1 Contextualization: an Abstraction Mechanism for Conceptual Modeling Joint work by: Manos Theodorakis Anastasia Analyti Nicolas Spyratos Panos Constantopoulos.

1

Contextualization:an Abstraction Mechanism for

Conceptual ModelingJoint work by: Manos Theodorakis

Anastasia Analyti

Nicolas Spyratos

Panos Constantopoulos

Institute of Computer Science

FORTH-ICS

Greece

FORTH-ICS 2

Outline

Why we need contexts Context definition Structuring the contents of a context Formal Theory Operations on contexts Applications Future Work Conclusions

FORTH-ICS 3

Different Perceptions

Different Perceptions

Ontology of mechanicfor house

Ontology of familyfor house

FORTH-ICS 4

Other examples of context

Distributed databases Travel agencies Anatomical map

Natural language Ambiguity resolution

Organization of large databases

FORTH-ICS 5

Context features

Viewing the information from different viewpoints

Support for context-dependent meaning

Viewing information at different levels of detail

Modular design

context-dependent reachability

Support for synonyms, homonyms

FORTH-ICS 6

Contextual Ontologies

Organize in a single framework,

several contextual representations

Reasoning based on contextual representations

FORTH-ICS 7

Our Definition of Context

A context is a set of objects, in which each object is associated with a set of names and (possibly) a reference to an other context.

Context

names of o object o reference of o(another context).

.

.

FORTH-ICS 8

Example

Context-dependent naming, referencing Viewing the information from different viewpoints Viewing information at different level of detail

Support for synonyms, homonyms Object Sharing

c2

c1

Crete, Kriti: o3

Map: o4Geography: o2

c3

Geography: o2

Transportation: o10

Hotels: o9 c9

c10

c6

c8

Cities: o15

Mountains: o14 c14c15

History: o16Tourist Guide: o1

Athens, Athina: o5

Crete: o3

Map: o7

Attiki: o6

c5

Dining: o8 c8

Greeece: o0

c0

FORTH-ICS 9

Structuring the contents of a context attr(attr_obj,from,to) in(in_obj,from,to) isa(isa_obj,from,to)

15th century: o2

c1

20th century: o3

Crete: o4

c3

City: o6

c4

Village: o7

Chandax: o8

Fortification: o9

A: o10

City: o6

c5

Village: o7

Heraklion: o8

Airport: o13

B: o12

: o11

: o14A: o10

Crete: o4

c2

...

...

in

FORTH-ICS 10

Attribution - Contextualization

c4

Persons: o2

c1

Places: o3

related to: o4

c2

Person: o2

Employee: o7

Student: o6

c3

Place: o3

Domestic Location: o7

Foreign Country: o6

born in: o11

Company: o13

works for: o12

Integer: o15

no of years: o16

located in: o14

Demographic Data: o1

isa

FORTH-ICS 11

Generalization - Contextualizationc0

Organization: o1

Hospital: o2

c'Employee: o3

String: o7

name: o6

cEmployee: o3

String: o7

name: o6

Department: o9

has dep: o6

Doctor: o4 Nurse: o5

isa

Refinement Relation

FORTH-ICS 12

Classification - Contextualization

cd

Schema 1: o1

Instance 1: o

. . .c1

. . . . . .

cin

cInstance 2: o4

Schema 2: o2

The same set of objects can be classified under different schemas Several set of objects can be classified under the same schema

in

FORTH-ICS 13

Context theory

Formal definitions

Model theory

Set of sound & complete inference rules.

FORTH-ICS 14

Formal Definitions

Contents of a context: cnts(c)

Basic SetsO : set of ObjectsCXT : set of ContextsN : set of Names

Reference PathsRPc : set of reference paths starting

from the objects of c

))((to))((from)(,.7,)(|,,)(.6

,)(|,,)(.5,)(|,,)(.4

)(:)()()(:)(.2

)()(.1

tftf

ctftf

ctftf

ctftf

oclexoclexcobjsooppcobjsoppocattrppcobjsoppocisappcobjsoppocin

cobjscrfcobjsclex

cobjs

RPRP

RPCXT3.

NPNP

Contextualized IBcnts,,, NCXTO

FORTH-ICS 15

Predicates - FunctionsPredicates

Functions

'refines'.5),,(),,(),,(,)(.4

)(,,),,(.3)(,,),,(.2

)(,,),,(.1

:

ccccppoAttrppoIsappoInppoIsLink

cattrppoppoAttrcisappoppoIsacinppoppoIn

tfctfctfctfc

tftfc

tftfc

tftfc

)(:.4:.3:.2:.1

NPRPCXTRP

RPRP

cc

cc

cc

cc

NamesRefToFrom

OO

FORTH-ICS 16

Inference System1. ISA Reflexivity: ),,( ppoIsac

2. ISA Transitivity: ),,(),,(),,( 313322211 ppoIsappoIsappoIsa ccc 3. Context Refinement:

1111'

'

')(')(')()()()('

)'()(')'()('

)'()('

cccoRefcoRefccoNamesoNamescobjsocobjsocc

cattrcattrcccisacisacc

cincincc

cc

cc

4. Refinement Reflexivity: cc 5. Refinement Transitivity: 313221 cccccc 6. Instance Upward Inheritance:

),,(),,(),,( 313322211 ppoInppoIsappoIn ccc

FORTH-ICS 17

Inference System

8. Interaction between Generalization-Contextualization:

21221121 )()(),,( ccpRefcpRefcppoIsa ccc

9. Interaction between Classification-Generalization-Contextualization:

212211

21

)()()'',,()'',',()',,(

ccoRefcoRefcppoInppoIsappoIn

cc

ccc

7. Inheritance of Built-in Information: nullCc

FORTH-ICS 18

Refinement, Equivalence Relations

)))',(),()',((),()',(:)'((

)()'()()'(

)()'()()'('

corefcorefnilcorefconamesconamescobjso

cisacisacincincattrcattrcobjscobjscc

Refinement Relation

)))',(~),())',(),(((

)',(),(:)(()'()(

)'()()'()()'()('~

corefcorefnilcorefnilcoref

conamesconamescobjsocisacisa

cincincattrcattrcobjscobjscc

Equivalence Relation

FORTH-ICS 19

Operations for Creating and Maintaining Contexts

CreateCxt(<contents>) insert( o, N, c ) deleteObj( o, c ) deleteName( o, n, c ) copyCxt( c ) deepCopyCxt( c )

Union Intersection Difference

20FORTH-ICS

Context Union

c5

Dinos: o1Head: o2

Nick, Nikos: o4

Dinos, Xulouris: o1

InfSys: o10

DSS: o20

InfSys DSS

Head: o2

Nick, Nikos: o4Dinos: o6

c4

InfSys: o10

DSS: o20 c5

Xilouris: o1

Head: o2

Dinos: o6

c4

FORTH-ICS 21

Context Intersection

c/5

Dinos: o1Head: o2

c/4

Xilouris: o1

Head: o2

InfSys DSS

Dinos,Xilouris: o1

InfSys: o10

DSS: o20

Head: o2

InfSys: o10

DSS: o20

c5

Dinos: o1Head: o2

Nick, Nikos: o4

Xilouris: o1

Head: o2

Dinos : o6

c4

22FORTH-ICS

Context Differencec4

. . .

Manos View: o1c1

Dr_Xilouris: o1

: o4

InfSys: o10

DSS: o20

Nicolas View: o2 c2

Dinos: o1

InfSys: o10

AVG: o21

c6. . .

Manos View Nicolas View

c'5Nick, Nikos: o4

: o4

Manos View: o1

DSS: o20

c5

Dinos: o1Head: o2

Nick, Nikos: o4

c4. . .

InfSys: o10 c'1

DSS: o20InfSys: o10

: o4

23FORTH-ICS

Commutativity:

Associativity:

Distributivity: (A B) C = (A C) (B C)(A B) C = (A C) (B C)

(A B) C = A (B C)(A B) C = A (B C)

A B = B AA B = B A

Properties of and

FORTH-ICS 24

Constraint: Well-definedness

A context is called Well-defined iff:• There is a name path that uniquely identifies each object recursively contained in the context• Acyclicity

A, B: o1c1

A: o2

: o3

D: o4

E: o5

A: o1c2

G: o3

C: o6

B: o1c3

C: o2

A: o6

Theorem: Closure of well-definedness under Union, Intersection and Difference

FORTH-ICS 25

Applications Partial View Support

Different people have different views of the same resources

Different applications have different (goal-oriented) models of the same resources

Cooperative work Workspaces: Private, Group, Public

Ontology Integration/Merging

Web search Modelling of user interests/Reply based on query context

FORTH-ICS 26

Applications (cont.)Pervasive computing

Agent context

Redefined contexts of agent situations

Central Manager

Collects Agent Contexts Reasons about them Maintains consistency

FORTH-ICS 27

Future Work

Extension of the web ontology languages RDF and OWL with contexts

Querying and reasoning with: contextualized RDF contextualized OWL

FORTH-ICS 28

Conclusions

A formal notion of context in information modeling

Formal definition Core axioms Operations

Supported features Partial views Relative semantics Modular design

FORTH-ICS 29

Thank you!