Ontology for Moving Points/Objects/Change...What can ontology contribute to our debate?

Andrew U. Frank

Geoinformation

TU Vienna

frank@geoinfo.tuwien.ac.at

www.geoinfo.tuwien.ac.at

4. Nov. 2008Andew U. Frank

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?

4. Nov. 2008Andew U. Frank

Ontology today

Ontology in information science is defined as

“an explicit formal specification of the terms in the domain and relations among them”.

4. Nov. 2008Andew U. Frank

Ontology captures structure

Structure of the data is represented in • is_a relations• part_of relations• Instance relations

4. Nov. 2008Andew U. Frank

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)

4. Nov. 2008Andew U. Frank

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.

4. Nov. 2008Andew U. Frank

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 ...

4. Nov. 2008Andew U. Frank

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!

4. Nov. 2008Andew U. Frank

Ontology languages 2: Description logicsconsists 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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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

4. Nov. 2008Andew U. Frank

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.

4. Nov. 2008Andew U. Frank

Example “Person - Gender”:<rdf:RDF

xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"

xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"

xmlns:owl="http://www.w3.org/2002/07/owl#"

xmlns="http://localhost:8080/OWLBuergerInformation.owl#"

xml:base="http://localhost:8080/OWLBuergerInformation.owl">

<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="http://www.w3.org/2002/07/owl#FunctionalProperty">

<rdfs:range rdf:resource="#Gender"/>

<rdfs:domain rdf:resource="#Person"/>

</owl:ObjectProperty>

<owl:DatatypeProperty rdf:ID="name"

rdf:type="http://www.w3.org/2002/07/owl#FunctionalProperty">

<rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#string"/>

<rdfs:domain rdf:resource="#Person"/>

</owl:DatatypeProperty>

<owl:DatatypeProperty rdf:ID="firstname"

rdf:type="http://www.w3.org/2002/07/owl#FunctionalProperty">

<rdfs:range rdf:resource="http://www.w3.org/2001/XMLSchema#string"/>

<rdfs:domain rdf:resource="#Person"/>

</owl:DatatypeProperty>

<Person rdf:ID="STilgner" firstname="Susanne" name="Tilgner">

<Gender rdf:resource="#female"/>

</Person>

</rdf:RDF>

4. Nov. 2008Andew U. Frank

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.

4. Nov. 2008Andew U. Frank

Example: definition of pizza

Gives list of incredients (structure) but not the process of baking one!

4. Nov. 2008Andew U. Frank

Extend ontology descriptions with time, change, processWhy 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

4. Nov. 2008Andew U. Frank

First order logic:

Difficult to represent change and process in first order logic

(complicated temporal logics would be needed)

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Using existing languages for ontology modelling:

Algebraic background, to be prepared to describe operations and change.

Mathematical rigor and simplicity:

functional languages.

4. Nov. 2008Andew U. Frank

Example:

Specification of classes “Boat House” and “Houseboat”.

(Kuhn:Cosit'06) in Haskell (www.haskell.com)

Gives:classes and subclasses

operations for objects of these classes

Semantics is defined by operations!

4. Nov. 2008Andew U. Frank

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.

4. Nov. 2008Andew U. Frank

Formalization Subclass:

Dogs are Animals; they breath and bark:

class Animals a wherebreath :: a -> StateChange World

class Animals => Dogs d wherebark :: d -> StateChange Worldeat :: d -> f -> StateChange World

4. Nov. 2008Andew U. Frank

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

4. Nov. 2008Andew U. Frank

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.

4. Nov. 2008Andew U. Frank

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.

4. Nov. 2008Andew U. Frank

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.

4. Nov. 2008Andew U. Frank

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.

4. Nov. 2008Andew U. Frank

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) = vcolor (ID, t) = c

4. Nov. 2008Andew U. Frank

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...)

4. Nov. 2008Andew U. Frank

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)

4. Nov. 2008Andew U. Frank

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.

4. Nov. 2008Andew U. Frank

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

4. Nov. 2008Andew U. Frank

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)

4. Nov. 2008Andew U. Frank

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

4. Nov. 2008Andew U. Frank

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)

4. Nov. 2008Andew U. Frank

Ontology description with algebra :

operations are explicit changing state to new statet1 = f (t0)

class hierarchy with parametrised polymorphism.

Tools: functional programming languages (eg. Haskell, Caml, Scheme, ML)

4. Nov. 2008Andew U. Frank

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?

4. Nov. 2008Andew U. Frank

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)

4. Nov. 2008Andew U. Frank

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.

4. Nov. 2008Andew U. Frank

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!

4. Nov. 2008Andew U. Frank

Finale

It is necessary and worthwhile to jump to a new paradigm and build ontologies with operations!