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Aristotelian Taxonomies

Below is an informal, FAQ-styled discussion of what Aristotelian Taxonomies/Ontologies are, why this is a good approach to creating taxonomies, and how they're useful to communities who need to manage their standardized vocabularies.

Note: For explanatory purposes, we're using the word 'taxonomy' in a loose sense.  A more accurate term is 'ontology', which we discuss later.

What is an 'Aristotelian Taxonomy'?

An Aristotelian Taxonomy is a taxonomy where each term is described in terms of a set of properties.

The list of terms with their properties is fed into a computer program, called a reasoner, which generates the taxonomic structure.  For example, in the medical field, you could create a 'Symptoms' taxonomy with the properties: Body Part, Tissue Mass, Fluid Emergent, etc, as follows:

A medical expert assigns these properties to symptoms:

A reasoner uses this information to generate the taxonomy of symptoms:


Why would you need an Aristotelian Taxonomy?

Many scientific communities already have taxonomies defined for their field of interest, however, there is often disagreement regarding the terms and the structure of the taxonomies.

Defining your taxonomic terms in terms of their properties

  • provides a clear definition of each term
  • provides scientific justification for the taxonomic structure
  • forms the basis for constructive debates within the community
  • creates wider consensus and adoption of the taxonomy within the community
  • may even lead to scientific discovery.

As the world moves to being more interconnected than ever before, greater acceptance of terminology and it's structure enables separate but related communities to interoperate using each other's standard vocabularies.

Aristotelian Taxonomies are well positioned to take advantage of computer systems that are able to reason and infer facts from the taxonomy and the data governed by the taxonomy.

How can creating an Aristotelian Taxonomy lead to scientific discovery?

First off, the process of deciding on the properties and their values for each term may do exactly that.

Secondly, the list of terms with their properties is fed into a computer program which generates the taxonomy structure. This usually leads to surprising results, especially on the first pass. Questions arise such as "Why was that term placed there?", "What makes these terms different?", "Why did it split there?". The only way to move a term to it's expected position is to review and adjust it's properties. Terms with the same properties will be deduced to be synonymous. These terms must either be accepted to be synonymous or a change in their properties is required to make them different.

This process is iterative with each pass creating a taxonomy closer to the expected result. You may discover there is no scientific reason to sub-categorize in a given place and decide to accept the new structure.  The generated structure may provide good ideas for restructuring your taxonomy.  Whether the structure changes or not, you end up with a well defined, justifiable vocabulary and structure.

Is it possible that terms could be placed under more than one category?

Yes, and this happens almost 100% of the time. Every area of real world scientific study is complex and it is next to impossible to box it into a simple structure.

Not surprisingly, attempting to do this has often been the cause for disagreement in scientific communities. For example, Geologists may define a Granite Rock as consolidated material that is acidic, has a plutonic genesis and crystal particles.  Additionally, their taxonomy includes the categories 'Acidic Rocks' and 'Plutonic Rocks'.  Now the question arises: Should a Granite Rock be classified under 'Acidic Rocks' or 'Plutonic Rocks'?

Our answer is: put it under both. This is simply because that's where it belongs!

Incidentally, the only real world taxonomy we know of where each term falls under only one category is the biological classification of living organisms in the Linnaean taxonomy. The fact that it can be categorized this way may provide evidence for evolution.

I'm not sure I agree, isn't it a bad thing to categorize things under multiple categories?

Traditionally the resistance to doing this is that it makes management of the taxonomy difficult. You could conceivably have one term duplicated several times throughout the taxonomy. Making a change to the taxonomy would require finding and reviewing all instances of the term. Additionally the duplicated term may be sub-divided multiple times and so these sub-structures would need to be duplicated and updated to be kept consistent.

However, these concerns fall away with the Aristotelian approach as a computer program generates the taxonomy, placing terms where they need to be. If you add a new term to the taxonomy, even if the term is a new high level category, the program takes care of all the house keeping and restructures the taxonomy as required.

Even though a term may appear in multiple categories, it is still straightforward to check whether one term is a subclass of another, to check the meaning of a term, and to determine the term that corresponds to a concept in your head.

What's this got to do with Aristotle?

Categorizing objects, the basis for modern taxonomies, has a long history. Aristotle (350 B.C.) suggested the definition of a class C in terms of:

Genus: a superclass of C. The plural of genus is genera.
Differentia: the properties that make members of the class C different from other members of the superclass of C.

He anticipated many of the issues that arise in definitions:
If genera are different and co-ordinate, their differentiae are themselves different in kind. Take as an instance the genus "animal" and the genus "knowledge". "With feet", "two-footed", "winged", "aquatic", are differentiae of "animal"; the species of knowledge are not distinguished by the same differentiae. One species of knowledge does not differ from another in being "two-footed".

Note that "co-ordinate" here means neither is subordinate to the other.

Can the properties be structured too?

Yes. As discussed above, each term in the taxonomy has an associated list of properties that defines the term. Each property can be arranged in a hierarchy called a Value Hierarchy. If you wanted to take it a step further, you could conceivably create properties for properties and let the computer derive the hierarchy of property values! We tend not to do this, however, as properties are typically much simpler (far fewer terms) than the taxonomy in the field of interested. Thus, generally a human decides on the structure and creates the Value Hierarchy.

A property has a domain, which is the subject area it relates to, and a range - the list of values that can be assigned to this property.

The root node (top level concept) of a property's value hierarchy is, more often than not, named 'Any' + <property name>. For example, the property 'Frequency' may have the following range of values: 'High', 'Medium', 'Low', where 'Medium' is sub-divided into 'Medium High' and 'Medium Low'. The Frequency value hierarchy would thus be:

The reasoner takes the property structure into account when generating the Aristotelian Taxonomy.

What is an 'ontology'?

A taxonomy is, and only is, a hierarchy of terms. To be able to specify properties and other attributes we need an ontology. An ontology in a nutshell, is 'a specification of a conceptualization.' (see: The term 'ontology' is borrowed from philosophy, where an Ontology is a systematic account of Existence.

An ontology is the explicit specification of a taxonomy and all it's supporting information, which includes properties, definitions, relationships and rules about the specification.

What technology is available to create Aristotelian Ontologies?

Web Ontology Language, or OWL, is a computer language, created by the World Wide Web Consortium (W3C) standards body, for creating ontologies. It is extensive and a number of varieties of it exist for various purposes. OWL is a standard and, thus, an interchangeable format used by many large communities. We use a small subset of OWL for creating Aristotelian Ontologies.

Fortunately you do not need to know about OWL to be able to use it - in the same sense as you don't need to know the details of the PDF document format to be able to create, read and exchange PDF documents.

OWL Reasoners. These are the computer programs that can derive a taxonomy structure from properties in the ontology. Reasoners can infer other information from an ontology, including determining synonymns.

Ontology Editors. Several commercial and free editors exist. Protégé is a popular free ontology editor, developed by Stanford Center for Biomedical Informatics Research at the Stanford University School of Medicine.

TLE. A tool written by Georeference Online that makes creating and manipulating taxonomies very easy.