How to Structure an Ontology
Andrew U. Frank
Geoinformation
TU Vienna
[email protected]
Overheads at:
http://www.geoinfo.tuwien.ac.at/presentations/frank.htm
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Overview
1.
2.
3.
4.
My approach
Separate ontology in tiers
Formal ontology as a theory
Construction of ontology
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My approach
Temporal ontology: individuals and processes!
Practical consistency is important:
Level of detail must correspond in different parts.
Error and uncertainty in description is
important
(not discussed today)
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Why a multi-tier ontology?
Most efforts to structure ontologies strive for
maximum generality.
Ontology with capital O (singular only!).
Philosophers propose a single set of rules
applicable to everything.
e.g. Aristotle's categories, mereology
Our experience shows that no single proposed
ontology covers all areas important in a GIS.
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Multiple tiers to integrate different
approaches
Tiers are similar to the top level classes in
DOLCE,
But:
Each tier follows its own logic.
The connections between tiers is formalized.
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Overview of the tiers
0. The physical environment
1. Observations of the environment and activities
2. The reality of objects
a. Objects and actions
b. Generalizations: classes and operations
3. Social reality
Legal reality
Subjective Reality
Communication
1 .. 3 are rather epistemologies,
projected ontologies or e-ontologies.
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Tier 0: Physical environment
Only part which is truly an Ontology,
the world as it is, without the presence of
cognitive agents.
There is little we know about this!
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Assume a field construction of world
Physical properties for every point in space and time:
f (x,y,z,t) = a
Not all functions are continuous,
but space and time is assumed continuous.
Physical laws (laws of nature) can be expressed as partial
differential equations in properties of points.
Many properties are determined;
not all of these are observable (or known) to us!
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Tier 1: Observation of physical
environment by agents
Observations for every point in space yield a
quantitative value.
obs (x,y,z, obs-type) = value
Differentiation between
environment and observing agent,
properties of the environment and observation
Connections to tier 0: observation functions and
activities of agents
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Tier 1: Activities change the
environment
Agents can act on the environment and effect
change in it.
The change in the environment can be
observed.
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Feedback loops ground semantics:
There are two linked feedback loop (morphism)
Physical activity – observed change
Body feeling of activity – sensory activity
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Observations types:
Point observations – values for material
properties, local motion, forces, temperature
etc.
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A Landscape
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What was shown?
3 types of observations:
wave energy in 3 frequency bands
for each observation type, 2.1 million observations
in a regular grid (central perspective from a
point)
Neither my sensor, nor the representation
contains any hint of mountains, trees,
buildings etc.
Did you see any?
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Tier 2: The Reality of Objects
People have a strong tendency to form objects
which maintain identity in time.
Objects are formed to maintain invariant
properties in time.
Object formation reduces bulk of representation
and leads to economic reasoning:
From many point observations we deduce a single
object with properties related to the point
observations.
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Connection to tier 1: Objects form areas
of uniform observation values
Areas of uniform value for an observation are
merged to objects.
Uniformity in values of observation can be in
- same color
- same speed or direction of movement
- same material
Objects are constructed to have identity and
continue in time.
This reduces the load on memory enormously.
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Lifestyles of Objects
Object continue in time.
Objects are created and destroyed.
Living things are born and die.
Some objects can have their existence
suspended.
Damir Medak (TU Wien) and
Kathleen Hornsby (U Maine)
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A Table Top
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Granularity
The observations where made with a certain
resolution.
Objects are formed from observations –
sometimes the resolution is reduced, because
less granularity is sufficient for the task at
hand.
Examples: Noodle dish is resolved into single
noodles only when you are eating it.
And what to do with the sauce?
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Object formation (2)
Philosophers talk a lot about
natural kinds
living objects,
animals or plants.
These are easy,
but there are other cases – very natural as well:
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Objects as uniform areas
Objects form partition of space (and time).
Multiple ways of subdividing space:
Different observations or combinations of
observations
Different spatial, temporal or observation
granularity.
Typically problems result from objects formed
from different observations.
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Connections from tier 2 to tier 1:
The actions change properties in some spatialtemporal region.
The property values of objects are the
integration of the observable property values
for spatial regions.
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Tier 3a: Subjective RealityIndividual cognitive agents
Individual internal reality
Feelings are subjectively real
The beliefs agents from about the world
resulting from observations
vary, even if two agents observe the same
reality.
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Reflection
We observe the actions of other and assume
similar causes (invisible feelings).
Socialization is a process at a hierarchically
slower pace than observation-action.
Connection to fixed point semantics of
denotational semantics.
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Tier 3b: Social reality
Much what we consider part of reality is only a
social convention.
Most important are the conventions in
language:
(applies to natural language or expert slang)
Names of things
Objects are named,
individual names like ‘Stella’, ‘John’, etc.
or classes, like ‘plate’, ‘fork’ , dog
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Institutional objects
Abstract objects are formed, to facilitate social
interactions:
Money, Parcels..
John Searle:
An object X counts as Y in the context of C.
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Example: Money
This is ‘legal tender’, but physically only
printed paper.
Social convention: can be used to buy things.
Rules for physical objects apply to the paper,
other rules apply to the ‘legal tender’
For example: temporal extend of physical object
and ‘legal tender’ is not the same.
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An Example:
Communication with Maps:
A map-making agent explores an environment,
Draws a map,
Map using agent uses map to navigate.
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Connection between tier 3a and 3b:
Social processes externalize in symbolic form
the individual socialization:
Cultural Reality
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Grounding and practical consistency in
Taxonomies
Most ontologies are hierarchies of classes with
an is_a relation between them and not much
else.
Existing taxonomies are lists of words for which
an is_a relation is assumed; for their
understanding they rely on the readers preexisting understanding of the natural
language terms
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Polysemy
Words do not have fixed meaning. Meaning
varies with context.
In this context, you would use the words
car and
bicycle
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A different meaning of bicycle
(ordinary) bicycle vs. tandem
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And this?
A motor tricycle and a water tricycle:
to differentiate from the land bicycle before.
Observation: Words often mean a class and the
(ordinary) subclass of it.
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Two classification trees possible:
Just different order of applying distinctions!
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Distinctions between classes:
Classes must be in some respect different from
other classes.
The two taxonomies are constructed with the
same distinctions:
Land – Water
Motorized – Human-powered
Bi-, tri- or four wheeled
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Order of distinguishing matters
The two taxonomies are different only in the
order in which the distinctions between
properties are applied.
Which one should one prefer?
It does matter:
Intermediate class definitions do not
correspond and cannot be translated.
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Lattice structures avoid this choice
Distinctions are applied in any order,
Not a hierarchy!
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Integration of taxonomies possible
The integration of taxonomies to produce a
lattice is easy with a 4 valued logic:
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Grounding in distinctions
Only the descriptions of the distinctions must
be explained. The classes follow
automatically.
Only few distinctions are necessary for large
taxonomies!
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Difference from mainstream ontologies
Founded in observable properties not in the
assumption of preexisting (ideal) classes.
Individuals are ‘areas of uniform properties’
and have observable attributes.
Classes are constructed as sets of individuals
with same properties.
Classes constructed form a lattice (not a
hierarchy).
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Formal Formal Ontologies
I want to consider a mathematical theory with a
small set of the relations and operations in
an ontology:
is_a, subclass_of, …
Avoid debatable, philosophical assumptions
and ontological commitments.
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How to Structure an Ontology