Type
structures, taxonomies and ontologies
Copyright 2017 Graham Berrisford. One of about
300 papers at http://avancier.website. Last updated 03/03/2017 18:35
Contents
Taxonomies as
classification structures
Ontologies as
richer type structures
Describers observe and envisage realities - past, present or future.
|
Practical idealism |
|
Descriptions <create and use> <idealise> Describers <observe and envisage>
Realities |
A reality is anything we can idealise/conceptualise into some kind of description.
If there is a reality out there that we can’t describe, it can play no role in science.
Taxonomy and ontology start with conceptualising the properties of similar things as types.
|
Ontology |
|
Types <create and use> <idealise> Ontologists <observe and envisage> Things |
Taxonomists and ontologists create structures that relate types in
what are called taxonomies and ontologies.
What is the
difference? There does not seem to be a universally accepted distinction.
So this paper
attempts to draw one; but first, we have to understand what a type is.
All animal intelligence involves abstracting types from realities.
Learning depends on matching newly observed things to past ones.
Human language, description and logic are based on types.
A feudal society is organised according to a defined structure of types (e.g. King, Bishops, Lords etc.)
The 11th century Domesday Book described England using a data structure that could be recognised by a computer.
In short, there were type structures before set theory
Static (enumerable) sets
In basic set
theory, a set is its members; it cannot gain or lose members.
E.g. The set of
single digit integers, or even numbers, never changes.
There are two
ways to define a set.
·
Enumeration:
Define set members by listing them or defining a process to generate them.
·
Typification: Define one set member by forming an "intensional definition".
Dynamic (typified) sets
People in natural
and computing sciences speak of sets that can gain and lose members.
The set members
cannot be defined by enumeration (unless you stop the universe).
Therefore, a set
member must be defined by a type.
A type implies
the existence of a dynamic (typified) set.
|
Type |
“Planet” a large physical body orbiting the sun |
“Human Resource” a person playing a role in a business |
|
Things that act as instances |
Mercury, Venus, Mars etc. |
Joel Smart, Joe Smith, Joan Soap etc. |
A type name alone
does not define a type.
A type must be
accompanied by a definition of its properties.
A taxonomy goes
some way to define the properties of a type.
A taxonomy
constrains the vocabulary used in a "bounded context" or "domain
of knowledge".
Simple taxonomies -single inheritance
The hierarchy can
be built from the top-down, from the bottom-up, or both.
The “base” type at the top of the hierarchy (e.g. resource) is definable by narrative, examples or axiom.
The base type is
divided into subtypes (e.g. human workers and machines).
Subtypes are further
sub-divisible into subtypes (e.g. human workers may be subtyped
into employees and contractors).
To describe a
thing using a type name is to presume it inherits the properties of all types
above it.
The additional
properties of a specific type may be defined more or less formally.
A simple taxonomy has one base type and one inheritance route to that from any subtype.
Taxonomies are used to help you find information.
If you find one term/type you can see all more generic types – which define that term.
You can find all next-more specialised types – and narrow your search.
Complex taxonomies - multiple inheritance
One thing may
exhibit/embody the properties of types in different taxonomies.
e.g. Joan Soap is an instance of “Human Resource” and “Woman” and “Soap family member”.
Also, one type may specialise more than one supertype.
e.g. Female Employee is a kind of both “Human Resource” and “Woman”.
Two-dimensional inheritance tables
Types drawn from
two taxonomies can be mapped to each other in a tabular form.
It can be of
interest to define a compound type at the intersection between two types.
E.g. The table below maps types in a Material taxonomy to types
in a Product taxonomy.
“Wooden Chair” is a type that inherits from
types in both taxonomies.
|
Product Material
|
Table |
Chair |
Cabinet |
|
Metal
|
|||
|
Wood
|
Wooden Chair |
||
|
Plastic
|
The periodic
table of chemical elements can be viewed as a mapping between two taxonomies.
It was initially used
to predict the existence of an element where a cell in the table contained no
known element.
This two-dimensional taxonomy of theories is interesting.
|
Theories of the universe |
Continuous |
Discrete (quantum leaps) |
|
Deterministic |
Relativity |
Most system
modelling |
|
Probabilistic |
Social systems thinking? |
Quantum Mechanics |
Note that
continuous systems are usually modelled as discrete
event-driven systems.
E.g. Forrester’s
“System Dynamics” models continuous systems this way.
And precisely
what system thinkers mean by “continuous” or “probabilistic” is not always
clear.
Coordinating disparate taxonomies
Is it possible to
superimpose an “upper level taxonomy” on different domains of knowledge?
Many have tried
to build such a generic taxonomy.
Different
attempts divide a base "Thing" between (for example):
·
Tangible
Thing or Intangible Thing
·
Type
(descriptive thing) or Instance (described thing)
·
Structure/Continuant
Thing or Behavioral/Occurrent Thing
·
Space-Bound
Thing or Time-Bound Thing.
People use
taxonomies to classify entities and events in the natural or business world.
However, imposing
a hierarchical classification on natural and business things is an artificial
exercise.
Difficulties
include not only multiple inheritance, but also that real-world things can
change type over time
That is why ontologies can include association relationships as well as
or instead of classification relationships
Data models are not (as some say) based on basic mathematical set theory.
The entities (named at the ends of relationships) are types.
An instance of an entity type belongs to a “dynamic” set, rather than a static one as in basic set theory
It belongs also to as many dynamic sets as that type has N-1 association and generalisation relationships.
Data modellers used generalisation relationships before “object orientation” came along.
But in models of
persistent data, associations are more common than (relatively fragile) generalisations.
There is a
further complication, especially in modelling
entities and events in the natural world.
There are monothetic types,
which exactly define and constrain the members of a set.
And polythetic types,
whose properties may be neither necessary nor sufficient to define a member.
This is where fuzzy logic and artificial intelligence enter the picture.
We order and organise our many views of the world various ways.
We use types, taxonomies, ontologies, class diagrams, data models etc.
All of these are descriptions imposed on realities - they are models or theories.
The degree to which a reality matches a theory can and should be determined by testing and measurement of the reality.
Set theory is relevant to ontology in so far as a set member can be defined by a type.
Types exist as descriptions, as theories to which realities may or may not conform.
Anything that exists in the natural or business world can be regarded as an instance of one or more types (a member of one or more sets).
But only in so far as it can be measured or judged as matching a set's type definition, near enough to satisfy interested parties.
In the natural world, types are polythetic and near-enough/fuzzy matching of things to types is acceptable.
Maths, computing and hard sciences are special cases in which perfect matching of realities to descriptions is expected.
But these can be seen as peculiar exceptions to the general case.
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