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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

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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?

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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”.

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

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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)

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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.

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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...

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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!

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

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4. Nov. 2008Andew U. Frank Example “Person - Gender”:

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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.

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

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

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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.

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4. Nov. 2008Andew U. Frank 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

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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

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4. Nov. 2008Andew U. Frank 2 nd 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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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.

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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.

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4. Nov. 2008Andew U. Frank Formalizing 2: Moving point as a function a moving point is a function p (t) =... e.g. p (t) = (x 0 + v x * t, y 0 + v y * 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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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) = v color (ID, t) = c

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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...)

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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)

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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.

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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

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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)

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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

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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)

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4. Nov. 2008Andew U. Frank 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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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?

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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)

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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.

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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!

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

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