Types of Statement in an Ontology =

Overview

An ontology or ontology-like artefact can contain a variety of types of statements about the domain being modelled, as well as statements about the artefact that is the domain model. This k-blog presents a three-way classification of types of statement with a binary split of each type. This article is a jumping off point to several other articles about the different types of statement.

Authors

Robert Stevens and Alan Rector
bioHealth Informatics Group
School of Computer Science
University of Manchester
United Kingdom
M13 9PL

Introduction

The categories of types of statement we’ll talk about are:

1. Domain vs meta-statements or metadata;
2. First order vs higher order statements;
3. Universal vs generalisation statements.

Domain Statements and Meta-Statements

An ontology describes a field or domain. The domain is the topic; some area of biology, chemistry, and so on. The domain is the entities of that domain and the relationships between those entities. So, the domain of the Gene Ontology is the major functional attributes of gene products – the molecular functions; the biological processes in which they participate and the cellular context in which they are found. The axioms in an ontology are statements about the domain being modelled. (We’ve not pointed to a specific article about domain statements, as most of the Ontogenesis k-blog is about such statements.)

In contrast to statements about the domain’s objects, the ontology also contains statements about the ontology itself or statements aboutt the statements (meta-statements or metadata). A well-made ontology should contain information about the author of statements; version of statements; dates of statements; provenance of the knowledge; and so on. Metadata are important for documenting the state and development of the ontology. They often have the same role as comments in software. There is a k-blog about metadata in ontologies.

Bundled within these metadata we can also put the labels for entities in an ontology and the natural language definitions for an entity. This latter case is interesting as it can also be thought of as domain knowledge; it is a description of an entity or entities from the domain. It is also a re-presentation of the mathematical, logical model, that is the domain model, to the human user of the ontology. In this sense we class them as meta-statements or metadata about an ontology as they are not part of the axiomatic model (this does not, of course, diminish their importance).

First Order and Higher-order Domain Statements

First order statements are about individuals in a domain. First order logic is the logic of instances in a domain. In OWL all axioms are about individuals; OWL-DL is based upon a description logic that is a fragment of first-order logic, so OWL describes individuals. When we place a restriction upon a class such as

Class: Nucleus
        SubClassOf: Organelle
                that isPartOf some Cell

WE first say there is a class of individuals we call Nucleus each of which share some characteristics that differentiate them from other organelles. We are saying that each and every individual nucleus in this class is also an individual of the class Organelle and each and every of those nucleus individuals holds a property of isPartOf to at least one individual of the class Cell, but may hold properties, including the partOf property, to individuals of another class. When we declare a property:

ObjectProperty: hasSex
SubPropertyOf: hasquality
InverseOf: isSexOf
Characteristics: functional
Domain: Animal
Range: Sex

we are talking about the behaviour of the property with respect to individuals and placing a characteristic upon that property that any individual holding that property can only hold that property with one distinct individual.

At the level of individuals, we can say facts about that individual:

Individual: Robert

        Facts:
                isBrotherOf richard

and this is, of course, a simple statement about two individuals. All axioms in an OWL ontology talk about domain individuals (we ignore punning in OWL2 for the moment).

When describing a domain we also wish to say things about the classes themselves; these are statements not about the individuals , but the class of individuals. For example, we wish to say that the class Electron is the anti particle of the class Positron. We don’t wish to say that each and every electron is the antiparticle of at least one positron; it doesn’t make sense. As first order statements are about individuals, so statements about classes of individual are second order statements. There are, of course, higher-orders of statement as well. Higher order reasoning is beyond the scope of this article, but higher-order statements are useful statements about a domain. This is particularly relevant when it comes to talk about species (10.1093/bioinformatics/btn158).

Universal Statements and generalisation Statements

Some domain statements about individuals are Universal knowledge – statements that always (i.e. Universally) hold for all individuals in a class. (This use of the word “universal” should not be confused with the philosophical, metaphysical notion of a universal.)These domain statements are things that are “universally” true about an entity — all members of this class hold this property. If an ontology is about anything it is about such universal statements about a domain’s entities. Class level restrictions in an OWL ontology are universal.

We’ve already implicitly said this -class level axioms (those axioms that describe classes — se the nucleus example above) in OWL are universal statements. When we say each and every nucleus is also an instance of the class organelle we are making an universal statement. It is true in each case with no exceptions. The same is true when we say each and every instance of nucleus is part of a cell; this is universal; there are no exceptions. Most of this Ontogenesis k-blog will be about such universal statements, so there will be no specific k-blog about universal statements.

In contrast to universal domain statements, we also have generalisation statements. Exceptions are, of course, rather common in biology. Things are often usually true about a domain or mostly true or only true in some contexts. These statements are generally true. Of course, universal statements are a specific case of a generalisation; a superclass is a more general kind than the subclass; so, wew’re really talking about universal statements and other generalisations. For example, “The first line treatment for pneumococcal pneumonia is amoxicillin” or “Rales are evidence for pneumonia”; “Eukaryotic cells have nuclei”; “roses have thorns” and, of course, the much used example of “birds fly”. Such statements are not universally true, but are an appropriate piece of domain knowledge to represent. Knowledge bases may contain indications of the strength of such statements, e.g. probabilities. These can be thought of as statements about statements. If one is ontologically strict, non-universal or generalisation knowledge is not directly representable in an ontology – it is facts about things not what things are. There are, however, tricks for approximating general knowledge within OWL. Such “tricks” will be part of the longer k-blog about generalisation statements.

Summary

This k-blog has outlined three major divisions of types of statements when representing knowledge. All are important when capturing knowledge about a domain. In theory these types of statement are independent, although we can think of a convincing case for a universal metastatement that would be likely to appear in an ontology. An example of such a statement might be “All classes in this ontology were authored by members of the Ontogenesis kblog” or “all classes in this ontology are under the copyright of the University of Manchester”; these statements are universal in that they apply to all entities (classes) in the ontology and are editorial metadata. It is also possible to think of universal higher-order statements and so on. Strictly, only universal domain statements are ontological, but all are important in representing knowledge about a domain; knowledge representation goes farther than just ontology. Including metadata helps in ontology management and presentation; higher-order srtatements capture more domain knowledge that doesn’t necessarily fit into the ontological fragment of knowledge representation. The latter need to contain all of the kinds of statements outlined and more, such as navigation hierarchies ; lexical support from thesaurae; and so on. These are all useful forms of knowledge, but not necessarily ontological knowledge.

Bibliography