1. Ontology for Moving Points/Objects/Change
Ontology for Moving Points/Objects/Change... What can ontology contribute to our debate?
Andrew U. Frank
Geoinformation
TU Vienna

2. From Moving Points to Moving Objects – an ontological contribution in 3 pieces:
1. andante: What should an ontology for moving objects contain?
2. largo: How to formalize an ontology for moving objects?
3. vivace: What can we achieve with it?
Andew U. Frank
4. Nov. 2008

3. Ontology today Ontology in information science is defined as
“an explicit formal specification of the terms in the domain and relations among them”.
Andew U. Frank
4. Nov. 2008

4. Ontology captures structure
Structure of the data is represented in
is_a relations
part_of relations
Instance relations
Andew U. Frank
4. Nov. 2008

5. 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)
Andew U. Frank
4. Nov. 2008

6. Discussing ontology means first discussing the formal methods to describe ontologies:
Natural language descriptions of ontologies are not clarifying the semantics an ontology purports to clarify.
Andew U. Frank
4. Nov. 2008

7. Formal methods to describe ontologies (highly simplified):
1. Construct a particular formal language for the type of ontology you are interested in:
- ontology for GIS
- ontology for moving objects
- ontology for flocks ...
Andew U. Frank
4. Nov. 2008

8. 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!
Andew U. Frank
4. Nov. 2008

9. 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.
Andew U. Frank
4. Nov. 2008

10. 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
Andew U. Frank
4. Nov. 2008

11. 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.
Andew U. Frank
4. Nov. 2008

12. 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>
Andew U. Frank
4. Nov. 2008

13. 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.
Andew U. Frank
4. Nov. 2008

14. Example: definition of pizza
Gives list of incredients (structure) but not the process of baking one!
Andew U. Frank
4. Nov. 2008

15. 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
Andew U. Frank
4. Nov. 2008

16. First order logic:
Difficult to represent change and process in first order logic
(complicated temporal logics would be needed)‏
Andew U. Frank
4. Nov. 2008

17. Using existing languages for ontology modelling:
Algebraic background, to be prepared to describe operations and change.
Mathematical rigor and simplicity:
functional languages.
Andew U. Frank
4. Nov. 2008

18. Example: Specification of classes Gives:
“Boat House” and “Houseboat”.
(Kuhn:Cosit'06) in Haskell (
Gives:
classes and subclasses
operations for objects of these classes
Semantics is defined by operations!
Andew U. Frank
4. Nov. 2008

19. 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.
Andew U. Frank
4. Nov. 2008

20. Formalization Subclass:
Dogs are Animals; they breath and bark:
class Animals a where
breath :: a -> StateChange World
class Animals => Dogs d where
bark :: d -> StateChange World
eat :: d -> f -> StateChange World
Andew U. Frank
4. Nov. 2008

21. 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
Andew U. Frank
4. Nov. 2008

22. 2nd Problem: Contravariance of Functions
functions are contra-variant:
applying a function to subsets of the arguments does not guarantee that the result will be a subset of the result of the original function.
Andew U. Frank
4. Nov. 2008

23. 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.
Andew U. Frank
4. Nov. 2008

24. Formalizing 1: Moving point
a moving point is a list of tuples (fixes)‏
t, x, y (,z)‏
this is what most understand by trajectory, interpreting that the same point was observed at the given location at the given time.
Andew U. Frank
4. Nov. 2008

25. Formalizing 2: Moving point as a function
a moving point is a function
p (t) = ...
e.g.
p (t) = (x0 + vx * t, y0 + vy * t)‏
but using a lookup function in the list of fixes and interpolating between known locations can be written as a function as easily.
Andew U. Frank
4. Nov. 2008

26. Formalizing 3: Moving and changing objects
an object can not only change position, but any other property (heading, speed, color, ownership...)‏
Model each property as a function from time and objectID to value
e.g. speed (ID, t) = v
color (ID, t) = c
Andew U. Frank
4. Nov. 2008

27. Formalizing 4: Many changing objects in a world
Populate a world with many objects which change (e.g. SWARM). How to check for interaction between objects, expressed formally!
(Model objects as autonomous agents, with capabilities to obseve the world...)‏
Andew U. Frank
4. Nov. 2008

28. Formalizing 5: Operations of objects produce change in the state of the world:
operations for objects start with a state of the world and result in a changed new world state:
op:: ID -> WorldState -> WorldState
w1 := op (id, w0)‏
Andew U. Frank
4. Nov. 2008

29. Formalizing with Monads:
op :: ID -> ChangeWorldState
(where ChangeWorldState = WorldState -> WorldState)‏
The result of applying an operation to an object (and possible additional parameters) is a function, chaning the world from current state to a next state.
Andew U. Frank
4. Nov. 2008

30. Special Monad, so called State Monad:
nice algebraic properties for the monad opereations “return” and “binb”:
"return" must preserve all information about its argument.
(return x) >>= f ≡ f x
m >>= return ≡ m
Andew U. Frank
4. Nov. 2008

31. Special Monad, so called State Monad:
Binding two functions in succession is the same as binding one function that can be determined from them.
(m >>= f) >>= g
≡ m >>= (\x -> f x >>= g)‏
Andew U. Frank
4. Nov. 2008

32. Special Monad, so called State Monad:
A monad can define a "zero" value for every type. Binding a zero with any function produces the zero for the result type, just as 0 multiplied by any number is 0.
mzero >>= f ≡ mzero
Similarly, binding any m with a function that always returns a zero results in a zero
m >>= (\x -> mzero) ≡ mzero
Andew U. Frank
4. Nov. 2008

33. Paradigm change necessary:
Two traditions that are hindering temporal GIS and the necessary ontologies with processes:
- logic (especially Description Logics)‏
- Inheritance in (imperativ) programming languages (especially C++ and Java)
Andew U. Frank
4. Nov. 2008

34. Ontology description with algebra :
operations are explicit changing state to new state
t1 = f (t0)‏
class hierarchy with parametrised polymorphism.
Tools: functional programming languages (eg. Haskell, Caml, Scheme, ML)‏
Andew U. Frank
4. Nov. 2008

35. Paradigm change must fix more than one problem!
I have argued for a paradigm change in the methods to describe ontologies.
Does this address other pressing problems?
Andew U. Frank
4. Nov. 2008

36. An ontology based on operations could be used to more than just “clarify semantics”:
The ontology gives a theory!
Constructing a model checks that the model corresponds to our intuition.
Formal ontologies should allow entering instances and observe their behaviour (e.g. Protege)‏
Andew U. Frank
4. Nov. 2008

37. How?
The data structure part (static ontology) can be used to present the data – this is standard for administrative data processing.
The operations described in the ontology give a computational model.
Andew U. Frank
4. Nov. 2008

38. Ontology with operations equals “prototype application”
Test the ontology! Improve code where not appropriate.
Ontology gives automatically (minimal, but standardized) interface.
Slogan:
GUI's from ontology for free!
How? Translate the operations to buttons and feed the user input to them!
Andew U. Frank
4. Nov. 2008

39. Finale
It is necessary and worthwhile to jump to a new paradigm and build ontologies with operations!
Andew U. Frank
4. Nov. 2008