1. How to Structure an Ontology
Andrew U. Frank
Geoinformation
TU Vienna
Overheads at:
Andrew Frank
11/23/2018

2. Overview My approach Separate ontology in tiers
Formal ontology as a theory
Construction of ontology
Andrew Frank
11/23/2018

3. 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)
Andrew Frank
11/23/2018

4. 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.
Andrew Frank
11/23/2018

5. 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.
Andrew Frank
11/23/2018

6. Overview of the tiers 0. The physical environment
Observations of the environment and activities
The reality of objects
a. Objects and actions
b. Generalizations: classes and operations
3. Social reality
Legal reality
Subjective Reality
Communication
are rather epistemologies, projected ontologies or e-ontologies.
Andrew Frank
11/23/2018

7. 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!
Andrew Frank
11/23/2018

8. 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!
Andrew Frank
11/23/2018

9. 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
Andrew Frank
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10. 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.
Andrew Frank
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11. 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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12. Observations types:
Point observations – values for material properties, local motion, forces, temperature etc.
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13. A Landscape
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14. 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?
Andrew Frank
11/23/2018

15. 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.
Andrew Frank
11/23/2018

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17. 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.
Andrew Frank
11/23/2018

18. 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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19. A Table Top
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20. 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?
Andrew Frank
11/23/2018

21. 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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25. 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.
Andrew Frank
11/23/2018

26. Connections from tier 2 to tier 1:
The actions change properties in some spatial-temporal region.
The property values of objects are the integration of the observable property values for spatial regions.
Andrew Frank
11/23/2018

27. Tier 3a: Subjective Reality- Individual 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.
Andrew Frank
11/23/2018

28. 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.
Andrew Frank
11/23/2018

29. 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
Andrew Frank
11/23/2018

30. 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.
Andrew Frank
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31. 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.
Andrew Frank
11/23/2018

32. An Example: Communication with Maps:
A map-making agent explores an environment,
Draws a map,
Map using agent uses map to navigate.
Andrew Frank
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33. Connection between tier 3a and 3b:
Social processes externalize in symbolic form the individual socialization:
Cultural Reality
Andrew Frank
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34. 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 pre-existing understanding of the natural language terms
Andrew Frank
11/23/2018

35. 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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36. A different meaning of bicycle
(ordinary) bicycle vs. tandem
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37. 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.
Andrew Frank
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38. Two classification trees possible:
Just different order of applying distinctions!
Andrew Frank
11/23/2018

39. 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
Andrew Frank
11/23/2018

40. 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.
Andrew Frank
11/23/2018

41. Lattice structures avoid this choice
Distinctions are applied in any order,
Not a hierarchy!
Andrew Frank
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42. Integration of taxonomies possible
The integration of taxonomies to produce a lattice is easy with a 4 valued logic:
Andrew Frank
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43. Grounding in distinctions
Only the descriptions of the distinctions must be explained. The classes follow automatically.
Only few distinctions are necessary for large taxonomies!
Andrew Frank
11/23/2018

44. 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).
Andrew Frank
11/23/2018

45. 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.
Andrew Frank
11/23/2018

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