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

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

• Andrew U. Frank
• Geoinformation
• TU Vienna
• frank_at_geoinfo.tuwien.ac.at
• www.geoinfo.tuwien.ac.at

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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?

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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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Ontology captures structure

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

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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)

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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.

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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 ...

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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!

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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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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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Actual languages

• The Web Ontology Language OWL (the culmination
  from a sequence of KL-ONE (1985).... DAML, OIL,
  DAMLOIL).
• A compromise between expressive power and
  tractability of logical deductions (goal
  consistent theory!)?
• Practically very limited and difficult to use.

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Example Person - Gender

• ltrdfRDF
• xmlnsrdf"http//www.w3.org/1999/02/22-rdf-synt
  ax-ns"
• xmlnsrdfs"http//www.w3.org/2000/01/rdf-schema
  "
• xmlnsowl"http//www.w3.org/2002/07/owl"
• xmlns"http//localhost8080/OWLBuergerInformati
  on.owl"
• xmlbase"http//localhost8080/OWLBuergerInform
  ation.owl"gt
• ltowlOntology rdfabout""/gt
• ltowlClass rdfID"Gender"/gt
• ltowlClass rdfID"Person"/gt
• ltowlClass rdfID"Woman"gt
• ltrdfssubClassOf rdfresource"Person"/gt
• ltowlequivalentClassgt
• ltowlRestrictiongt
• ltowlonProperty rdfresource"Gender"/gt
• ltowlhasValue rdfresource"female"
  rdftype"Gender"/gt
• lt/owlRestrictiongt
• lt/owlequivalentClassgt

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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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Example definition of pizza

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

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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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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.

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Example

• Specification of classes
• Boat House and Houseboat.
• (KuhnCosit'06) in Haskell (www.haskell.com)?
• Gives
• classes and subclasses
• operations for objects of these classes
• Semantics is defined by operations!

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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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Formalization Subclass

• Dogs are Animals they breath and bark
• class Animals a where
• breath a -gt StateChange World
• class Animals gt Dogs d where
• bark d -gt StateChange World
• eat d -gt f -gt StateChange World

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Programming with inheritance

• The is_a relation does not translate directly to
  the operations.
• class Numbers n where
• division n -gt n -gt n
• instance Numbers Rational
• instance Numbers Int
• Int is subset of Rational

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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.
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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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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.

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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.

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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

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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...)?

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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 -gt WorldState -gt WorldState
• w1 op (id, w0)?

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Formalizing with Monads

• op ID -gt ChangeWorldState
• (where ChangeWorldState WorldState -gt
  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.

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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) gtgt f f x
• m gtgt return m

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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 gtgt f) gtgt g
• m gtgt (\x -gt f x gtgt g)?

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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 gtgt f mzero
• Similarly, binding any m with a function that
  always returns a zero results in a zero
• m gtgt (\x -gt mzero) mzero

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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)

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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)?

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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?

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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)?

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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.

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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!

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Finale

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