order models the domain of discourse D is not required to be non-empty.
This is likely just an oversight in [
guage.
C = hD;W; Ri is a conceptualization iff
2. R is a set of intensional relations; i.e. any r 2 R is a function r : W ! Ã(Dn), for some arity n 2 N.
K = hD;W; R; Ii is an ontological commitment for L iff 1. hD;W; Ri is a conceptualization; 2. I is a total function I : VL ! D [ R such that I(v) 2 D if v 2 VcL and I(v) 2 R if v 2 VpL.
Since an ontological commitment K is an intensional first-order structure for a language
L, it provides for any possible situation (a possible world) the extensions of the relations
in this situation. Guarino et al. assume a rigid interpretation of the constants and a
constant domain. (We will revisit this assumption in section 4.3.) Under these assumptions
K determines what models of L are possible. These are the intended models of the L
according to K (see Definition 5), which corresponds to Definition 3.3 in [
A model M = hD; R; Ii of L is an intended model of L according to K iff for any c 2 VcL , I(c) = I(c); there exists some w 2 W such that, for all p 2 VpL, I(p) = (I(p))(w).
Intended(L; K) = fM 2 ModL j M is an intended model of L according to Kg Definition 5 allows us to finish our rewrite of Definition 2 by substituting Intended(L; K) in Definition 3. This results in Definition 6.
Let L be a logical language and K = hD;W; R; Ii be an ontological commitment for L.
fM 2 ModL j M j= Og fhD; R; Ii 2 ModL j
8c 2 VcL : I(c) = I(c) and 9w 2 W 8p 2 VpL : I(p) = (I(p))(w)g
If we compare Definition 6 with Definition 1, it turns out that the ‘shared’ aspect was lost, but the other components of Definition 1 are represented. The ontology is ‘formal’ and ‘explicit’, since it is a set of sentences of a first-order language L. The conceptualization hD;W; Ri is part of the ontological commitment K. And the specification relation is represented as the approximation relation that holds between the models of O and the intended models of K.
In this section we discuss three different technical objections against Definition 6.
According to Definition 6 an ontology is a set of axioms in a first-order logic L whose models approximate the set of models that are possible according to a given intensional first-order logic structure (a.k.a. ontological commitment). This intensional first-order logic structure consist of a conceptualization and an intensional interpretation function. Conceptualizations are represented as intensional relational structures (see Definition 4).
One obvious challenge against Definition 6 is its first-oder logic centricity. Most ontologies are not written in first-order logic, but in the Web Ontology Language OWL. However, we assumed explicitly in section 3 that L is a first-order logic language.
What happens if we ignore that L is supposed to be first-oder logic? For the sake of the argument, let’s assume L in section 3 is OWL 2 DL with Direct Semantics2 that uses a particular OWL vocabulary V, and let K = hD;W; R; Ii be any ontological commitment, where I is a suitable mapping that maps V to the conceptualization hD;W; Ri.
An OWL 2 DL model is a 10-tuple that involves two different universes of discourse
and seven different interpretation functions and a distinguished set of named individuals
[
One obvious strategy to fix the problem would be to introduce an OWL-analog for
all definitions in section 3, in particular by introducing an OWL-conceptualization, which
consists of mappings of possible worlds to OWL models, and an OWL-ontological
commitment. This would be a rather straightforward task, but it would be philosophically
incongruent with the whole approach of [
According to [
2A similar argument can be made for the RDF-based semantics for OWL 2.
4.2. The
Definition 6 contains a glaring ‘then a miracle occurs’-element: the “approximates as
well as possible”-relationship . While the rest of the definition of ‘ontology’ is
explained in detail, [
In spite of the vague nature of this relationship, one can still easily see that its current formulation is highly problematic. Assume you have a logical theory O1 that axiomatizes a conceptualization K in some L3. Further assume that during debugging it turns out that O1 lacks an axiom f , thus f is added to the theory, yielding theory O2 = O1 [ ff g. The interesting question is now: Is O1 an ontology for K? Since O2 is a better axiomatization of K than O1, it follows that the models of O2 approximate the intended models of K better than the models of O1. Hence, the models of O1 do not approximate the intended models of K as well as possible. Thus, according to Definition 6 (and given the reading of as “approximates as well as possible” ), O1 is not an ontology for K.
If we would take this seriously, it would mean that very few of the artifacts we call ‘ontologies’ are ontologies. Because any existing ontology that models a complex domain (e.g., regardless of whether it is an upper level ontology like DOLCE or a domain ontology like the Gene Ontology) has areas where it would be possible to fill out the details by adding additional axioms and, thus, achieve a closer approximation of the intended models. Obviously, the conclusion is not that these logical theories are not ontologies, but that the “as well as possible”-requirement is too strong.4
Assume O is an ontology in some first-order logic with equality L about subway systems, which contains the term “passenger”. Given Definition 6, since O is an ontology, it is an ontology of an ontological commitment K = hD;W; R; Ii and the models of O approximate the intended models according to K. The ontological commitment K determines the meaning of “passenger” by providing its extensions in all possible worlds; more technically, the interpretation of “passenger” is a function from possible worlds in W to subsets of the universe of discourse D. Thus, the set D includes all possible passengers. This includes about 7.5 billion people that are currently living on Earth, all past people, all people who will live in the future, and all people who might have lived and used a subway. Further, since we talk about all possible situations we also may want to include aliens, robots and other entities that could, possibly, be passengers of a subway.
Since the same consideration is true of any other class in O (e.g., train, station, platform), it is save to assume that the cardinality of D is going to be large. However, regardless of size, according to Definition 4 there exists a specific set D that is the domain 3In the following we often omit references to L for the sake of readability.
4As mentioned in the introduction, [
Why is the universe of discourse D of the ontological commitment of our subway ontology so interesting? Because according to Definition 5 the same set D is also the universe of discourse of every intended model of K in L. Therefore, Intended(L; K) j= f .
This consequence is absurd. If somebody builds an ontology of subway systems, the ontologist intends to represent the relationships between the classes and relations in this domain. The ontologist who is axiomatizing O has no specific intent concerning the exact number of entities in the universe of discourse and, probably, does not really care about individual entities in the universe of discourse unless they are particularly relevant to his task. Thus, Definition 5 should not require all intended models of O to share exactly one universe of discourse D. Rather, to accurately reflect the the intentions of the ontologist, the intended models of O should vary with respect to their universes of discourse.
The fact that Intended(L; K) j= f has additional unintended consequences. Since by Definition 3 the ontology O is supposed to be a logical theory whose models approximate Intended(L; K) as well as possible, it follows that the ontologist who develops our train system ontology O is supposed to include axioms in O to reflect that Intended(L; K) j= f . Now, given the fact that our D includes all possible entities in all possible worlds (including entities that actually never existed) it is probably hard to for our ontologist to pinpoint whether there are exactly 314159265359 entities in D or only 314159265358. However, it is save to say that every currently living person is a passenger in some possible world. Thus, if we take Definitions 3 and 5 literally, our ontologist is supposed to include the formalization of “There are at least 7.5 billion entities” as axiom in O.
Of course, no ontologist would include such an axiom in a subway system ontology. This example just illustrates that Definition 5 leads to absurd consequences, because it implies that all intended models use as their domain the universe of discourse of the ontological commitment D.
In the previous section we argued against the definition of ontology in [
In section 4.1 we argued that the identification of a conceptualization with an intensional relational structure hD;W; Ri is problematic: the definition is tuned to first-order logic, but since it is possible to write ontologies in many logics, a conceptualization cannot be something that is specific to a particular logic.
However, the problem runs deeper. For a given intensional relational structure
hD;W; Ri, the set W is the set of all possible situations, D contains all entities that occur
in these situations, and R determines, for any relevant relation, the extension of the
relation in any given situation. If conceptualizations were intensional relational structures,
all of this information would be in the mind of an agent A who develops an ontology.
Thus, if [
Possible world semantics and intensional relational structures are useful tools in logic and linguistics for studying semantics. The utilization of these tools in the definitions in Section 3 provide us with a formal model for the capability of people to classify objects and relationships in new circumstances based on recurring patterns of reality that they observed in the past. (One could call this capability “conceptualization”.) However, this does not mean that we can identify the capability to classify objects and relationships with intensional relational structures. There are no possible worlds in people’s minds.
There is a second reason why conceptualizations cannot be intensional relational structures. If our conceptualizations were intensional relational structures, then each of our concepts would be a function from situations (possible worlds) to the extension of this concept in these situations. Thus, in any given situation (world), we would be cognizant of the extensions of the concepts in that situation. However, that is not necessarily the case. For example, the author of this paper knows that there are aspens and birches, but if confronted with a bunch of trees in a forest, he would not be able to tell them apart. The reason is that the conceptualization of trees in the mind of the author is too shallow: he knows that Aspen tree and Birch tree are two disjoint classes and that both are deciduous trees with white bark. This conceptualization is sufficient to distinguish these trees from pines and palm trees, but too shallow to determine the extension of these classes in a given situation. This observation contradicts any analysis of a concept as a function from possible situations (worlds) to its extension in the situation.
One possible counterargument against the argument above is the following: The concepts Aspen tree and Birch tree are functions from possible worlds to sets of entities.
about the situation (possible world) that you are in. Thus, according to this argument the uncertainty of how to classify a tree is not caused by shallow conceptualizations of Aspen tree and Birch tree, but by the inability to distinguish the various possible worlds one may be in. However, this argument fails to explain our ability to change our conceptualization without a change of extensions. E.g., if the author would study aspens and birches and learn about the shapes of their leaves, he would presumably gain the ability 5A variant of the same argument could be made by considering ontologies that are only satisfiable by models with an infinite universe of discourse (e.g., the Peano axioms). In these cases the universe of discourse of any corresponding intensional relational structure would need to be infinite, and, thus, not fit into the memory of a finite being. to determine the extensions of Aspen tree and Birch tree in any given situation. Thus, the conceptualization of these classes in the mind of the author would have changed. However, the extension of these classes in any given situation would have not.
Therefore, intensional relational structures are not only different from conceptualizations, they even provide flawed models for the capability of people to classify objects and relationships in different situations.
In the last argument we argued that the conceptualization of a domain (e.g., trees) may vary in depth and that one may deepen one’s conceptualization by acquiring additional knowledge. For example, one may know that birches and aspens are different trees without knowing how to distinguish them. Note that such a shallow conceptualization is derivative, because it relies on the fact that somebody else possesses a conceptualization of the domain that is deep enough to identify birches and aspens. This conceptual division of labor is not an exception, but the norm. Since the acquisition of a conceptualization of a given domain requires effort, we tend to develop rich conceptualizations only on subjects that are important to us; for other subjects we rely on the expertise of others.
A conceptual division of labor raises difficulties for the assumption in [
Large ontologies are the result of a collaborative effort of many people. Each of these collaborators has, typically, a rich conceptualization of the subdomain that is covered by the part of the ontology that they are responsible for, but a limited conceptualization (or even no conceptualization) of other areas that are covered by the ontology. Therefore, there is no single, shared conceptualization that is represented by the ontology. In contrast, the ontology is a reflection of many conceptualizations, which may differ significantly from each other.6
In [
While this paper argues that the definition of “ontology” in [
I would like to thank Till Mossakowski for an interesting discussion on the nature of ontologies, which lead to this work. In addition, I’d like to thank the anonymous reviewers for their insightful comments and suggestions.