John Bateman Till Mossakowski Oliver Kutz Joana Hois

Ontology Structuring Mechanisms and Ontological Modularity

ongoing research and targeted applications

John Bateman Till Mossakowski

Oliver KutzJoana Hois

http://www.sfbtr8.uni-bremen.dehttp://www.fb10.uni-bremen.de/ontology

BREMEN ONTOLOGY RESEARCH GROUP

University of Bremen + DKFI, Bremen

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2Bateman/Mossakowski/Kutz/Hois 2008

Overview of our topics today

● General orientation and our position on ontologies

● The formal framework within which we are working

● Examples of ontological modularities and re-use

● Conclusions

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Several Research Areas currently under Investigation

● Mobility support

● Spatially-embedded tasks

● Exploration, Route Planning

● Navigation

● Interaction with diverse user groups

● Disabilities

● Age

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Problem foci

● Spatial assistance systems● Route planning and navigation● Real-world environments

involving ‘common-sense’ entities● Interfacing with geographic information● Interfacing with language technology● Interfacing with visual presentations (maps)● Interfacing with robotic sensor data● Embodied systems● Human-Robot Interaction

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Problem

● Many different kinds of knowledge are required to get people into the loop in a way that is empowering and enriching rather than restricting

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Voronoi map From Voronoi map From SFB/TR8 project: SFB/TR8 project: A1-[RoboMap]A1-[RoboMap]

Voronoi calculation on a scanned floor plan

“where are you?”

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Sources of relevant knowledge

Location-based services

Geographic Information Systems

Commonsense objects and activities

Spatial awareness and understanding

Natural language capabilities

Robot perception

Use

r K

now

ledg

e U

ser

(dis

)abi

litie

s

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Problem restated

● Getting these diverse areas of expertise to talk to each other is a serious issue● different communities● different interests● different representations

● The kinds of knowledge maintained by such systems are very different

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Essential idea…

● Providing channels to ontologies provides access to detailed contextual ‘world-knowledge’ that does not then have to be worked out again…

Application

Ontology

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Many perspectives on ‘reality’: many ontologies

event

time

space-1

space-2

event

Ontologically diverse

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Example of communication problems: When is a road not a road?

● Community 1:● transit system designers● roads and highways as connections between

destinations (cities, towns, etc.)

● Community 2:● environment and wildlife department● species have habitats● habitats have divisions separating them

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Ontologically mediated inter-operability

city A

city B

Hwy 456

nodenode

transit system

graph ontology

environment

species A

region ontology

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Ontologically mediated inter-operability

city A

city B

Hwy 456

nodenode

transit system

graph ontology

environment

region ontology

species A

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Methodological starting point

● There is no sense in which a simple ‘merging’ of the ontologies involved is a sensible strategy to follow

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Solution we are pursuing

● High degree of interoperability between diverse knowledge-rich systems is to be achieved by ontological engineering, taking in:

● knowledge of the human world (commonsense)● knowledge of the robot world (programmed, emergent)● geo-knowledge (GML, other standards)● spatial knowledge (spatial calculi)● knowledge of language (linguistics)

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Ontological diversity inter-ontology mappings

description

time

landmarks

choremes

event types

CASL

CASLCASL

route graphs

CASL

CASL

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Perspectives / Viewsrather than inheritance

lake

geographical region

Alternate theories / ontologies

obstacle

recreational area

source of pure water

link in transport network

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Inter-ontology mappings

● ... can only work if there is sufficient content to get hold of!

● That is: not a relationship between ‘terms’ but a relationship between ‘theories’.

● For this, need deep ontologies, so-called ‘axiomatized ontologies’

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Choosing between types of ontologies

● ‘Light’ ontologies: semantic web?

● ‘Heavy’ ontologies:● Rich axiomatization● Formal principles ● Well-defined design criteria

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Our ontological starting point

Leo Obrst

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Theories...

● We all have theories...● theories of the world● theories of how buildings are● theories of the best way to get from A to B● theories of how to persuade your boss for a

raise

● ‘A-ontologies’ set such theories out in an explicit specification.

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Prerequisites for success

● unless you can reason with the axioms: non-starter

● unless you can chunk your axioms: non-starter

● unless you can parameterize and re-use theories: non-starter

● unless you can state relations between the meanings of chunks: non-starter

logic

building theories

structured logic support

inter-theory mappings

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Essential ingredients we are drawing on in Bremen

● Existing ontologies

● DOLCE (Masalo/Borgo/Guarino) (for cross-category binding and axiomatization)

● BFO (Barry Smith) (for sites, niches and places and for SNAP/SPAN)

● GUM (John Bateman) (for linguistic semantics and natural language processing)

● State of the art logical tools● CASL + Hets Tool

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Ontology construction

● Axioms are grouped into logically appropriate theories● Theories may be extended via parameterization to

achieve semantic re-use● Theories may be created and related by views: theory

morphisms

Only with this re-use factor can the complexity of distinct axiomatized ontologies really be harnessed and used to scale-up.

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Approaches to ‘simplifying’ the ontologist’s life...

● Making sure that each component of a library of theories only specifies the axioms which are relevant at that point (cf. John Sowa: “That is the whole point of Ockham's razor: eliminate any axioms that are not absolutely essential to the task at hand.”)

● Making sure that unnecessary detail is hidden in ‘upstream’ libraries: CASL

● Possibilities for ‘common subsets’:

● packages such as our spatial calculi

● packages such as DOLCE’s ‘constitution’, ‘participation’, ‘quality spaces’, BFO’s ‘sites’

● language-based generic ontology (GUM)

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This is essential: because in analysis there are a lot of pieces to put back together!!

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Combining theories for semantic interpretation

driving along

the road to Bremen

on the right

is a church

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Combining theories for semantic interpretation

driving along

the road to Bremen

on the right

is a church

o>

hp

oriented path

route graph

half-planes

physical object occupying a region

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OK, go towards the mountains along the main road

until you reach a large wooden house.

Be careful, the road gets a bit narrow where the old church sticks out.

Turn right at the house and,

then, at the third intersection, turn right leaving the city limits.

Then turn downhill towards the river.

At the river, take the ferry over to the café.

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OK, go towards the mountains along the main road

until you reach a large wooden house.

Be careful, the road gets a bit narrow where the old church sticks out.

Turn right at the house and,

then, at the third intersection, turn right leaving the city limits.

Then turn downhill towards the river.

At the river, take the ferry over to the café.

theory of landmarks: mountain

theory of destinations: the house

theory of structural landmarks / constraints on movement and decisions: (along) the main road

Theories needed for interpretation

theory of shapes of physical objects: narrow road, old church (sticking out)

theories of orientation: towards

theory of landmarks: the house

theories of orientation: right

theory of ordered sequencestheories of orientation: right

theories of regions (administrative): city

theories of orientation: towardstheories of topography: slopestheory of landmarks: the river

theory of structural landmarks: intersections

theory of structural landmarks: (over) the rivertheory of landmarks: river

theory of destinations: the café

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Theories...

● Each of these contributions to the meaning of what is being said is considered to draw on a range of more or less related theories of the world…

● axiomatised ontologies set such theories out in an explicit specification.

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John Sowa(email/web discussion)

IEEE StandardUpper OntologyWorking Group

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• What kinds of ‘modules’ are these?

• What is the nature of relationships that can hold between them?

• How do these relate to different communities’ theories of the world?

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A general approach…

In the next section of the talk we discuss how we are formalizing these notions of ontological modularity and inter-module relationships.

● Formal framework: CASL● Generic framework for describing how

ontologies and modules can be related: ‘alignments’

● Some examples

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CASL - Common Algebraic Specification Language

• Standardised first-order specification language;

• designed by CoFI “Common Framework Initiative for algebraic specification and development” since 1995

• approved by IFIP WG 1.3 “Foundations of Systems Specifications” (1998), extensive documentation (LNCS 2900, 2960)

• various extensions and sublanguages, including higher-order dialects, modal logic, OWL-DL;

• supports structured specifications including imports, hiding, renaming, union, extensions, etc.

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CASL language constructs

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CASL example: basic

Basic specification of “Services located at rooms”

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CASL example: structured

Named structured specification of a distance function

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CASL example: view

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GenMereology

GenParthood

Lüttich & Mossakowski (FOIS 2004)DOLCE in CASL

GenParthood

Primitives

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spec MEREOLOGY =PRIMITIVES

then%%Ad7, Ad8, Ad9 and Ad10 are generated by %% instantiation of GenMereology

GENMEREOLOGY [sort T]then

GENMEREOLOGY [sort S]then

GENMEREOLOGY [sort PD]end

GenMereology

GenParthoodPrimitives

Mereology

Lüttich & Mossakowski (FOIS 2004)DOLCE in CASL

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The Tool HeTS

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Varieties of Modules

● logically self-sufficient/independent conservativity;

● part of a larger “integrated” ontology DDLs, E-connections, etc.

● coupling through interface alignments

● tradition, convenience, elegance, etc. general structuring techniques

“Parts” of an ontology can be considered a “module” for a variety of reasons:

Realised through various theory morphisms

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Shapes of Alignments

● we represent various alignments as diagrams of certain “shapes”

● connected through “interfaces”● we assume alignment mappings are given● colimits are used for an overall integration● composition of diagrams as composition of

alignments● definitional extensions do not add ‘substance’

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Structuring mechanism

Arrows in Diagrams

● black: imports;● dashed black: automatically constructed imports● blue: definitional or conservative extensions;

dotted red: proof obligations; theorem links; interpretation into theory;

green: = proven “red” obligation;

Postulating links

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V-alignment through interface

● cannot handle subclass alignments

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W-alignment with bridge ontology

● Integration through bridge ontology

Woman Person

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M-alignment: bridges and extensions

● Integration through bridge along extensions

Woman,Bank

Person,BankPerson

Person,Bank

Woman, Person, Financial_Bank, River_Bank

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Bibliographical Ontology in DL

logic DL

spec Biblio_DL = Class: Researcher

SubclassOf: name some Thing

ObjectProperty: hasArticle InverseOf: hasJournal

Class: Article SubclassOf: author some Thing,

title some Thing, hasJournal some Journal

Class: Journal SubclassOf: name some Thing, hasArticle some Thing, impactFactor some Thingend

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Bibliographical Database

Biblio_RS

logic RelationalScheme

spec Biblio_RS = tables person(key: id,name); author_of(person,paper); paper(key: id,title,published_in); journal(key: id,name,impact_factor)

links author_of.person -> person.id; author_of.paper -> paper.id; paper.published_in -> journal.idend

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A Heterogeneous Mappinglogic CASL

view Biblio_RS_in_DL : Biblio_RS to { Biblio_DL with logic DL -> CASL then %def preds journal(j,n,f:Thing) <=> Journal(j) /\ name(j,n) /\ impactFactor(j,f);

paper(a,t,j:Thing) <=> Article(a) /\ Journal(j) /\ hasArticle(j,a) /\ title(a,t);

author_of(p,a:Thing) <=> Researcher(p) /\ Article(a) /\ author(p,a);

person(p,n:Thing) <=> Researcher(p) /\ name(p,n) } = logic RelationalScheme -> CASLend

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Structure of bibliography example

Biblio_DL Biblio_RS

Ext_Biblio_DL

Heterogeneous mapping between ontologies

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● ‘window’ in T1

‘window’ in T2

map objects in T1 to materials in T2

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E-connections many sorted: extended M-alignment

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Summary

● Relations between modules can be characterized in general in terms of the shapes of these alignment diagrams

● Providing support for expressing these structured relationships adds considerably to the ontologist’s toolkit

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One further exploratory example…

● relating linguistic spatial information and non-linguistic descriptions

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Bateman/Mossakowski/Kutz/Hois 2008

Further M-Alignment Example:Linguistic and Spatial Ontology

● natural linguistic spatial interaction

linguistic ontology

spatial ontologies

specificspatial calculi

space-specificparts

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M-Alignment ExampleLinguistic and Spatial Ontology

orientations:(e.g. DCC-8)linguistic

ProjectionRelations

FrontProjection BackProjection RightProjection LeftProjection

● R(linguistic,spatial) : LeftProjection . placement [LeftProjection] ⇒ leftFront ∨ left ∨ leftBack

front

leftFront rightFront

right

leftBack

left

leftBack

back

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orientations:(e.g. DCC-8)linguistic

ProjectionRelations

FrontProjection BackProjection RightProjection LeftProjection

front

leftFront rightFront

right

leftBack

left

leftBack

back

● R(linguistic,spatial) : LeftProjection . direction [LeftProjection]

⇒ leftFront

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● R(l,s): LeftProjection.placement[LeftProjection]

⇒ leftFront ∨ left ∨ leftBack● R(l,s): LeftProjection. direction[LeftProjection]

⇒ leftFront

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Relation between linguistic and non-linguistic characterisations…

combines different alignments between the linguistic semantics and the spatial characterisation

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Conclusions and ongoing and future directions

● Dealing with information flexibly requires ontological treatments that are contentful

● Axiomatised ontologies are a way of approaching this

● But structured ontological specifications with well-specified possibilities for relating between ontologies/modules are then essential

● Offers us a structured path towards interoperability

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Appendix

Biblio_RS

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Modules based on Conservativity

Model-theoretic implies proof-theoretic conservativity, but not conversely.

model-theoretic conservativity: Every T1-model can be expanded to a T2-model.

A theory morphism is proof theoretically conservative if

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Modules based on Conservativity

Documents

John Bateman Till Mossakowski Oliver Kutz Joana Hois