Abstract:Upper level ontologies are used to facilitate the semantic integration of domain ontologies and guide the development of new ontologies. For this purpose, they contain general categories that are applicable across multiple domains. Upper level ontologies usually provide rich definitions and axioms for their categories. Different upper level ontologies provide different distinctions based on the kinds of entities they include, their theories of space and time as well as the relation of individuals to space and time.

Author: Robert Hoehndorf, European Bioinformatics Institute

What is an upper level ontology?

An ontology is a shared conceptualization of a domain. Ontologies are used to specify the meaning of the terms in a vocabulary that is used within some domain. To represent the meaning of terms, ontologies contain categories. These are organized in an is-a hierarchy, the taxonomy. Some categories are more general than others with respect to the is-a hierarchy. When defining these general categories within a domain, it is often possible to introduce more general categories. For example, in an ontology of cell components, the most general category may be Cell component. When we want to define Cell component, we can introduce another, more general category, and provide distinguishing properties. For example, we can define Cell component as an Object which is part of some Cell. Object is the more general category here, and Cell component will be a sub-category of Object. We can then further define Object as an Entity which has spatial extension and is wholly present at one point of time.

The assumption behind upper-level ontologies is that, when this generalization is performed in ontologies of multiple domains, we will come up with a small set of categories that is the same in all these domains. Most domains will deal with objects, processes, properties, relations, space, time, roles, functions, categories, individuals or similar. An upper-level ontology is an ontology that defines and axiomatizes these most general categories.

There is considerable disagreement about what these general categories that are relevant in any domain are. There is even more debate about what the properties of these categories are. For example, what are the properties of time? Are there only time points, and a time interval is defined as the set of all time points between two distinct time points? Or are time intervals primitive and time points are derived from infinite sets of time intervals that meet? Are there atomic time intervals or is time continuous?

Many of these questions have been debated in philosophy for thousands of years. As a result, upper level ontologies often rely much more on philosophical theories and commitments to particular philosophical views than domain ontologies. Upper level ontologies also rely much more on axioms than on formal or natural language definitions, because it is often hard to define an upper level category using other categories that are uniformly understood. Instead, the way these categories interact with other categories becomes more important. Therefore, although it is often sufficient for many domain ontologies to define categories in natural language or through explicit definitions, rich axiom systems are necessary to establish the meaning of upper level categories.

A foundation of a domain ontology in an upper ontology consists at least of assignments of super-categories from the upper level ontology for all the categories of the domain ontology. Because the domain ontology will usually be structured in the form of a taxonomy, only few categories will have to be explicitly assigned a super-category from the upper level ontology. A more expressive method of foundation is the ontological reduction of a domain category to an upper level ontology, where domain categories are explicitly or implicitly defined using the categories of the upper level ontology.

Why use upper level ontologies?

The main application of upper level ontologies is to provide semantic interoperability of ontologies across multiple domains. Because upper level ontologies provide general concepts which are common to all domains, they can provide a common ontological foundation for domain ontologies.

For example, consider an ontology for physics with a category Electron, and another ontology in the manufacturing domain with a category Transporter. Both Electon and Transporter may be defined as a sub-category of Object. Yet, Object in an ontology of physics and Object in an ontology of manufacturing may have different properties, they may in fact be completely different things. For example, instance of Object in physics may always have a temporal extension, or their location may not be determinable at the same time as their momentum. In the manufacturing domain, objects may always have a price, they may always have two or more components, and so on. An upper level ontology provides well-defined primitives to make these conflicts explicit, and provide a common foundation for both. Electron could be classified as a sub-category of Process, while Transporter becomes a sub-category of Endurant in an ontology. Therefore, upper level ontologies help to make the ontological commitment of a vocabulary explicit.

Upper level ontologies provide restrictions on the categories they provide through axioms. These restrictions are inherited by the domain ontologies which are founded in the upper level ontologies. Consequently, upper level ontologies provide a means to verify domain ontologies with respect to a particular foundation in an upper level ontology. This is particularily useful when a new ontology is developed with the intention to semantically interoperate with an already existing ontology.

When applied in the ontology development process, upper level ontologies provide a means to verify basic ontological constraits. They can also be used to verify the compatibility of the developed ontology with other ontologies that are founded in the same upper level ontology. Consequently, they can provide a high-level compatibility and plausibility check for domain ontologies and their semantic integration.

Categories and individuals

A fundamental upper level distinction is one between individuals (or particulars) and ontological categories. Although there is considerable discussion about the nature of individuals in philosophy, the common definitions states that an individual is an entity that cannot be instantiated. A category can be instantiated. The relation between a category and its instances is the instance-of relation.

Most upper level ontologies focus on the kinds of individuals that are present in some domain. However, there are other entities that are relevant in several domains. In any knowledge representation task or in the process of ontology engineering, we use categories. Categories have definitions, a history, an intension, there are axioms pertaining to categories, authors and creators of categories, categories may be consistently defined or inconsistently defined, and so on. Based on these properties, there are different kinds of categories. Consequently, there are upper level ontology who distinguish at a very basic level between categories and individuals. The instances of a Category category will be ontological categories such as Dog, Electron, Red, Species, while the instances of an Individual category will be individuals: my spider Nero, the red of the apple I eat now, the 1999 Berlin Marathon. Some of the instances of Category will be sub-categories (via is-a) of Individual, such as Dog or Red.

Whether the upper level ontology provides general upper level categories for both categories and individuals, or only for individuals, is the first distinguishing feature between upper level ontologies.

Time and space

A fundamental component of most upper level ontologies is a theory of space and time. The basic distinctions are between time points and time intervals, as well as spatial points and spatial regions.

A simple model of time are the real numbers (or dense linear orders). The basic entities in an ontology of time based on real numbers are time points, which correspond to real numbers. Time intervals are derived by pairs of two real numbers. For example, the real number e can be considered a time point, and [e,10] a time interval. Such an ontology of time has difficulties when time intervals are divided. If we want to divide the interval [0,2] into two intervals of exactly the same length, we have two options: either [0,1] and the half-open interval ]1,2], or the half-open interval [0,1[ and [1,2]. In each case, there is one time interval for which we cannot determine the first or the last time point that belong to the interval, because one time interval will be half-open. This is often counter-intuitive.

To solve this approach, temporal-based ontologies of time were proposed. In these ontologies, time intervals are considered to be primitives and time points derived. Time intervals can meet other time intervals: an interval I meets an interval J when I and J do not overlap and there is no interval between I and J, i.e., I ends at the same time that J starts. Time points are derived as sets of intervals that meet one interval. In interval-based ontologies of time, time intervals can be divided into exactly two halfs, and for each a start and end point can be constructed.

In addition to point-based and interval-based ontologies of time, mixed approaches are being developed. The ontology of Brentano-time uses two temporal categories: time intervals and time boundaries. In Brentano-time, time intervals are primitive and each time interval has exactly one left and exactly one right boundary. Time boundaries are dependent on time intervals, and two time boundaries can coincide. When two time boundaries coincide, they are at the same time. When a right boundary of an interval coincides with the left boundary of another interval, these intervals meet. If two left boundaries coincide, the intervals start at the same time and overlap in their beginning. If two right boundaries overlap, the intervals end at the same time and they overlap at their end. Dividing a time interval in two parts yields two intervals, both with left and right boundaries. The right boundary of the first interval coincides with the left boundary of the second, yet both boundaries are distinct entities. This allows referencing both the last point of the first and the first of the second interval, while both intervals are divided into exactly two halfs.

Space is usually similar to time. Ontologies that use the real numbers as a model of time use $latex {R^3}&fg=000000$ as a model for space. Using time intervals as basic entities of time goes together with using spatial regions as primitives and deriving planes, lines and points from those. Similar to Brentano-time, Brentano-space treats spatial regions as primitives, and spatial regions have two-, one- and zero-dimensional boundaries which can coincide. Similar to time, we can ask how to divide a spatial region into exactly two halfs and find similar solutions in the different ontologies of space.

The ontology of space and time in upper level ontologies is our second distinguishing feature.

Objects and Processes

Based on the ontology of space and time, different categories of individuals can be derived. When the ontology of time is based on time points as primitives, three-dimensional objects which are present at points in time will naturally be available in the ontology. Based on the definition of time intervals in such a model, processes can be introduced in which objects may participate. Objects at time points are called endurants or continuants. An endurant is an individual which is wholly present at each time point at which it exists, and it persists through time. Wholly present means to be present with all its parts. In particular, endurants have no temporal parts.

The main problem for endurants is their persistence through time. How, in what sense, is John F. Kennedy as a child the same person as John F. Kennedy before his death? What makes an endurant persist through time, while loosing and gaining parts and changing most of its properties? The solution to this problem is to assign identity conditions to an endurant, such that an endurant is considered to be the same endurant as long as it has a property which assigns identity it. These identity conditions do not have to be intrinsic to the endurant, but can be assigned to it within specific contexts. Therefore, it may be that two objects at two different time points are the same with respect to one identity condition, and distinct with respect to another.

Endurants conflate presence at time points and persistence through time. In particular, there is not an instance of an endurant, but always an instance of an endurant at some time point. Similarily, endurants have parts only at time points and properties only at time points.

An alternative to using endurants in an ontology which uses time points is to separate both aspects: persistence through time and whole presence at time points. In such a setting, two categories must be introduced: one for entities existing at time points, another to provide the identity criterion for persistence through time.

On the other hand, occurrants are entitites which have temporal parts, they unfold through time. In particular, processes are occurrants. Endurants may participate in occurrants.

Examples of endurants are my spider Nero, the red of the apple in front of me or the Eiffel Tower. Examples for occurrants are the World War, the 1999 Berlin marathon or the process of writing this blog post.

Ontologies that employ a theory of time based on time intervals will contain temporally extended objects as primitives, and need to derive objects at time points in some form. Some ontologies get by without temporally non-extended entities, in particular the General Process Theory (GPT). These are strictly four-dimensional ontologies as all entities in these ontologies are are temporally extended. Objects may be very small processes, properties are layers of processes, etc.

Ontologies using Brentano-time and Brentano-space are bi-categorical in a different sense than endurant-based ontologies. Endurants are wholly present at time points. In Brentano-time, some entities are wholly present at time boundaries. These entities are called presentials. Similar to the case for endurants, criteria must be established for persistence through time, using a persistant category which provides identity criteria for persistence through time. Because Brentano-time is based on time intervals, additional constraints are usually established to require that the presentials belonging to one persisting object (persistant) are embedded in a connected process.

One particular feature of ontologies based on Brentano-time is that it is possible to have two distinct presentials at coinciding time boundaries (at the same time) which are identical with respect to some persistant. One application of this feature is to divide processes in two parts and assign properties to the participants of the objects. For example, a ball thrown into the air will move upwards for some time, and downwards for another. In Brentano-time it is possible to find the first presential in the downward process, and the last presential in the upward process, and both exist at coinciding time boundaries, therefore the same time.

A further kind of entity included in some ontologies are abstract entities. Abstract entities are independent of space of time. This means that they either exist outside of space and time, or they exist at all times and everywhere.

Further distinctions

Further distinctions drawn by upper level ontologies pertain to existential or ontological dependence. An entity a is existentially dependent on another entity b, if, whenever a exists, necessarily, b exists. The important ontological problem with existential dependence it the formalization of necessarily. For example, according to the axioms of set theory, whenever a exists, so does the singleton set {a}. Therefore, a is existentially dependent on its singleton — a rather counter-intuitive assertion.

Ontological properties (or qualities) are often considered to be existentially dependent on their bearer: whenever a property exists, necessarily, so does a bearer of the property. Similarily, relations can be dependent on their relata, roles on their players or processes on their participants.

The major distinctions drawn in most upper level ontologies pertain to those: individuals vs. categories, theories of space and time, persistence through time, the relation between objects and processes and dependent vs. independent entities.

Implemented top-level ontologies

Basic Formal Ontology: The Basic Formal Ontology (BFO) is an ontology of non-abstract individuals that uses real numbers as its model of space and time, and includes two categories of endurants (called Continuants) and occurrents.

Descriptive Ontology for Linguistic and Cognitive Engineering: The Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE) is an ontology of individuals, both abstract and concrete. DOLCE uses real numbers as its model of space and time, and includes endurants, occurrents and abstract individuals.

General Formal Ontology: The General Formal Ontology (GFO) is an ontology of categories and individuals. It uses Brentano-time and Brentano-space and is a four-dimensional ontology. It includes processes, presentials and abstract individuals, and additionally contains a classification of ontological categories.

Further upper level ontologies include the Suggested Upper Merged Ontology (SUMO), the KR Ontology or the Cyc upper ontology.