1. Time and Process in GIS: What can ontology contribute?
Andrew U. Frank
Geoinformation
TU Vienna
Andrew Frank
11/14/08

2. Dynamic GIS: The current GIS maintain static views of the world.
The user want to understand how the world evolves in time (e.g. “Global Change” discussion).
The users are interested in
computational models of geographic space and the processes in it.
Andrew Frank
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3. GIS should be Computational Models:
Current GIS are static data collections, described by static ontologies.
The new GIS must combine
data
with
processes
to model the dynamic reality!
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4. Ontological challenge for dynamic, temporal GIS:
Current ontologies describe the static structure of the world.
Not included are the processes and their semantics.
A dynamic GIS must be described with an ontology that contains objects and operations!
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5. Structure of talk: 1. What is an Ontology?
2. The multi-tier system of ontologies
3. Add operations to ontology to capture processes
4. How to describe ontologies with operations
5. More uses for ontology: create graphical user interface from the ontology
6. Conclusions: Paradigm change is necessary!
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6. Goal of talk 1. Include operations in the ontology
2. The ontology (with operations) is more useful,
e.g. a user interface can be derived
3. More useful ontology will find more use and produce more benefits!
The challenge is, to find methods to describe ontologies with operations!
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7. Ontology today
Ontology in information science is defined as “an explicit formal specification of the terms in the domain and relations among them”.
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8. Ontology captures structure
Structure of the data is represented in
is_a relations
part_of relations
Instance relations
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9. Two critical observations:
1. a static view: no process, no operations, nothing changes;
2. it is very difficult:
imagine how difficult it is to describe the structure of a dish (e.g. apple pie) in contrast to the recipe (a description of a process)
Overview
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10. My Goal:
I need an ontology to understand the practical difficulties in the use of Geographic Information:
vagueness, error, resolution
spatial and temporal data
differences in semantics hindering interoperability
In all cases, operations are key to understanding!
Andrew Frank
11/14/08

11. My approach to ontology must be comprehensive:
I am interested in the whole of human interaction with the world, not only the verbal, propositional and mostly conscious part classical philosophy concentrates on.
We cannot avoid to consider the human living in the world and moving about with his body and feelings if we want to produce useful Geographic Information.
Andrew Frank
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12. Conscious vs. non-conscious mental operations
I have the suspicion, that
Operations as necessary conditions for classifications are mostly non-conscious
Object and object classification are mostly conscious
This explains perhaps the focus on nouns and taxonomy in classical ontology and logic.
Andrew Frank
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13. Terminological difficulties:
Many discussions are caused by misunderstandings and differences in the use of words.
For example, the notion ‘ontology’,
but also ‘reality’, ‘think’
and even more difficult:
‘is’, ‘exists’, ‘that is not the way the world is’.
Modelization – for example using UML – is confused by different notions of ‘exist’.
Andrew Frank
11/14/08

14. Verbal vs. pictorial expression of problems:
Much conceptualization is already done when words are used to describe the reality.
I use here pictures to connect my presentation more directly with your bodily experience; I work on the integration of feelings in the ontology.
Andrew Frank
11/14/08

15. Why a multi-tier ontology?
Most efforts to structure ontologies strive for maximum generality.
They propose a single set of rules applicable to everything.
e.g. Aristotle's categories, mereology
Our experiments show that no single proposed ontology covers all areas important in a GIS.
Andrew Frank
11/14/08

16. Multiple tiers to integrate different approaches
Each tier follows its own logic.
Much what others have discovered about ontology is extremely useful, but proposals are contradictory in detail.
A multi-tier approach separates different suggestions in different tiers and integrates them.
This approach is comparable to Constructivism (Heinz von Foerster, Cybernetics).
Andrew Frank
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17. 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
3a. Subjective Reality
3b. Social reality
Legal reality
Communication
are rather epistemologies, projected ontologies or e-ontologies.
Andrew Frank
11/14/08

18. 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
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19. 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 differential equations in properties of points.
Many properties are determined; not all of these are observable (or known) to us!
Andrew Frank
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20. 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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21. 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.
There are two linked feedback loop (morphism)‏
Physical activity – observed change
Body feeling of activity – sensory activity
(Schmidt: Selective – Contingent)‏
Andrew Frank
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22. Observations types:
Point observations – values for material properties, local motion, forces, temperature etc.
Synchronous observations of many (usually regularly located) points.
Example: vision
(philosophers would call observation types “categories”).
Andrew Frank
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23. A Landscape
Andrew Frank
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24. 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
11/14/08

25. 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
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26. Andrew Frank
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27. 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
11/14/08

28. Lifestyles of Objects Object continue in time.
Objects are created and destroyed.
Living things are born and die.
Some objects can be suspended.
There are rules of what operations are applicable to certain types of objects.
Damir Medak (TU Wien) and
Kathleen Hornsby (U Maine)
Andrew Frank
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29. A Table Top
Andrew Frank
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30. 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
11/14/08

31. 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:
Andrew Frank
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32. Andrew Frank
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33. Andrew Frank
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34. Andrew Frank
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35. 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
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36. Actions
Actions
- complex sequences of (physical) activities which change the environment.
- cause the values of properties of objects to change
Philosophers could use the Hegelian terms Voraussetzung (observation of environment abstracted to object properties) and Setzung (actions).
Andrew Frank
11/14/08

37. 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
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38. Tier 2b: Generalization to types
From many similar physical objects, we form objects types (classes).
Similar actions are generalized to operations.
Objects must have properties to permit actions.
Object types are classes of objects which have the necessary properties for operation.
Gibson used the term ‘affordances’ for the properties of objects which link them to operations.
Andrew Frank
11/14/08

39. Tier 3a: Subjective Reality- Individual cognitive agents
Individual internal reality
Feelings are subjectively real
Situations as complex associations of objects are assessed with the corresponding feelings.
Andrew Frank
11/14/08

40. Individual differences in observation
Agents use observation methods which are limited and subject to error.
Object formation can vary
(e.g. effects of granularity)‏
and is influenced by the task at hand (context).
The beliefs agents from about the world
resulting from observations
vary, even if two agents observe the same reality.
Andrew Frank
11/14/08

41. Memory consists of assessed situations
Situations are assessed with respect to feelings.
Memory is assessed situations of objects and relations.
Feelings are bodily and cognitively real, at the limit between conscious and unconscious (Gerhard Roth).
Conscious Generalizations:
Histories: Situations and Emotions (past)‏
Plans: Desired situations and potential actions (future)‏
Andrew Frank
11/14/08

42. 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
11/14/08

43. Connection between tier 2 and 3:
Reflection and Fixpoint:
Individual agents assume that other agents decide and act following similar patterns than they themselves.
Hierarchy of processes:
observations – operations
Objects – actions
Object types – action types (algebraic operations)‏
Histories – Plans (reflections)‏
Andrew Frank
11/14/08

44. 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
11/14/08

45. 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
11/14/08

46. 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
11/14/08

47. Example: Communication
It is an obvious fact, that we can communicate.
Communication is based on the exchange of physical signs in the environment.
Communication is not always perfect.
What are the rules?
Andrew Frank
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48. 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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49. Connection between tier 3a and 3b:
Social processes externalize in symbolic form the individual socialization:
Cultural Reality
Andrew Frank
11/14/08

50. Why Formalization: Limitations of human abilities
Our abilities for logical analysis of complex situations is limited.
Typical problems:
Levels of generalizations confuse us,
Polysemous words trick us into false, seemingly logical conclusions,
Confusion between instances (tokens) and types.
Andrew Frank
11/14/08

51. Formalization with Tools
Formal tools are urgently needed.
The effort reported here is designed for implementation (and is in large parts implemented).
We have constructed simulations with multiple, cognitive and communicating agents.
Andrew Frank
11/14/08

52. Ontology languages 1: UML
Informal, but extensive use:
Uniform Modeling Language (UML) – limited by lack of formal definition – no conclusions drawn or consistency checked automatically.
Tools (graphical editors) for UML are available:
Nice, easy to use, flexible – but no formal background, therefore no fixed semantics, not much can be checked for consistency!
Andrew Frank
11/14/08

53. Ontology languages 2: Description logics
consists of
A set of unitary predicates denote concept names
A set of binary relations, which denote role names
Recursive constructors to form more complex constructs from the concepts and roles.
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54. Many variants of Description Logics:
Various DL with different levels of expressive power and computational complexity, depending which constructors are included:
union and intersections of concepts
negation of concepts
value (universal) restriction
existential restriction
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55. Actual languages:
The Web Ontology Language OWL (the culmination from a sequence of KL-ONE (1985).... DAML, OIL, DAML+OIL).
A compromise between expressive power and tractability of logical deductions (goal: consistent theory!)‏
Practically: very limited and difficult to use.
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56. Example “Person - Gender”:
<rdf:RDF
xmlns:rdf="
xmlns:rdfs="
xmlns:owl="
xmlns="
xml:base="
<owl:Ontology rdf:about=""/>
<owl:Class rdf:ID="Gender"/>
<owl:Class rdf:ID="Person"/>
<owl:Class rdf:ID="Woman">
<rdfs:subClassOf rdf:resource="#Person"/>
<owl:equivalentClass>
<owl:Restriction>
<owl:onProperty rdf:resource="#Gender"/>
<owl:hasValue rdf:resource="#female" rdf:type="#Gender"/>
</owl:Restriction>
</owl:equivalentClass>
</owl:Class>
<owl:ObjectProperty rdf:ID="gender"
rdf:type="
<rdfs:range rdf:resource="#Gender"/>
<rdfs:domain rdf:resource="#Person"/>
</owl:ObjectProperty>
<owl:DatatypeProperty rdf:ID="name"
<rdfs:range rdf:resource="
</owl:DatatypeProperty>
<owl:DatatypeProperty rdf:ID="firstname"
<Person rdf:ID="STilgner" firstname="Susanne" name="Tilgner">
<Gender rdf:resource="#female"/>
</Person>
</rdf:RDF>
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57. Ontology editors, e.g. Protege
Ontology editor based on description logic.
Produces ontologies in different output languages (e.g. OWL-Light).
Very difficult to use, very time consuming.
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58. Example: definition of pizza
Gives list of incredients (structure) but not the process of baking one!
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59. Extend ontology descriptions with time, change, process
Why is this difficult?
1. First order logic is essentially static, adding time
- adds confusing bulk to expression:
move (P, A, B, T) :-
is_at (P, A, T1) & is_at (P, B, T2) & before (T1, T) & after (T2, T)‏
- frame problem:
need to state what does not change to allow logical inference
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60. First order logic:
Difficult to represent change and process in first order logic
(complicated temporal logics would be needed)‏
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61. Ontologies with operations is an object-oriented ontology!
In an object orientation view the world consists of
objects with operations!
The object-oriented research in software engineering concentrates uses an algebraic approach to model object classes and operations applicable to the objects.
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62. Example Dogs are Animals and breath:
class Animals a where
breath :: a -> StateChange World
class Animals => Dogs d where
bark :: d -> StateChange World
eat :: d -> f -> StateChange World
Used: Monads from Category Theory
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63. Programming with inheritance:
The is_a relation does not translate directly to the operations.
class Numbers n where
division :: n -> n -> n
instance Numbers Rational
instance Numbers Int
Int is subset of Rational
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64. 2nd Problem: Contravariance of Functions
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65. Solution Parametric polymorphism, as shown in the above example, where
class Numbers n where ...
has a parameter n.
The usual ad-hoc polymorphism of current programming languages (C++, Java) is not theoretically clean.
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66. Formalization (2): Second order language
Spatio-temporal models: Change is caused by actions, operations.
The formal language must treat operations as ‘first class objects’ – i.e. the formal language must be second order.
First order = variables only for individuals
Second order = variables for operations
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67. Formalization (3): Practical tool
Functional programming language:
Haskell (download from
Strongly typed
Lazy
Pure functional
(i.e. mathematically clean, no unknown assumptions)‏
Executable – result can be tested
Andrew Frank
11/14/08

68. Conclusions
Integration of many ideas about ontologies in a multi-tier framework.
Conceptualization is influenced by task; this creates the data fusion problem.
Andrew Frank
11/14/08

69. Conclusions (2)‏
Formalization is crucial to achieve integration of different concepts (as necessary for data fusion),
otherwise the complexity overwhelms!
Processes are linking the tiers. Formalization must have operations.
Andrew Frank
11/14/08

70. Conclusions (3): connections between tiers:
The connections between the tiers are different:
Tier 0 – Tier 1: observation of point properties of the environment, activities change properties
Tier 1 – Tier 2:
Areas of Uniform properties aggregated to objects
Sequences of connected activities aggregated to actions
Tier 2 – Tier 2b: generalization to object types and action types
Tier 2 - Tier 3a – feelings, assessment of situations (associations of objects and actions)‏
Tier 2 and 3a – Tier 3b –
X counts as Y in the context Z
Socialization (hierarchy of processes)‏
Andrew Frank
11/14/08

71. Conclusions (4): Closed loop semantics
The symbolic realm for which we have to give the semantics must be connected to reality by two paths:
From reality to symbols (perception, conceptualization, etc.)‏
From symbols through decisions to actions
If the loop is closed, the semantics is defined by perception-action (compare to “affordance”)‏
Andrew Frank
11/14/08

72. Formalization of ontology:
Describe operations as algebras of object classes.
Describe the perception and the action as an algebra.
Construct linkages as morphism (structure preserving mappings)‏
In the context of this algebra (and this ontology)‏
data quality
information content
can be measured.
Andrew Frank
11/14/08

73. Process is fundamental!
Classical ontologies are verbal and focus on objects. They suffer from internal contradictions.
Only a process oriented ontology can integrate the different tiers of reality.
Andrew Frank
11/14/08