Some ontology background material first published in 2013
The purpose of a formal ontology is to provide a useful, and where possible, accurate model of the real world. Ontologies are made up of elements and relationships. Those elements and relationships are named. It is important to distinguish between the element and its name(s).
In the example above we have a hierarchy of types and their names. The similarity between this and a taxonomy is clear, and from a simple example like this it is hard to see what an ontology offers above and beyond a taxonomy. Taxonomies exist in Names-Space only – they define broader and narrower terms. These are relationships between the names, not the things the names represent. This rather difficult concept is better illustrated in the example below:
The terms “Aeroplane” “B29” and “Enola Gay” are narrowing terms and would be perfectly valid in a taxonomy. However, Enola Gay is an individual aircraft while B29 is a type of aircraft (this cannot be expressed in a taxonomy) and the relationship between the first two objects is different to the relationship between the second two. The first is a specialisation relationship (super-subtype) that states the thing named “B29” is a special type of the thing named “Aeroplane”. The second asserts that the thing named “Enola Gay” is an instance of the thing named “B29”. This also cannot be expressed in a taxonomy. If the ontology is re-drawn as a Venn diagram, the difference is more obvious:
Ontologies are much more expressive than taxonomies in terms of the relationships they allow – where a taxonomy is a tree structure, an ontology is a web. IDEAS provides some fundamental relationship types that cover most of what is needed:
- wholePart – a relationship between two physical things (“Individual” in IDEAS) that asserts one thing is part of another. An example of this would be Enola Gay’s left wing being part of Enola Gay.
- superSubtype – a relationship between two Types that asserts one is a special type of the other. An example of this would be B29 being a subtype of Fixed Wing Aircraft.
- typeInstance – a relationship that asserts something is of a Type. An example of this would be Enola Gay being an instance of B29. It is very easy to conflate typeInstance and superSubtype (as seen in most taxonomies), and it often helps to draw a Venn diagram to help with this problem.
- beforeAfter – a relationship that asserts one Individual occurs before another. This is a uniquely 4D concept that one item occurs before another. An examples would be that Richard III was before George III. However, in most cases this is used for processes – i.e. one thing happening before another.
More complex relationships can generally be unpicked into a chain of the above relationships or revealed under analysis to be simply one of the above. For example, if we want to talk about two things that overlap each other, it breaks down into two whole-part relationships:
In the example above, two Individuals share a common part (the overlap) – i.e. there are two whole-part relationships, both of which point to the shared part. In many cases, what appears to be a new type of relationship is (in a 4D ontology) just one of the fundamental ones. For example, a person’s role in a process becomes a simple whole-part in a 4D ontology:
In the example (space-time map) above, the role is simply a part of the person. It is also a part of the process, so this is another overlap pattern.
Working with Ontologies
The re-use of fundamental elements and relationships is a characteristic of formal ontologies – especially of 4D ontologies. This “deep simplicity” comes at a price though. The concepts that underpin it are uncomfortable for many people. It is not natural to think four-dimensionally, so it is not natural to think of a person’s role in a process being part of that person. Strangely, it is more intuitive to think of the role being part of the process. The reason for this is that we naturally think of processes as stretching through time. We tend to view objects “in the now” so it is far less intuitive to apply 4D principles to people, equipment, places, etc.
Formal ontologies also bring with them some logical and set theoretic principles that can be hard to work with. As previously mentioned, the typeInstance relationship is often conflated with superSubtype. This becomes a particular issue when we have Types that are instances of other Types – we tend to naturally assume the relationship between them is superSubtype.
Space-Time Maps
Given that IDEAS is four-dimensional, the models are sometimes best explained using a timeline approach. In these “space-time maps”, the x-axis is time, and the y-axis is space (i.e. three dimensions crammed into one). In the example below, an aircraft is shown departing London Heathrow Airport and flying to San Francisco. The diagrams are topological; they don’t attempt to accurately represent distances and timescales. They are used to illustrate sometimes quite difficult four dimensional problems.
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